Analyzing One-Dimensional Collisions (Physics Lab)

[toittoiger]

I am doing a Physics Lab where you have to measure initial and final velocities of two carts colliding in order to find the momentum. In this first category, you push a cart with a bumper into another cart with a bumper so that the first one completely stops right when it hits the second one. I am just wondering how you would calculate the initial velocity of the first cart I had to push off. Is the initial velocity right before it hits the cart or when it leaves my hand...etc. If you could please tell me what you think the initial velocity might be from this following data, that would be great. Here is the data:

t (s) d (m) ∆d (m) ∆t (s) v (m/s)
0 0
0.1 0.01 0.01 0.1 0.1
0.2 0.027 0.017 0.1 0.17
0.3 0.062 0.035 0.1 0.35
0.4 0.114 0.052 0.1 0.52
0.5 0.19 0.076 0.1 0.76
0.6 0.287 0.097 0.1 0.97
0.7 0.39 0.103 0.1 1.03
0.8 0.491 0.101 0.1 1.01
0.9 0.588 0.097 0.1 0.97
1 0.682 0.094 0.1 0.94
1.1 0.772 0.09 0.1 0.9
1.2 0.858 0.086 0.1 0.86
1.3 0.9431 0.0851 0.1 0.851
1.4 1.022 0.0789 0.1 0.789
1.5 1.097 0.075 0.1 0.75
1.6 1.16 0.063 0.1 0.63
1.7 1.227 0.067 0.1 0.67
1.8 1.244 0.017 0.1 0.17

 

[HallsofIvy]

Strictly speaking, the initial velocity is just as it leaves your hand which would be
Δ d/Δ t for the first two times in your data list. However, that's really assuming that velocity remains constant until the collision. You might want to consider (distance at collision- distance at start)/(time of collision- time of start) as a better approximation.

 

[charng]

The initial velocity of the first cart can be calculated using the formula v = ∆d/∆t, where ∆d is the change in position and ∆t is the change in time. In this case, the initial velocity would be the velocity of the cart right before it hits the second cart, since that is when the collision occurs.

Looking at the data, it appears that the initial velocity of the first cart is increasing as it approaches the second cart, reaching a maximum of 1.03 m/s right before the collision. However, it is important to note that this calculation assumes that the carts are moving in a straight line and that there are no external forces acting on them.

It is also worth considering the uncertainties in the data, as some of the values for ∆t are quite small. This could affect the accuracy of the calculated initial velocity. It may be helpful to repeat the experiment multiple times and take an average of the initial velocities to get a more precise value.

Overall, it is important to carefully analyze the data and consider any potential sources of error when calculating the initial velocity of the first cart in this collision experiment.