6.8 Power

The bar charts can be used to apply energy and momentum constancy.

It's very fast but reasonable for a bul et to fire from a gun.

Determine the initial energy of the bullet, the final potential energy of the block-bul et system, and the increase in internal energy of the system.

The energy is converted at a faster rate when you run up the stairs.

The watt is the SI unit of power.

A cyclist in good shape pedaling at moderate speed will convert about 400-500 J of internal chemical energy each second.

Power can be expressed inhp: 1hp is 746 W.

Horsepower is used to describe the power rating of machines.

The internal energy of the fuel is converted into other forms of energy at a rate of 50 * 746 W.

The barbell has a dead lift on it.

She lifts a bar that is moving at a smal constant velocity, the external force from the floor to just below her waist is very nearly constant.

The process can be represented with an energy bar chart.

The process is shown below.

The barbel and Earth are the system.
The initial state of this process is the most important.
The last state is after she finishes lifting.

This is a good power for lifting a barbell.

If you use an exercise machine that displays the power output, compare what you can achieve to this number.

Lifting assume that Xueli lifts the same barbell from her shoulders to above her head.

Estimate the power of the process.

The pro arm is 49 cm and her energy is zero.
She needs 1.0 s to lift cess.
She works at the bar.

N pointing at the direction of the car.

25hp is a relatively small power.

Determine the power of Jim's erblades on a smooth linoleum floor.

When an object is close to Earth's surface, this expression is valid.

Imagine if a space elevator was built to transport supplies from the surface of Earth to the International Space Station.

The supplies leave the surface.

The International Space Station is chosen via a space Earth and supplies.
We will lift the supplies.
The only type of energy force diagram that we can keep track of is gravitational potential energy.

A complex math ematical procedure is needed to determine the work done by a variable force.

The International Space Station is not from the center of Earth.

Check to see if the equation makes sense.

The initial state and the final state are both described in two quantities.

We can use it.

If we know the mass of any two spherical or point-like objects, we can see a bar chart.

There was positive work done on the system by the cable.

The final potential energy of the system is zero.

The potential energy is zero when the object is far away.

When the object is far from Earth, the negative potential energy is zero.

The initial state is when the object is close to Earth and the final state is far away.

The amount of work needed to raise 1000 kilograms of supplies to the International Space Station can now be determined.

Had we used our original expression, we could have calculated what this would have been.

The surface of Earth has a zero level.

The bars on which the best Olympic high jumpers leap are about 8 feet above Earth's surface.

When leaving the ground, we can estimate a jumper's speed.
The zero level of gravitational potential energy at ground level was chosen as the system.
The potential energy of the system is converted as the jumper leaves the ground.

M is 1.6 N>kg.

We draw a sketch first.

The system to choose is the process.
The planet will be the initial state.

The constant is 6.67.

The above equation can be used to determine the escape speed.

In the initial state, the system has 2370 m>s of energy.

The potential energy for Earth is zero in the final state.

The bar chart shows the Sun's mass and the work-energy equation.

Something amazing is suggested by the escape Equation (6.12).

The es mass of the escaping object could be made large if the mass speed did not depend on the star or planet.
Light leaving the star's surface wouldn't be fast enough to leave Earth.
Why don't you escape the star?
The star would be very dark.

Imagine if Earth began to shrink so that it was compressed into a smaller volume.

It's hard to imagine Earth being compressed to the size of a marble.

The mass would be the same, but it would be very dense.
The first equation was created by astronomer Pierre-Simon Laplace, who used classical mechanics to predict the presence of dark stars.

How small would our Sun need to be in order to return to this question in later chapters?

The mass of the Sun needs to be shrunk to 1030 kilograms.

All we need to do is use the book.

We've been talking about objects that are larger than light.

Physicists used to think that the force of gravity on light would always be zero.
Albert Einstein's theory of general relativity improved greatly at the beginning of the 20th century.
Light is affected by gravity.
The size of a black hole is predicted by the theory.

The energy potential of the Sun and Earth is negative in this section.

It is a number.

It is a number.

The faces of the system objects rub against each other as the internal energy of the system changes.

External forces can change the energy of a system.

Positive work is done by a person lawn.

Earth is one of two 1-m displacements in the system.

The spring exerts a 1-N force on object 2 in the direction of is released, and in the final state, one cart is moving up a 10-m displacement.

Earth did negative work when someone was lifting the description, but choose a process and system that matches the following energy.

Imagine that you stretch a spring 3 cm and then another lowest position; the system is the pendulum bob and 3 cm.

Do you do the same amount of work?

The system is a pendulum bob and a string.

There are three processes described.

The cart is part of the system as the spheres stick together and swing upward.

A spring rests upright on a table.

The final compress the spring must be determined slowly.

The impulse-momentum equation increases speed to the bottom.

A and B are thrown from a cliff by a spring.

The process in which an ex is thrown vertically upward and stone B is thrown vertically ternal force does negative work on the system is described in the statement.

The person is not standing up.
Part of the system is explained by which of the fol owing statements.

It travels a longer path and takes a longer time to apply.

Your friend thinks the escape speed should be increased.

How can you measure the quantities?

A rabbit and an Irish Setter have the same kinetic mark that requires you to make a drawing or graph as part of the energy.

How fast is your solution if the Setter is running at 4.0 m/s?

A pickup truck and a compact car have the same speed.

Jay fills a wagon with sand and pulls it with both vehicles, pushing them from rest over the same distance, a rope along the beach.

The tension force on the 10 is 20-N.

When does the energy of a car change?

You have a suitcase and you lift it up by 0.80 m. If you are able to move the 22 m/s, you will be allowed to leave the highway.

