Collisions I

Elastic Collisions

Purpose: To investigate the elastic collision between two gliders along a frictionless track.

Objectives

To investigate how momenum is transferred during elastic collisions.
To investigate how energy is transferred during elastic collisions.
To determine the effect of mass on the momentum transfer between the gliders.
To learn how to measure the velocity of objects using photogates, Pasco Interface, and the Data Studio software.

Equipment

Air track and Air Track Accessory Kit
Two Photogates connected to PASCO Interface
Two Gliders
Mass Scale

Theory

The Linear Momentum of an object is defined as the product of its mass and its velocity

Momentum = (mass) × (velocity)

For a system of objects, their total linear momentum is the sum of the individual linear momenta:

Total Momentum = (momentum of object 1)&nbsp+ (momentum of object 2) + ⋯

In the absence of external forces, the linear momentum of a system of objects remains the same regardless of the collisions between the objects. For a system of two objects A and B, we can write for their momentum before and after the collision:

(m_A)(v_A,before) + (m_B)(v_B,before) = (m_A)(v_A,after) + (m_B) (v_B,after)

The computer will be using the formula

speed = distance / time

to calculate the speed of each glider.

Experiment, Data and Results

We will investigate four different collisions between the gliders A and B. In all collisions, glider B will be at rest initially before the collision. Only glider A moves before the collision.

Preliminary Setup

Level the air track. We must ensure that gravity remains in a direction perpendicular to the air track so that it cannot affect the momentum of the gliders. Place the gliders on the track, turn on the airpump and adjust the slope of the track until they stop drifting along the track.
Photogate and Computer Set up. The computer setup is very similar to that for the Picket Fence and Photogate Instructions. This time, however, we must set up two photogates.
Data Studio Settings. Measure the length of the gliders and tell the computer so by clicking on the Constants Tab for each photogate and setting it to 0.128 m.
Photogate Check. As the gliders move through a photogate, the light on that photogate must remain “ON” for the duration and then off when the glider has passed completely.
Measurements.Select and drag a table over the velocity at Photogate 1 and Photogate 2.
Logistical Considerations: Please, run the air-pump for short amount of time just for the measurements. Running the air-pumps for extended period will create a significant noise level in the lab and might cause the air pumps to break.

Activity: Elastic Collisions

Place a rubber band end-piece and a flat-metal end-piece on each end of gliders A and B. When they collide, the rubber band should be pressed by the metail piece.

Run 1. Glider A is more massive than B

Place two metal cylinders (one on each side) of glider A.
Measure the mass of both gliders and write it down in the table below.
Place glider A outside the photogates and glider B in between. The elastic rubber band of one glider should face the metail piece of the other.
Push glider A so that it collides with B in between the photogates. Write down their velocity before and after the collision. Remember, the velocity of B before the collision will be zero.

Run 2. Glider A is lighter than B

Remove the metal cylinders from glider A and place them on glider B.
Repeat the steps from Run 1.

Results. Write down your results in the following table.

Questions:

Velocity of glider A.

For Run 1, in what direction does glider A go after the collision?

For Run 2, in what direction does glider A go after the collision?

Challenge

In what direction do you think glider A would go if it had mass equal to that of B?

Momentum transfer for Run. 1

How much is the total momentum of gliders A and B before the collision?

How much is the momentum of gliders A and B after the collision?

To how many significant digits do they agree?

Energy transfer for Run 1.

How much is the total energy of gliders A and B before the collision?

How much is the energy of gliders A and B after the collision?

To how many significant digits do they agree?

Run #	Mass of A	Mass of B	Velocity of A before	Velocity of B before	Velocity of A after	Velocity of B after