Question

The situation is: using two gliders, 4 collisions on a linear track are observed. In each collision, the initial speed of glider 2 is zero. Collisions 1 and 2 use an elastic band and a bumper attachment on the gliders to create an elastic collision where the two gliders touch for just a moment and the area of contact is minimal. Collisions 3 and 4 use a needle and wax receptacle so that during the collision, the needle bites into the wax and the two gliders stick together.

I have a position-time graph with about 100 lines of data (pre and post collision). I have access to the mass of each glider (with uncertainties). How would I find the answer to this type of question:

Based on the experimental data, 1. calculate the total momentum (in kg·m/s) of the system after the collision; 2. calculate the uncertainty of the total momentum (in kg·m/s) of the system after the collision.

Answer 1

calculate the total momentum (in kg·m/s) of the system after the collision

it can be simply found as

m1v1f + m2v2f

where m1 and m2 are masses of gliders and v1f , v2f are final velocities. Be very careful about the final direction of gliders and use sign accordingly, if glider is moving to the left after collision, use negative sign

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calculate the uncertainty of the total momentum (in kg·m/s) of the system after the collision.

There are two ways

one using the equation

other using the standard deviation

The one with standard deviation is easy and accurate !!!

Here are the steps

Step 1 - find mean ( average) of your total momentum after collision

Step 2 - subtract each value of data from mean

Step 3 - square the value found in step 2

Step 4 - divide the value found in step 3 by (N - 1) here N is total number of readings you took

Step 5 - take the square root of value found above and you have the standard deviation.

Step 6 - divide the standard deviation by and this will give uncertainty