We will study the relationship of force and the duration of the collision. In doing so we will observe the max force experienced by an accelerating cart when it impacts another cart with a spring. A stiff spring will be used. We will collect the information through two items. We will use distance and time as information collectors. This will measure the acceleration, velocity, and position of the cart as it moves down the track. The most important measurement collected is the velocity; which will be used to calculate the momentum. We will also explore how mass impacts in the change of momentum, and if there can be a non-changing impulse between the two carts with different masses.
Experimental results: ” Analyzing Exploding Carts – Lab Activity” Handout (back part)
1 meter stick
1 Cart with string
1 Mass block of 1.0kg
1 Mass block of 0.5kg
Setup materials: Construct horizontal track, using the meter stick to create it. To surround it (and to prevent the carts from falling), set the 2 blocks/books at the edge of each side. Set the string to its first module. Total track should be 1.0m; however, distance travelled by the carts will be 0.52m. Record the interval as d in Table 1. Put the carts next to each other, with the string separating them (but still together). Mark this location with a small piece of tape if necessary. Run a few tests until the time for the both of them to cover different distances is the same (this is because they have different acceleration and masses). In order to determine the velocity, measure the time it takes for each cart to travel the known d. After this, repeat the trials; but add 0.5kg of mass. Repeat until timing is precise. Once this finished, calculate the velocity of all trials; v1 and v2, using d1 (distance travelled by cart 1) and d2 (distance travelled by cart 2). Also calculate momentum; p1 and p2.
Hence, the equations used will be:
v = d/t
Comments and observations:
Setting the material was simple. The activity was interesting. We had lots of experimental error; lots of variations in velocity and some for time. This was equal for cart1 and cart2. We had to run many trials in order to get the most precise results.
Total track was 1.0m long however, only 0.52m was travelled. The two carts were set in different spots along the track. Cart1 had an initial weight of 1.0kg, while cart2 was 0.9kg. The cart on which mass was added was cart1. We can see here all the trials and how each changed in comparison to the one done before. Between each mass change for cart1, distance travelled decreased 0.02m (or 2.0cm). Velocity decreased at different rates; so there was a different acceleration. This was on cart1, because mass was being added to it; which not only involves a bigger mass but also brings a higher force of friction acting on it.
We conclude that it is not only possible for two collisions with the same initial velocity to have the same impulse but mandatory. That is, as long as the time of the impulse is free to change. We had some error in our experiment, in the difference in momentum and the integrated impulse. I believe that this was caused by two factors. We did not really measure the force sensor between each run. This could lead to a miss measurement of force and would account for the doubled error for the spring. Also we did not release the cart from the same point on the track (although this was made to have them finishing at same time; easier to administrate). The difference in the mass and distance traveled would naturally cause the final velocity before impact to be different (this is because of friction). The max force that occurs during a collision is a function of the change in velocity over a change of time. The shorter the time span, the larger the force must be. However, this will not change the impulse. If we had correct calibration and similar momentums for both our runs, I am confident that we would have seen an even more accurate account of impulse. Even with our error we had conclusive results.