On your vacation in San Francisco, you decide to take 3.

You use a rope to slowly pul a sled and a cable car to see the city.
A cable car goes up a 20 incline and exerts a 150-N force on the rope.

A rope is attached to a truck and a motorcycle.

The jump was to a height of 40 cm.

Determine three of them by making a list.

You slowly carry the child 10 m to the assumptions you made.

Do you do any work on the child?

Make a list of your assumptions.

A truck runs into a pile of sand as it slows down.

The amount of work that the sand does on the blood during a lifetime.

Indicate any assumptions you made.

Air moves across Earth in regular patterns.

The cables should be vertical.

In 2005, the United States consumed 1020 J of energy.

If the ankle is pushing up, the tibia bone in the lower leg of an adult human will break.

If you step off the chair, it will be 0.40 m above the floor.
If you made any assumptions in your answer to this question, tell me about it.

The first successful ascent of Mt.

was made by Sir Edmund Hil ary and Tenzing Norgay.

How many slices of bread did each climber have to eat?

Jim is driving a pickup truck at 20 m/s and releases pensate to increase the potential energy of his foot from the pedals.
The assump things exert on the car.
The average mag tions are used.
List the physical quantities you see in the reading passage at the end of this section.

The initial and final states should be specified.

It is difficult to stretch a door spring.

You have to identify the assumptions in your answer.

As the car leaves the 18-m-long patch of mud, you can determine the car's speed.

The tennis ball has a stretch position after falling 18 m. Determine the average potential energy change as it moves from the 3.0- cm stretch resistive force of the air in opposing the bal's motion.

A spring is compressed by a certain distance.

You take the ball-Earth system.

An expression for her speed at ing at a speed of 7.0 m/s can be developed with 40,000 J of work-energy ideas.

When the car hits a wall and analysis and limiting case analysis, use the unit bumper to evaluate your result.

What do you know about the bumper's spring?

A child needs 40 tion because of a 400N effective friction force.

The elastic cables on the sides connect the first car and the mass.

The road is small.
A policewoman pulls a car over for an ex seat and stretches the cables.
The speed limit is 35 mph.

Then use the symbols to move the puck.

There are work-energy principles for that process.

A frisbee is stuck in a tree.

You want to get it out quickly.
The process of throwing a 1.0- kilogram rock straight up at the Frisbee is a thing of the imagination.
If the rock's are in line with the equation and bar chart.

A driver loses control of a car, drives off an embankment, and lands in a canyon.

The car's speed was 42.

The box is moving at increasing speed.

How many different situations do you need?

Evaluate his solution.

There is a motorcycle, including the driver, and any assumptions you made.

The problem can be solved by changing the ramp up to a 10-m long one above the paved road.

A hailstone the size of a golf ball is falling at 16 m/s on the paved surface.

Any assumptions used in your estimate are cate.

The insect 44 is thought to be the Froghoppers.

Compare this to a platform that sits on top of a spring of force that exerts on the bug.

The generalized work-energy principle can be applied to that process.

Justify your results.

A rope is being used to lower a crate 55.

The motion was opposed by a 24-N force.

Determine expressions rest and move 10 m. Make a list of the final velocities of the blocks.

The block is moving at 2.0 m/s toward the west.

The initial surface of the system has an elastic head-on collision with the final states of the process.

Determine the speed of each block.

If you fire an 80g arrow so that it is moving at 80 m/s when the least initial kinetic energy actualy gains energy and the it hits and is embedded in a 10 kilo block resting on ice, it will move at 80 m/s.

The 7.2-N force is against the motion.

The system air cools.

You fire a 50-g arrow.

A fire engine has a vertical distance of 20 m 49.

How much power is needed for the wa periment?

You hang your sta from the strings.

The bike is 0.50 m higher than the block's cycle for 30 min at a speed of 8.0 m/s if they swing up after the arrow joins the block.
The starting point for your body is 10%.

The system must be specified.

The initial and final states of the process can be lost by a large tree.

Jay rides a skateboard.

is climbing.
A hiker climbs to the sum energy of the system.

A climber's vertical elevation increases 540 m as a child moves on a skateboard at a speed of 2.0-h.

6.0 m/s when she comes to a ledge that is 1.2 m above Determine.

She pushes off of the climber-earth system and the power of the board before reaching the ledge.
The board leaves the ledge to increase the energy.

A list of the physical quantities describing the motion of the Tower stair climb is the fastest time for the Sears.

A pere made while perched on an elevated site.

The falcon dives into mechanical energy at a speed of 90 m/s.
The falcon has a mass of 0.60 kilo calories.

The col ision is 60 m/s in the same direction.

Make a list of the assumptions you made.

The journey took about 74 minutes.

Determine the maximum number of days Earth's Moon would have, and the fish consumed energy at a rate of 2.0 W for each to have in order for it to be a black hole.

You want to bungee jump, but want to make sure it's safe.

There is a brochure at the ticket office.

Justify the numbers used in the estimate.

There is a problem with work-energy ideas and real energy change.
Pick two different systems potential energy to solve the problem.

Your dormitory has a nice balcony that looks over a pond the shed exerts on the car as a function of a position in the grass below.

You hold the rope while standing on the balcony.

The initial and final states should be specified.

Choose speed and was stopped in the same way and in the same numbers, only now by a more solidly constructed shed.

The car is moving at 24 m/s at half the energy of the bottom of the loop.

The mass of oxygen is 16 times greater than the hydrogen.

The average random energy in the atmosphere is the same for hydrogen and oxygen.

Instead of rolling down the oxygen molecule.

Determine the escape speed for a rocket.

