Purpose: To determine the impulse of an object from a force vs. time graph and to test the idea that that the amount of momentum change for a moving object is equal to the amount of the net impulse acting on the object.
For this lab, we conducted three experiments. The first being an elastic collision, the second an elastic collision with more mass and the third an inelastic collision.
Part 1: Elastic Collision
For the first experiment, we attached a force sensor and rubber stopper to a cart. This is the only cart that moves during the experiment. At one end of the track, we clamped a cart with a spring to a rod. When setup properly, the rubber stopper from the cart hits the spring of the stationary cart and reverses direction. On the other end of the track, we setup a motion sensor to measure the moving cart's speed. The force sensor mounted on the cart will help us measure the impulse of the cart during the collision.
With the setup shown above, we finally conducted the experiment. We setup LoggerPro so that it will give us Force vs Time and Velocity vs Time data.
In order to prove the idea that the amount of momentum change for a moving object is equal to the amount of the net impulse acting on the object. We had to calculate both impulse and the change of momentum for the moving cart. The impulse was determined by taking the area under the Force vs Time graph; since J = the integral of ( F*dt). The change in momentum of the cart was calculated using the equation: mVf-mVo
- Vf and Vo were found using the Analyze feature on LoggerPro.
- Measured mass of cart = 0.763 kg
In the v vs t graph shown above, Vo is the point right before the decline occurs. Vf is the point just before the decline levels out.
Vo=.566 m/s and Vf=-0.501 m/s
From the graphs:
- Impulse = -0.7329 N*s
- Change in momentum = mVf-mVo = -0.8142 kg*m/s
Part 2: Elastic Collision with more mass
Part 2 follows the exact same procedure we used for Part 1 except we added mass (300g) to the moving cart.
The impulse was still found by taking the area of the F vs T graph. The change of momentum was found using mVf-mVo.
- Measured mass of cart: 1.063 kg
- Vo= .464 m/s
- Vf= -.385 m/s
From the graph:
- Impulse = -0.8504 N*s
- Change in momentum = mVf-mVo = -0.9025 kg*m/s
Part 3: Inelastic Collision
This experiment follows the same procedure as shown above to find impulse and change in momentum of the moving cart. The major difference being that this is an inelastic collision. Therefore, the stationary cart with spring is replaced by a piece of wood with clay and the moving cart now has a nail attached to it.
Now, the moving cart will stick to clay and stop.
- Measured mass of moving cart: 1.063 kg
- Vo=0.355 m/s
- Vf=0 m/s
From graph:
- Impulse = -0.3380 N*s
- Change in momentum = mVf-mVo = -0.3773 kg*m/s
Conclusion:
In all three experiments, the impulse and change in momentum never equaled each other but were fairly close. This was seen in both elastic and inelastic collisions. The discrepancy can be explained by other forces being present during the experiment. For example, we didn't take in account friction because we assumed the track is frictionless. Nonetheless, we proved the idea that that the amount of momentum change for a moving object is equal to the amount of the net impulse acting on the object. We came to this conclusion because the impulse and change in momentum were fairly similar for each experiment.
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