2.7 Falling Objects

2.7 Falling Objects

• Look for what could cause the identified difficulty if the answer is unreasonable.
• There are two assumptions that are suspect in the example of the runner.
• The time could be too long.
• Think about what the number means when you look at the acceleration.
• The person's speed is increasing by 0.4 m/s each second.
• The time must be too long if that is the case.
• It is not possible for someone to accelerate at a constant rate.

• There are falling objects in motion problems.
• We can estimate the depth of a vertical mine shaft by dropping a rock into it and listening for the rock to hit the bottom.
• We can learn a lot about gravity by applying the kinematics developed so far to falling objects.

• In a given location, all objects fall toward the center of Earth with the same constant acceleration, regardless of their mass.
• Light objects are expected to fall slower than heavy objects because of the effects of air resistance and friction.

• If air resistance is not considered significant, a feather and hammer will fall the same way.
• David R. Scott demonstrated on the Moon in 1971 that this is a general characteristic of gravity.

• Air resistance can cause a lighter object to fall slower than a heavier object in the real world.
• A tennis ball will hit the ground after a baseball hits it.
• Air resistance affects the motion of an object through the air, as well as the motion between objects, such as between clothes and a laundry chute or between a stone and a pool.

• The force of gravity causes objects to fall.
• We can apply the equations to any object that is falling because of the constant acceleration due to gravity.
• This opens a lot of interesting situations to us.
• The magnitude of the acceleration due to gravity is given a symbol.

• Unless otherwise stated, the average value will be used in this text.
• The downward direction of the acceleration is towards the center of Earth.
• What we call vertical is defined by its direction.
• The value of the acceleration in the equations depends on how we define our coordinate system.
• If we define the upward direction as negative, and the downward direction as positive, then we are done.

• The simplest situations are the best way to see the basic features of motion.
• Straight up and down motion with no air resistance is what we start with.

• The initial velocity is zero if the object is dropped.
• The object is in free-fall when it has left contact with something.
• The motion is one-dimensional and has constant acceleration.
• The symbol will be used for horizontal and vertical displacement.

• A sketch can be drawn.

• At various times, we are asked to determine the position.
• The initial position should be zero.
• One-dimensional motion in the vertical direction is the problem.
• Positive and negative signs are used to indicate direction.
• The initial velocity must be positive since the rock is thrown upward.
• The acceleration is negative because of gravity.
• It's important that the initial velocity and the acceleration have different signs.
• The acceleration due to gravity will slow and eventually reverse the initial motion.

• We will refer to the values of position and velocity as and and and.

• The knowns should be identified.

• The best equation to use is identified.
• The value we want to find is unknown, so we will use it.

• Plug in the known values and solve the problem.

• The knowns should be identified.

• We know from the solution above that.

• The best equation to use is identified.

• The rock is still moving upward, according to the positive value.
• As expected, it has slowed from its original pace.

• The same procedures are used for calculating the position and velocity.

• Graphing the data helps us understand it better.

• A rock is thrown vertically up at the edge of a cliff.
• You can see that velocity changes linearly with time.
• The position vs. time graph only shows the vertical position.
• The shape of the graph looks like a path of a projectile, so it's easy to see that it shows horizontal motion.
• The horizontal axis is time, not space.
• The path of the rock in space is straight up and straight down.

• Interpretation of the results is important.

• The rock is still above its starting point, but it is moving downward.

• The rock is below its starting point and moving downward at 3.00 s. When the rock is at its highest point, its acceleration is still zero, but its velocity is zero.
• It is moving up and down at the same time.
• The total distances traveled are not included in the values for the positions of the rock.
• Both have the same acceleration, which remains constant the entire time.

• When astronauts are training in the Vomit Comet, they experience free-fall while arcsing up as well as down, as we will discuss in more detail later.

• You can determine your reaction time with a simple experiment.
• A friend should hold a ruler between your thumb and index finger.
• The ruler has a mark between your fingers.
• Try to catch the ruler between your fingers when your friend drops it.
• The ruler has a new reading.
• If it's due to gravity, calculate your reaction time.

• When the rock is 5.10 m below the starting point, it will be thrown downward with an initial speed of 13.0 m/s.

• A sketch can be drawn.

• The initial velocity is negative and the acceleration is due to gravity.
• The rock will continue to move downward so we expect the final velocity to be negative.

• The knowns should be identified.

• The easiest way to solve the problem is with the kinematic equation.
• The equation works well because it is unknown.

• The negative root indicates that the rock is still going down.

• The rock had the same initial speed when it was thrown straight up.
• This is not a coincidence.
• The speed of a falling object depends on its initial speed and vertical position relative to the starting point.

• The positive value occurs when the rock is at 8.10 m and heading up, and the negative value occurs when the rock is at 8.10 m and heading back down.
• The speed is the same but the direction is different.

• The rock has the same speed at the same distance below the point of release.

• Its position is on its way back down.
• On its way down, it has the same speed as on its way up.
• If we have thrown it upwards or downwards, we would expect it to be the same.
• If the speed with which the rock was initially thrown is the same as the speed on its way down, then the rock's speed on its way down is the same.

• Data taken in an introductory physics laboratory course can be used to calculate the precise acceleration due to gravity.
• The time it takes to fall a known distance is measured when an object, usually a metal ball, is dropped.
• For example, Figure 2.43.
• If care is taken in measuring the distance fallen and elapsed time, very precise results can be produced.

• The positions and velocities of a metal ball are determined by air resistance.
• With time, displacement increases with time squared.
• It's equal to gravitational acceleration and acceleration is a constant.

• A sketch can be drawn.

• We need to find a solution for acceleration.
• displacement and acceleration are negative in this case.

• The knowns should be identified.

• The equation you choose will allow you to use the known values.

• Substitute 0 for the equation to solve.

• The negative value shows that the acceleration is downward.
• It makes sense that the value should be around the average value.
• The local value for the acceleration due to gravity is more precise than the average value since the data going into the calculation is relatively precise.

• A chunk of ice breaks off a glacier and falls into the water.

• We can use the equation to solve the problem.