The cart is being pressed.

To leave the solar the track around the loop, you have to know the escape speed for a rocket.

The appropri system has a spring.

The spring is initially compressed.

65 mil ion years ago, the reign of dinosaurs ended and the metabolisms of people under several different species became extinct, opening the way for mammals to become the dominant ries.

The theory provides about 70 kcal of energy.

In 1 hour of heavy exercise a person metabolizes an asteroid that crashed into Earth.

A mountain climber is moving up a slope.

When you pul one bal to the side and let it strike the next ball, only one bal can swing out.

Two bal s swing out when you use two balls to climb a hit.

You are an engineer helping to design a roller coaster that will carry 87 passengers.

A person wants to lose 4.5 lbs in 2 months.
The time that this person should spend in moderate exer speed must be great enough when at the top of the loop so that the rider stays in contact with the cart and the cart stays consumption.

Is 9.8 m>s2.

The values of 1.9 h and 2.4 h are reasonable.

The chemical energy of the foods we eat is what gives us energy for our activities.

The metabolism rate is 2.

There is a change in foot orientation when taking off and landing.

The red kangaroo is moving fast.

The forward force of the kangaroo is not real.

The gra Pushing back vitational force that Earth exerts on the kangaroo by Earth is three times the vertical impulse due to force.

If the net vertical impulse on the 50 kilogram animal is due to pushing off for another step behind the body, then it would be.

The answer is closest to the vertical height above the ground.

It's a major health problem if you have back pain.

The point-like model for an object should be defined.

Understanding the physics principles underlying lifting can help us minimize this compression and prevent injuries.

When the shapes of objects don't affect the consequences of their interactions with each other, this method is appropriate.

The human body is very complex, with many internal parts that move relative to one another.
A new way of modeling objects and analyzing their interactions is needed to study the body and other complex structures.

We focused on situations in which real objects with nonzero dimensions could be modeled as point-like.

We assumed that an object's size and internal structure were not important for understanding the phenomena, since any real object is extended in three dimensions.

Even though the car as a whole moved in a straight line, we neglected the parts that moved internally, such as the turning wheels, the moving engine parts, and so forth.

The size of the car was neglected.
We looked at the turn's radius for all parts of the car.
We ignore the fact that different parts of the same object move differently when we model an object as a point-like.

We will be analyzing more complex objects when they are not in use.

We can't answer these questions by modeling the man and woman as point-like objects.
A new model for extended objects and a new method for analyzing the forces that ob jects exert on each other are needed.
The model for objects is our first task.

The dancers' bodies are not moving with respect to each other in the photo.

They are acting like a single object.
The model of an object that is point-like is not useful in analyzing the balance of dancers.

There are 231 parts of the object that don't move with respect to each other.

The place where the force exerts is important.

A rigid body is a model of an object.

Buildings, bridges, streetlights, and utility poles are examples of everyday objects that can be modeled as rigid bodies.

What conditions are needed for a rigid body to remain at rest is the subject of this chapter.

There are some simple experiments to start with.

The cardboard is placed on a small surface like a pencil.

The pencil falls off.

Since point-like objects don't tilt, the model of the object can't explain it.
Maybe we should model the cardboard as a rigid body.

The cardboard tips can be supported on the bottom.

Pushing a board so it doesn't turn.

As it moved, we exert the force.

We push against the cardboard when it moves.

As it moves, the heart does not turn as turn.

We had to push through all of the lines to get the cardboard to where we wanted it.

The cardboard will turn as it moves if it is pushed at the same locations in other directions.

The object will not turn if a force is put on it directly or away from that point.

The center of mass appears to be at the geometric center of the board, which is at the center of the object.

If the idea is correct, we push the lines along which the forces are on the cardboard so that in each experiment all cross at one point.

Without turning, a cardboard heart is moving.

The location of the Rolin Graphics object's center of mass is affected by the mass distribution of an object.

The mass of the object is not evenly distributed around the center of mass, even though the location of the center of mass depends on the mass distribution of the object.

We will learn more about the prop erties of the center of mass, but we want to caution you not to call it that.

We couldn't balance cardboard's center of mass at the beginning of the chapter.

Imagine drawing the center of mass forces on a piece of paper.

There are two objects that the cardboard interacts with.
The force of the eraser on the card board is upward.
Earth exerts a downward force on the cardboard.

We should go back to the heart-shaped cardboard from the Observational Experi ment Table 7.1.

The force of the eraser moves through the center of mass.

All of the object's mass is located at its center of mass when we model it as a point-like object.

If we apply the rules to the centers of mass, we can apply what we know about point-like objects to rigid bodies.

You have a framed painting.

The turning effect of an individual force depends on where and in which direction the force is exerted.

The inertia of the object's center of mass is not affected by where the force is exerted.

The turning ability of a force that exerts on a rigid body is covered in this section.

In the case of a spinning top, the axis may be a fixed physical one, like the hinge of a door.

In this chapter, we will look at the conditions under which objects that could potentially rotate do not.

Consider a door.

The harder you push near the knob, the faster the door starts moving.

The turning ability of a force is affected by three factors: the place where the force is exerted, the magnitude of the force, and the direction in which the force is exerted.

Let's make a titative expression for this ability.

To build a physical quantity that characterizes the turning ability of a force, we need to perform experiments where we exert measured forces at measured positions on a rigid body.

A meter stick is balanced on a spring scale.

The scales can be placed and pulled so that the stick does not move.

The stick does not rotation.

The Stick does not move because of equal forces pulling at different distances.

The stick does not move.

The stick does not move.

The stick does not move.

The stick does not move.

