I need help with an experiment i did to test newtons 3rd law in my lab class. My

Question

I need help with an experiment i did to test newtons 3rd law in my lab class. My setup consisted of two carts (cart one weighed 516.5 grams and cart 2 weighed 509 grams). I set them on opposite sides of the track, with 2 photogates in the middle. I pushed the carts towards eachother so they would crash into eachother in between the photogates. The photogates then gave the initial and final velocities of the two carts. I tried using F=MA to prove that the force exerted by the carts on eachother are equal and in opposite directions, but i couldnt calculate the acceleration since i would have needed 4 photogates for that. So now i guess my only option to do this experiment would me using momentum (force=absolute value of change in momentum over change in time and set the two carts change in momentum equal to eachother). for my first trial i got an initial velocity of .698m/s and a final velocity of .368 m/s for cart 1, and an initial velocity of .656m/s and a final velocity of .466m/s for cart 2. (cart 1 came from the left towards the right to hit cart 2). The time from the start to when the carts stopped after they hit eachother was on average 3.2 seconds for cart 1 and 2.3 seconds for cart 2. QUESTION: could someone help me make sense of this?

Explanation / Answer

For cart 1:

m = 516.5 g = 0.5165 kg

Vf = final velocity = 0.368 m/s

Vi = initial velocity = 0.698 m/s

P = change in momentum = m (VF - Vi) = (0.5165)(0.368 - 0.698) = - 0.17 kgm/s

for calculating the force , the time we need is the the time for which the two carts collide.

so please note the time for which the carts were in contact during the collision. then we can calculate the force using the formulas

F = P/t

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