Lab 14: Impulse-Momentum Activity
Chris Ceron, Amy, John
Goal of Lab
Observe and verify the impulse-momentum theorem
Theory/Introduction
The impulse-momentum theorem relates both through Newton's Laws. The definition of momentum is:
Impulse is the relation of the sum of forces in respect to time:
The theorem states that both are equal. This means that Impulse (J) is equal to the change in momentum:
This conservation of momentum also relies and assumes there is no external forces acting on our apparatus. Our apparatus and lab consists of a collision that demonstrates this conservation of energy. In a perfectly elastic collision, we can predict that the speed in which the cart hits the spring is equal to its speed after the collision. However, because we understand that our apparatus and collision is not perfectly elastic, we can also predict that our final speed will be slightly less than the initial.
Apparatus and Procedure
For the first part of our experiment, we have a frictionless cart on a leveled track. We leveled the track by ensuring the cart would stop moving when gently pushed and when simply placed on the track. We placed a force sensor on the cart and a rubber stopper on the force sensor. On the opposite end of the track, we placed another cart with a spring plunger.
The cart on the track collides to the fixed cart by hitting the spring plunger with the rubber stopper on the force sensor. We record the process using the force sensor and a motion sensor to determine the amount of force the cart experiences during the collision and to record the velocity of the cart before and after the collision. We can find the impulse of our apparatus by taking the integral of a force vs time graph during the collision. We can compare this value to our calculated value through the change in momentum of the cart before and after the collision.
For the second part of our experiment (the inelastic collision), the cart collides with clay that is attached to a piece of wood. The rubber stopper on the force sensor is replaced with a screw/nail. The conduct the experiment similarly to the first, except the cart sticks to the clay after the collision, causing the final velocity of the cart to be 0. To compare the values of impulse between the first and second part of the lab, we provided the carts with very similar initial velocities.
Data, Graphs, and Calculations:
Mass of cart with force sensor: 0.677 kg
Graphs for Elastic Collision:
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| Initial velocity of cart = -0.364 m/s |
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| Final velocity of the cart = 0.246 m/s |
Impulse value = 0.3168 N*s
Calculated value:
Graphs for Inelastic Collision
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| Initial velocity of cart = -0.324 m/s |
Impulse value = 0.1971 N*s
Calculated value:
Conclusion
Our initial prediction for the first part of the lab was that energy would be conserved within our apparatus. However, we can look at our initial and final velocity (0.364 m/s and 0.246 m/s) and easily see that there are some uncertainties that caused energy to be lost. One source of error could be the initial point in which we began to record velocity of our cart. We placed the cart close to our motion sensor, which also happens to be the opposite side of the track. Through our velocity graph, we can see a slope in our velocity vs. time graph before the collision occurred. This shows that our frictionless track is not entirely frictionless.
Our values for the second part of the lab were much more similar, 0.1971 and 0.219. This shows the the force sensor recorded more accurately on the second part. This could also show that the rubber stopper could have caused inaccurate readings, likely due to the friction and slippage happening during the collision. We also noticed that the first part of the lab took some trial and error to get the rubber stopper to line up with the spring plunger. It is a possibility that both weren't lined up as needed to have a perfectly elastic collision.
Overall, we were able to produce similar values to verify the impulse-momentum theorem.
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