The object is in static equilibrium because the turning ability of the force on the left cancels the turning ability of the force on the right.

An object does not accelerate translationally if the sum of the forces on it is zero.

If it is original y at rest and does not accelerate translation, then it stays at rest.

When the sum of the forces on the cardboard was zero, it could start turning.

This idea is helped by another simple experiment.

The forces of Earth and the table on the book do not cause turning because they pass through the book's Y on B1 center of mass.

The corners of the book cause it to turn.

The forces are at the same distance from the center of mass.
You can imagine that the desk has an axis of rotation that goes through the center of mass.
You would think that the turning effect caused by each force around the imaginary axis is the same as it was for scales 1 and 3 in the experiment.

T on B rotation is positive.

The force is exerted from the axis of rotation.

The force tends to turn the object clockwise.

The object does not move.

Let's see if the new quan tity is useful for explaining other situations.

You can do this experiment at home.
Lifting a bag with one hand is easy if you hold it at the end.
When the stick is tilted up, try to hold the handle end of the horizontal.

The broomstick can turn around an axis through the hand that is closest to you.

The broomstick is far from the axis of rotation when the bag exerts force.
In order to determine the turning ability of the bag on the broomstick, we must find a large quantity.
The bag must be balanced.

It is difficult to exert force on your hand.

It's difficult to hold the broomstick to your body.

The actual direction of the force is not taken into account.

The turning ability of the force is affected by the angle at which we exert a force relative to the broomstick.

We know from experience that pushing on a door on its outside edge does not cause it to move.

The broomstick is being tilted.

It's easier to hold if we improve our model for the physical quantity.

There is a constant force of 10.0 N downward at a 90 angle on the far right end of the meter stick.

On the far left end of the stick, scale 1 will pull at different angles so that the meter stick stays horizontal.
The turning ability of the force on the right is balanced by the force on the left in all cases.

Bag on Stick is needed to produce the same turning ability.

An experiment to determine the angle dependence of the turning ability the turning ability of a force is caused by a force.

1u2 is a function of the angle.

Take a look at the last row of Table 7.3.

The force makes the angle smaller.

The sin 30 is 0.50.

A method to determine the +112.6 N210.5 m21sin 532 is provided.

The method for calculating the turning ability is shown in Figure 7.10 If the force has a counterclock, the Torque is positive, the Draw the force wise turning ability is negative, and the beam is positive.

The British system unit islb # ft, while the SI unit is newton # meter, N # m.

The units of 1N # m2 are the same as the units of energy 1N # m. Torque and energy are not the same.

The unit of energy and the unit of Torque will always be referred to as joule and newton # meter 1N # m2 respectively.

An expression for the distance from the axis of rotation to the place where the force is exerted.

The force makes a 30 angle relative to a line from first and the smal est magnitude Torque last, if you rank the magnitudes of the Torques that the strings exert on the beam.

If the pivot point is the place where the string exerts the Torques have equal magnitudes.
The force on the beam needs to be answered.
Before looking at the answer below, String 5 exerts a force paral el to the question.

The rank order is t2 + t4 + t1 + t3 + t5.

The Torque produced by each force is shown to be low.

Each string tends to turn the beam counterclockwise.

Pretend that a pencil is the rigid body to determine the sign of the force that exerts on it.

A method for determining the sign of a Torque.

A painter stands on a ladder and chooses the axis of rotation where the feet are relative to the ground.

He is standing with his feet on the ground.
The Torque was produced by the ladder.

Our system is not the same as the ladder that Earth exerts on the painter.

The painter tends to rotate the ladder clockwise about the axis of ro about two different axes of rotation.

A 37 angle axis is relative to a line from the axis of rotation to the place parallel to the top of the ladder.

The painter's feet exert a lot of Torque on the ladder.

The painter's feet exert themselves on the ladder.
The diagrams show the different axes of rotation.

When we choose the axis of rotation at the top of the lad der, the downward force by the painter's feet on the ladder tends to rotate the ladder counterclockwise about the axis.

A line from the axis of College Physics has an angle of 143 with respect to the place where the force is exerted.

The axis of rotation affects the to Pearson rque.

We use it.

The floor tends to exert force.

An example of a situation in which a force is zero with respect to one axis of rotation but not zero with respect to another is given.

We can combine our previous knowledge of forces with our new knowledge of Torque to determine what conditions rigid bodies remain in at rest.

An object can be at rest for a short time.

A ball that stops for an instant at the top of its flight does not stay at rest.
The words "with respect to an observer in an inertial reference frame" are an important part of the definition of static equilibrium.
If an observer is not in a reference frame, an object can accelerate with respect to the observer even if the sum of the forces on it is zero.

Earth is the most common point of view for observing real-life situ ations.

The meter stick from spring scale 2 is again suspended.

The center of mass of the meter stick is no longer the suspension point.

You and your friend pul on the stick at scales 2 and 3, but not at scales 1 and 3.

The stick to rotate is caused by pul ing at other positions while pulling at the same posi tions.

A meter stick is equal to 1-6.0 N2 + 9.0 N + 1-1.0 N2 + 1-2.0 N2

The distances in the equations for each force are determined by this choice.

A meter stick is shown at the locations shown.

The sum of the Torques on the meter stick is zero.

The first pattern is familiar to us.

You can't zero translational acceleration.
There is no vertical acceleration because the sum of the vertical forces determine the Torque produced on the meter stick is zero.
The meter stick couldn't accelerate horizontally because we didn't specify the zontal forces.
In the experiments presented in the table, the object relative to the axis of net Torque is zero and the meter stick does not start turning.
In rotation, we will learn.

