# Collisions II

## Inelastic Collisions

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

Objectives

• To verify that in the absence of external forces the linear momentum remains the same before and after the inelastc collision of the two gliders.
• To determine whether the energy of the gliders just before the inelastic collision is equal to that just after.
• To learn how to measure the velocity of the gliders 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:

(mA)(vA,before) + (mB)(vB,before) =  (mA)(vA,after) + (mB) (vB,after)

Inelastic Collisions. Collisions in which objects stick together. After an inelastic collision, the objects move with equal velocities.

Experiment, Data and Results

We will investigate only the inelastic 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.
• Inelastic Collision set up. Place the needle end piece on the glider A, and the putty-filled end piece on glider B. During the collision, the needle should slide into the putty and hold the gliders together.
• 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.
• 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 1: Inelastic Collisions between two gliders.

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 needle on glider A should face the putty-side of glider B.

• 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.
• Place two metal cylinders (one on each side) of glider A. Repeat the collision and record the velocities.
• Remove the metal cylinders from glider A and place them on glider B. Repeat the collision.
• Write down your results for the three runs in the following table.

 Mass of A Mass of B Velocity of A before Velocity of B before Velocity of A after Velocity of B after massA ≈ massB massA > massB massA < massB
• Questions. For the run that you feel most confident that everything is accurate and correct, answer the following questions:How much is the 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?

Note on the accuracy: If the momentum before and the momentum after agree numerically at least in their first two digits, you can say that the momentum is most likely conserved. If the first two digits of your results disagree, however, you must go back and investigate possible factors that have changed the momentum, e.g. track was not level, photogates were not working, etc.

Only if your calculations showed significant change in the momentum before and after the collision (that is if you answered 3 or higher on the previous question), list all the factors that you identified that could have possibly caused that change:

• Challenge Question.

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

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

Is the kinetic energy conserved?

If you answered “NO” on the previous question, can you trace the flow of energy? Begin with the energy being in the form of kinetic energy of glider A, and then explain where it goes: