Lab 4, Work-Energy and Momentum

Cuong NguyenSection 12

September 26, 2014

1 Abstract

For this lab, we observe the change in kinetic energies and momenta of two cartsbefore and after their collision in two cases - with Velcro and with a plunger.

2 Procedure

The experimental equipments include two carts, two motion detectors and atrack. The motion detectors are placed at the two ends, facing the middle ofthe track. One of the cart, called cart A, is loaded with mass and the other,called cart B, is not. Initially, cart A is placed 20 cm in front of the motiondetector on the left and cart B is in the center of the track. In the first case, oneof the carts is placed such that its Veclro is faced with each other. Then, cartA is given a momentary push toward cart B and the velocity data is acquired.In second case, the procedure is the same except for that the plunger of the oneof the two carts is headed to the other.

3 Data

3.1 Collision with Velcro

The following figures show the collected velocity of the two carts before andafter the collision with Velcro. We can see the sudden change in velocity duringthe collision between time 2s and 2.4s. The two carts are stick together so thattheir speed is very close to each other after the collision.

1

Figure 1: Graph of velocity in respect with time of the two carts in the collisionwith Velcro. The x-component of velocity of cart A and B is measured beforethe collision to be 0.3404 m/s and 0 m/s respectively

Figure 2: Graph of velocity in respect with time of the two carts in the collisionwith Velcro. The x-component of velocity of cart A and B is measured after thecollision to be 0.0823 m/s and 0.0848 m/s respectively.

Note: The velocity of cart B is measured by the motion detector on theright, so the signed is reversed to comply with direction of the motion detectoron the left.

2

3.2 Collision with plunger

The following figures show the collected velocity of the two carts before and afterthe collision with plunger. We can see the sudden change in velocity during thecollision between time 1.8s and 2s.

Figure 3: Graph of velocity in respect with time of the two carts in the collisionwith plunger. The x-component of velocity of cart A and B is measured beforethe collision to be 0.3840 m/s and 0 m/s respectively

Figure 4: Graph of velocity in respect with time of the two carts in the collisionwith the plunger. The x-component of velocity of cart A and B is measuredafter the collision to be 0.0015 m/s and 0.1701 m/s respectively.

3

4 Discussion

Next, we calculate the kinetic energies and momenta of the two carts based onthe acquired data and see if the final results (showed in Table 1) comply with theWork-Energy Theorem and the Law of Conservation of Momentum.

(a) Cart A is at constant velocity. Cart B is atrest

(b) Two cart colliding

Figure 5: Free-body diagrams of two carts on a frictionless surface in two situ-ations.

The Work-Energy theorem states that the work done on an object isequal to the change in its kinetic energy:

WAB =

∫ B

A

~F · d~r = KB −KA

The Law of Conservation of Momentum states that the total momen-tum in a closed system is constant.

n∑i=1

~pi = ~p1 + ~p2 + ~p3 + · · · + ~pn = const

Table 1: Kinetic energies and momenta calculated from acquired data.

4

In Table 1, the data pair ∆pA and ∆pB of the experiment with the plungershould be equal and opposite. This statement is consistent to the free-bodydiagrams in Figure 5. The reason is that the force ~FBA in the diagram isopposite to the velocity va so it reduces the momentum of cart A. At the sametime, the force ~FAB acting on cart B increases the momentum of cart B. Thesetwo changes should be equal but in opposite direction. The empirical data inTable 1 also supports this argument (∆pA = −0.1928 and ∆pB = 0.1735).The discrepancy between two value exists due to the fact that the track is notperfectly frictionless.

In the two experiments, the value ∆K/Ki are very different. In the casewith Velcro, the collision is highly inelastic because the two carts are sticktogether after the collision. Therefore, a larger amount of kinetic energy islost. On the other hand, the collision with plunger is near elastic if there isno friction, so the loss in kinetic energy is smaller. In both cases, the lostenergy is converted into heat and sound. The work done on the two carts is theremaining of the kinetic energy in cart A before collision. This work is equalto the change in kinetic energy of the two carts. The values ∆P/Pi in bothexperiment remain approximately the same because in any cases, the Law ofConservation of Momentum is unchanged.

5