If the ob rigid body is at rest with respect to the different parts of the in turning or rotating static equilibrium, the Earth can be combined into server.

The ends of a standard meter stick can be placed on scales.

The mass of the meter stick is deduced from the fact that the scales read 0.50 N.

If you place a brick 40 cm to the right of the left scale, the scale will read it.

The meter stick is modeled as a scale 1 and scale 2 with a uniform mass distribution.

Colle ends the stick.

The place where the scale touches the stick is where we chose the axis of rotation.

Analyzing the situation with the axis of ing the Torque produced by the normal force exerted pc 3/26/12 18p0 x 10p5 rotation on the left side of the meter stick by the left scale on the stick zero

It sounds reasonable that the condi is positioned closer to it.

The outcome on the meter stick should be zero, as should the sum of the predictions.

The brick on the stick has a rotation axis that we can choose from, so we have the freedom to do what we want.

Let's try it again with the axis of rotation at ity around the axis of rotation and produce a negative 40 cm from the left side of the brick.
See the numbers.
The stick force diagram shows the force exerted by the right scale.
The force condition of equilibrium has a counterclockwise turning ability and does not depend on the choice of positive Torque.
The stick has zero Torque since it is at the axis of rotation.

The axis of rotation has moved to a new position.

The stick has to exert a balancing force on the brick.

When we chose a Rolin Graphics xis of rotation at the left end, it was new.

The left scale on the stick exerts 0 force on LS.

Earth and the brick exert force on the meter stick.

The force on the left end is greater because of the brick's choice of the axis of rotation.

Chapter 7 extended bodies at rest of rotation does not affect the results.

The meter stick tips over the edge if it is extended more than 30 cm.

Stick doesn't affect the outcome of an experiment.

The outcome of actual experiments should not be affected by the concepts of axes of rotation and coordinate systems.

A uniform meter stick with a 50-g ob ject is positioned as shown below.

The edge of the table has a stick over it.
If you push the stick to the side, it tips over.
The mass of the meter stick can be determined using this result.

It is helpful to place the axis on the rigid body where the force you know least about is exerted.

You can use that equation to solve for some other unknown quantity when the force drops out of the second equilibrium condition.

The human body is a good example of an extended body not being rigid.

The rest of the body is at a lower elevation so that her center of mass is always slightly below the bar.

We change the position of our center of mass with respect to other parts of the body a lot.

Try this experiment.
Try to stand up without using your hands.
If your back is vertical, you can't raise yourself from the chair.

The front of the abdomen is the center of mass for an average person.

If you managed to lift yourself off the chair and keep the back straight, the experiment would look like a force diagram.

Earth and the floor exert downward and upward force on your feet.

The rotation of the chair is caused by the Torques caused by these two forces.

To stand, you have to tilt your head in a clockwise direction and move your feet under the chair.

You don't have to use your hands to get out of a chair.

You should bend forward so that your feet are on the floor.

Torques caused by these two forces allow you to stand without touching the chair seat.

Section 7.1 deals with the location of an object's center of mass and how to push it on a smooth surface.

At dif ferent locations on the object, we found that lines drawn along the directions of the pushing forces all intersect at the center of mass.
It is impractical to find the center of mass in a diffi cult.
The method of balancing the object on a pointed support was investigated.
This isn't very practical with respect to humans.

Blocks are represented as an expression for the center of mass.

The system exerts 1 forces.

The total of al Torques ex- the force of gravity on the system is zero.

Each of the people blocks are modeled as point-like objects and the seesaw is modeled as a rigid or body.

To get an expression for the location of the center of the force.

Let's look at this result.

If the result makes of all forces relative to sense, then we know the locations.

There are no people sitting on the ground.

We assumed its mass was uniformly distributed.

If we increase the mass of one of the people on the seesaw, the location of the center of mass moves closer to them.

The term "center of mass" is not true.

The weight lifter is on each side.
This is not the case.

30 kilo is the number 3.

The origin can be anywhere.

The center of mass of per son is on the left side.

The mass on each side of the center of mass is not equal.

There is more mass on the left side of the center of mass than on the right side.

There will be 3 m of balance here.

There is more mass on the left side of the center of mass than on the right side.

The whole system of seesaw will balance here.

The mass of people are not equal.

The mass on the left side of the center of mass is more than the mass on the right side.
The larger mass on the left is closer to the center of mass than the smaller mass on the right.
Torques of equal magnitude are caused by the product of mass and distance on each side.
We could change the center of mass to be the center of Torque, but since this is not the term used in physics, we still use the term center of mass.

The mass on the left and right side of the center of mass may not be equal.

The two fingers are shown below.

2 are connected by a rod.
How does the mass of the knife on the left compare to the mass of the knife on the right?

The mass of the handle end must be greater than the mass of the bread knife.

A barbel has a 10- kilo plate on one end and a 5- kilo plate on the other.

The center of ward normal force and Earth exerts a down mass of the barbell, which is also the balance point for ward gravitational force.
The plates on the ends must be connected by two forces if the rod is to be stable.

There is 0.67 m from the end.

It would tip.

The New Rolin Graphics force is at the knife's center of mass.
The 13p0 x 6p7 center of mass must be above the finger.

Earth on each side of the center of mass has the same magnitudes, but the objects themselves are not necessarily equal.

In front of the elbow joint, the muscles in the upper arm pull up on your forearm.

Push down on the forearm.

The Biceps equilibrium equations allow you to estimate the muscle tension forces.

The general strategies are applied on the right side of the table.

ceps contracts to push down

Imagine holding a 6.0- kilo lead ball with your arm bent.

