8.6 Collisions of Point Masses in Two Dimensions

8.6 Collisions of Point Masses in Two Dimensions

Cart 1 carries a spring.

During the collision, the spring releases its potential energy and converts it to internal energy.
The cart and the spring have an initial velocity of.
Cart 2 has a mass of 0.500 kg and an initial velocity of.

The force of the spring is internal and we can use it to find the final velocity of cart 2.

We can compare the internal energy before and after the collision to see how much energy was released by the spring.

The final velocity of cart 2 is large and positive, meaning that it is moving to the right after the collision.

The internal energy in this collision increases.
The energy was released by the spring.

The incoming and outgoing velocities are all along the same line when there is a one-dimensional collision.

We will see that their study is an extension of the one-dimensional analysis already presented.

A pair of one-dimensional problems can be solved at the same time.

The objects might move before or after a collision.

Two ice skaters will spin in circles if they hook arms as they pass each other.
We arrange things so that no rotation is possible until later.
That is structureless particles that can't spin.

We start by assuming that.

One of the particles is at rest in the simplest collision.
With the chosen coordinate system, the components of momentum along the and -axes are initially zero, but they will also be conserved.
The facts simplify the analysis.

A two-dimensional collision with the coordinate system chosen so that it is at rest and parallel to the - axis.

The laboratory coordinate system is sometimes called the laboratory coordinate system because many scattering experiments have a target that is stationary in the laboratory, while particles are scattered from it to determine the particles that make-up the target and how they are bound together.
The particles may not be observed directly, but their initial and final velocities are.

The situation after the collision is indicated by the subscripts and primes.

The velocities along the - axis have the form.

Particle 1 moves along the - axis.

Particle 1 moves along the - axis.

Particle 2 is at rest.

The velocities along the - axis have the form.

In analyzing two-dimensional collisions of particles, the equations of momentum along the - axis and - axis are very useful.

Two equations can only be used to find two unknowns, and so other data is needed when collision experiments are used to explore nature at the subatomic level.

The following experiment can be performed.

An object is slid on a surface into a dark room, where it strikes a stationary object with a mass of 0.400 kilogram.
The object emerges from the room at an angle.

The surface is not slippery.

The quantities that we wish to find are not known in the equations.

We have two equations that are independent and can be used to find unknowns.

This angle indicates that it is scattered to the right in Figure 8.12, as expected, because the angles are positive in the counter clockwise direction.

The equation for the - or - axis can be used to solve the problem, but the one with fewer terms is the easiest.

Before and after the collision, it is important to calculate the internal energy of the system.

The collision is inelastic if you do this calculation, because the internal energy is less after the collision.
A physicist wants to explore the system further.

A stationary object scatters the incoming object.

The stationary object's mass is not known.
It is possible to calculate the magnitude and direction of the initially stationary object's velocity after the collision by measuring the angle and speed at which the room emerges.

There are some interesting situations that arise when two objects collide.

This situation is similar to when billiard balls collide and when particles collide.
We can get a mental image of a collision of particles by thinking about billiards.
An elastic collision conserves energy.
Let us assume that object 2 is at rest.