The elbow joint is 0.35 m from the ball.
The bicep muscle is attached to the forearm 0.050 m from the elbow joint, and it exerts a force on the forearm that allows it to support the ball.
The elbow joint is 0.16 m from the center of the 12-N forearm.
The bicep muscle exerts force on the forearm and the upper arm exerts force on the forearm at the elbow.

The axis of rotation is where the upper arm bone is.

The forearm is pressed at the elbow joint.
The axis of rotation will be eliminated.

Pick a system for analysis.

The system of interest is the forearm and hand.

Decide if you will model the sys as a rigid body or a point-like object.

The coordinate and hand should be included.

The force diagram can be used to apply the equilibrium con t.

If you want to find interest, solve the equations for the quantities of Substitute sin 90 and rearrange the equation.

Biceps' magnitudes are reasonable and if they are 3112 N210.16 m2 + 159 N210.35 m 24 > 10.050 m2 they have the correct signs and units.

If they have the expected values in limiting cases.

The bal on the forearm exerts 59-N force, while the biceps on the forearm exerts 450-N force.

The force applied by the biceps is closer to the axis of rotation than the force applied by the lead ball.

The biceps would have to exert a larger force if the center of the forearm were farther from the elbow.

Biceps in the equation would mean that the bicep would need to exert force on the arm when lifting something.

The forces that were put on the system were put at the right angles.

Consider the next example.

A drawbridge across the mouth of an inlet on the coastal highway is lifted by a cable to allow sailboats to enter the inlet.

When the bridge attendant accidentally activated the bridge, you were driving across it.
You stopped the car at the end of the bridge.
The cable goes over the horizon tal bridge.
The mass of your car is 1000 and the mass of the bridge is 4,000.
Estimate the tension force that the cable exerts on the bridge as it slowly lifts it.

The situation should be low and the bridge should be used.

Since four objects exert axis of rotation where the drawbridge connects by forces on the bridge, the equilibrium will be dependent on the roadway at the left side of the bridge, as we have no information about that force.

Exploration as just started to rise, so it is 34,000 N and Discovery, 1e horizontal.

Pearson will assume that it is static.

The unit is correct.

It is unknown in magnitude and direction.

When the bridge is close to the axis of 53 angle above the horizontal, the cable on B should have a smaller Torque.

Our knowledge of equilibrium conditions allows us to understand how one can increase or decrease the turning ability of a force if they exert the force in a dif ferent location or in a different direction.

If you need to get a car out of a rut in the snow or mud, consider a situation.
Push the middle of the force that you exert on the rope.

Push from if you want to exert a large force on a stuck car.

The side on the tautly tied rope has to remain stationary for that small section of rope to remain stationary.

The rope exerts more tension than the force you exert on it.

If the backpack is not supported by a hip belt, each strap has to pull down on the trapezius muscle.

The force that the muscle exerts on its connection points is greater than the force that the strap exerts on it, just as the force that you exert pushing on the rope is greater than the force that you exert pushing on the rope.
A heavy backpack can cause injury.

On each side of the strap there is a strap muscle.

The trapezius muscle exerts force on its connecting points on the neck and shoulder like the rope to the tree and the car did.

The situation is shown in a sketch.

The system of interest is the section of muscle under the strap.

The force on the backpack is less than the force on the Earth.

A 70 kilo tightrope walker stands in the half of the rope exerts on a short section of rope beneath the middle of a tightrope that moves upward with each walker's feet.

A person has a backpack.

The person's trapezius muscle exerts a 240-N force on the bones that are attached to it.

You can sit on a living room couch without tipping for a long period of time.

For a short time interval, equilibrium can be achieved if you sit on a chair and tilt it back too far.

If you spread your feet apart in the di rection of motion, it is easier to balance and avoid falling in a moving bus or subway train.

You are watching the train from the ground.

The train is moving out from under them.

The left foot of each person is seen by the platform observer.

The earth's force on B causes it to recover from the tilt without falling.

The person falls if the feet are together.

The person recovers after the feet are apart.

If a vertical line passing through the object's center of mass is within the object's area of support, the object does not tip.

The object tips if the line is outside of the support area.

Testing our tentative rule about tipping.

The geometric center of mass is the center of mass.

If you release the slightly tilted can, it returns to the vertical position.

If you tilt the can more and more.

For a can with a diameter of 6 cm and a height of 12 cm, this angle matches the prediction.

The tipping rule states that if an object is in static equilibrium, the line must pass within the object's area of support.

The object tips over if it isn't in the area of support.

The Leaning force goes beyond the area of support as E on Tower passes through the base.

If the Tower of Pisa does not tip over.

Building con struction uses this idea a lot.

The Eiffel Tower has a wide bottom and a narrower top.
TheObservational Experiment Table 7.5 explains why you need to keep your feet apart when standing on a subway train.

There are several holes in the ruler.

The ruler swings back and forth with maximum displacement from the equilibrium position if you pul the bottom of the ruler to the side.
The ruler swings down if disturbed.

If the bottom of this ruler is released, it will return to equilibrium.

If the top of the ruler is stable.

There is no displacement that has displaced from equilibrium.

The axis of rotation does not exert any force on the ruler or the object.

The net force on the ruler by Earth and by the displaced is tipped over if the ruler is both positions a and b.

The center of mass of objects is usually lower when the Torques are produced.

If it is possible for the object to be tilted so that its center of mass is lowered, it will do so.

If we hang the ruler using the center hole, it stays in its original position.

The normal force that the nail exerts and the gravitati nail onal force that Earth exerts produce zero Torques.

The ruler has no effect on displacement.

Is it possible to balance the pointed tip of a pencil.

There is a sketch of the Net clockwise situation.

There is an E on P. The axis of rotation is the tip of the pen.

This instability is caused by F on P-K tation.

The pencil is shown below.

Try to understand new situations and ideas that are ready to be discussed.

The equilibrium is most stable when the center of mass of the system is in the lowest possible position or the smal est value.

Circus tricks are included in the rules of equilibrium and stability.

Vending machines are an application center of mass.

A bicycle on a high wire may not be as dangerous as it looks.

According to the U.S. Consumer Product Safety Commis- model the vending machine is just barely off sion, tipped vending machines caused 37 deaths between chine as a rigid body.

A vending machine that is 1.83 m high, 0.84 m deep, and 0.94 m wide is shown in the side view.

Four corners of its base are supported by a leg on the force diagram.

The back floor has an axis of rotation.

The person exerts force on the vending machine.

The vending machine that was erted by the floor on the back legs did not produce a will tip.

Both answers seem reasonable.

To keep the vending machine tilted above the horizontal, you need to just barely lift the vending machine's front off.

The chance of being injured by a tipped vending machine is small since a large force must be put on it to tilt it up, and it must be tilted at a fairly large angle before it reaches an unstable equilibrium.

In regions prone to earthquakes, falling bookcases is a more common danger.
The base of a bookcase is not very deep.
The bookshelves above the base are the same size as the base bookshelves.

The bookcase can tip over.

In earthquake-prone regions, people attach a bracket to the top of the bookcase and anchor it to the wall.

We will apply our understanding of static equilibrium to analyze three common situations: standing on your toes, lifting a heavy object, and climbing a ladder.

In a less stressed situation, we will analyze what happens to your ankle.

The magnitude of the force that the tibia exerts on the ground if you stand on your toes with your heel slightly is what it is.

We sketch the foot with the distance from the joint to the Achil es tendon attachment.

The system of interest is caused by the Torque condition of equilibrium.

A very light foot is a rigid body.

The force that Earth exerts on the foot is two and a half times the force that Earth exerts on the body.

We will ignore it because it's 10 N>kg for a 70 kilogram per ing.
The force diagram shows the force at 1750 N.

When moving, the forces are greater.

Every time you lift your foot to walk, run, or jump, the tendon ten sion and joint compression are more powerful than the force that Earth exerts on your entire body.

If the person's mass was 90 kilograms instead of 70 kilograms, the Achil es tendon on the foot of the person would increase in magnitude.

Let's apply equilibrium to this system.

A bad way to lift.

Improper lifting techniques can cause back problems.

The downward pul causes a large clockwise Torque on her upper body.

To prevent her from tipping over, her back muscles have to exert a lot of force.
The force of the back muscles can cause damage to the disks in the lower back.
The equilibrium equations can be used to estimate the lifting forces.

The axis of rotation is where the back muscle body is located.

A force dia is drawn in her lower back when she lifts a barbell.

133 kg219.8 N/kg2 is 323 lbs.

179 N 140 lbs2 is calculated using 118 kg219.8 N/kg2 and 176 N 140 lbs2 The force by which it is exerted makes a 12 angle relative to the horizontal backbone.

D doesn't produce a Torque.

The barbel exerts force on the upper distribution and the Earth exerts force on the upper distribution.

The axis of rotation is at the left end of the body, while the tension of the back muscles on the upper body represents one of the disks.

Our model of a person lifting a barbell is below.

The force that the disk exerts on the bone is the same as the force by the back of the disk.

The back muscles exert a force more than four times the grav out if the denominator of the terms in this equation is found.

Two linemen standing on a 1-inch-diameter disk are equivalent to M on B cos 12 tebral disk.

It's a better way to lift things.

Lift your legs with your knees.

The back muscle exerts a third of the force when it is not being lifted correctly.
The disks in the lower back are only half the size they are.

Consider the physics of using a ladder.

You want the ladder to remain static when you climb it.

The ex terior wall of the house is very smooth, meaning that it exerts a negligible friction force on the ladder.
The floor and ladder have the same coefficients of static friction.

We sketched the situation.

If the ladder is too large an angle from the vertical, it will slide down the wall.
The force diagram der and the painter should be used together.

Rather than determining the center of mass, we have kept the forces of Earth on the ladder and painter separate.

Ladder out of each seems reasonable and similar to what we do when someone uses a ladder in real life.

There is a warning not to have the angle exceed 15.

Earth exerts less force on the object being lifted than the muscles in the body do.

You can use your understanding of static equilibrium to get rid of this phenomenon.

A leaf flutters.

A chemistry book rests on top of a physics textbook.

You have an object that is irregular.

A hammock is between trees.

The ropes have an equal chance to break.

The objects are not in the axis of rotation.

Why do you tilt your body?

Give an example of an object that is moving quickly.

10 is the force that the body muscles exert on bones.

A ladder is leaning against a wall.

For each force, identify two interacting objects.

Is it possible that an object won't be in equilibrium when 22?

It takes a large example to pul ing directly on the nail.

Is it harder to do a sit-up with stretched hands?

The two conditions are not the same.

It's better to estimate the problem rather than make a specific answer.

You have to make a drawing or graph as part of your calculations.
This is your solution.

You have a computer.

The more difficult problems should be estimated.

The Torque that balances those produced by shown object O is caused by 3 on O.

A 100N force was found on the knot by 4 on O.

64 N is the B knot's location.

A ladder resting against a house wal makes a 30 angle with the wall.

Between the top of the ladder and the wall the coefficient of static friction is zero, while between the ladder feet and the ground it is 0.40.

Luis (rope 3) was ex- 13 The machine shop you work in needs a force that balances the first two so that the knot doesn't move the big engine to the left in order to slide.

The rope- pulling exercise described in the previous two problems was joined by Kate.

They tied four ropes to the ring.
The ring should be in equilibrium with 4 on R. You exert a 630@N force on rope 2 in the previ and use the first condition of equilibrium to write a two-equa ous problem.

If you replace the light in safe, the ropes will exert on the knot.

The rope length is 20 m and the problem is with a heavier object and ropes.

The numbers 2 and 3 are shown in Figure P9.

If the tension of Chapter 7 exceeds 6700 N, the rope will break.

A man is sitting on one end and the other.

A woman sits on the other end of an apparatus to lift hospital patients.

You have a flat tire.

If subjected to a Torque greater than 3300 N#m, ject A will break.

The bers in Figure P7.24 seesaw are 1.2 m from the ground.

You are standing at the end of a diving board.

You can make a list of physical quantities and show how you will change them with different dimensions.

You put one penny in the bottom left cup, three pennies in the bottom right cup, eleven pennies in the middle right cup, and five pennies in the top left cup.

Kate is sitting on a swing.

Kate sits on the right side of the swing because it is wet on the left side.
Kate's mass is 55 kilo and the swing seat's mass is 10 kilo.
The two cables exert force on the swing.

Ray decided to paint the outside of his uncle's house.

He uses a board supported by cables to paint the second floor.
The board has a large mass.
Ray is 1.0 m from the left cable.

You put a board across a chair to seat three.

A group of physics students are at a party at your house.
2.5 m from one end is where Dan sits.
Komila needs to balance the seesaw by sitting at the other end of the board.

The table exerts force on the bag of vegetables at one end and the bag of fruit hand at the other end.

2 at the right when you lift a barbel.

A person has a broken leg.

A person is standing at one end of a boat.
The block 80 cm with respect to the bottom of the lake should be the size of the rope pulling on the leg if the boat moves so fast that it exerts a 120@N force on it.

Two people are holding hands and standing on erblades.

A person with a height of 1.88 m is lying on a light board with scales under their feet and under their head.

When he bends over 43, estimate the location of the per son's center mass.

He is touching the floor with his hands while you are working out.

A seesaw has a mass of 30 kg, a length of 3.0 m, and a fulcrum cord attached to a hook on the wall.

Determine the mag on one end and a person sits on the other.

The thigh bone exerts on the calf bone at the knee joint.

You have a 10 kilo table with each leg of mass 1.0 kilo.

A man is holding a child with both hands and his elbow bent 90 degrees.

Determine the force that each of his muscles must exert on the forearm in order to hold the child in this position.

You use the ar of the arm to hang the flowerpot.

The force that his triceps muscle must exert on his forearm is not known, but it looks light.

It is much easier to push a rock than it is to pull in an experiment.

You can draw a picture to explain your decision.

You are trying to tilt a very tal refrigerator so that your friend can put a blanket under it to slide it out of the kitchen.

You need to exert force on the front of the 45.
At the start of its tipping, you decide to hang another plant from the refrigerator.
The horizontal y horizontal beam is attached to the wal by a hinge above the floor.

A cable goes above the beam.

A machine with two blocks each of mass is connected to a wall by a hinge.
The string goes from the beam to the wal.

You let it go while pul ing down on one block.

You are on a moving train.

The beam is at a 37 thing.

The force that the cable exerts on the beam is determined by your back at work.

Determine the forces that support posts 1 and 2 exert on the board when a person is standing on the end of the board.

The box is on the floor with the edge pressing against a ridge.

If two different magnitude forces are put on the same object, their rotational effects can be canceled if they are the same magnitude but opposite sign.

The cable is horizontal.

The cable is horizontal.

Two experiments are needed to determine the mass of a ruler.

The 60 are your available materials.

She has a barbell in her hand.

The center of mass of her arm and the table is m and the board is m.

A person is on a tightrope.

Two balls hang from 0.50@m-long strings at each end of the bar.

Indicate the assumptions made for each part of the problem.

A professor sits on a chair.

The barbel has a rope attached to it.
Determine both the force that the deltoid exerts on end of the beam and the force that the lifter's shoulder joint wraps around the professor.

There is a football running in the middle of the beam.

The axis of rotation has the center of mass in front of it.

The head/helmet is balanced by the Torque caused by the downward forces exerted by a complex muscle system in the neck.

The trapezius and levator scapulae muscles are included in the muscle system.

A person is on a ladder.

The hori ladder is tilted 60 above the horizontal and you hold a 10-lb bal in your hand.
The upper arm has a 90 angle with the coefficients of zontal.

The ladder has a mass of 10 kg and a length of 6.0 m.

There is a ladder against a wall.

It's easier to hold a heavy object with a bent arm than it is with a 70.

Two muscles can produce a bigger Torque than one.

A nega muscle is attached to two bones via a tendon and one can produce a positive Torque.

One muscle can pull on the bone and the other can push it.

The other bone is still in its original position.

Medical researchers use the conditions of equi origin to estimate the internal forces that body parts exert on frame, like a door spring attached to a door librium.

The pull port at the bottom of the beam is the only place a muscle can exert a push.

The opposing backbones are at the same joints.
The muscles that bring two limbs together exert the same force on their flexor muscles.
There are serious back problems that can be caused by those that extend the limb.

Earth exerts a force on the upper stomach and the extensor muscle can be used to extend the chest region.

This is similar to flexor-extensor pairs.

Flexor Figure 7.27c has the largest distance listed first.

A person's back is analyzed when they lift from a bent position.

There are signs of the forces causing the Torques.

The expression below describes the Torque caused by 80.