+momentum of collisions in 2-D help

[sodr2]

For an experiment in physics class, I had to roll a steel ball down a ramp so that it makes a collision with another steel ball of the same size, knocking it off a support near the edge of the table, and go off in different directions and land on a sheet, on the bottom of the table, which marks where the two balls landed. We are studing the momentum of this collision, but I am having trouble finding the initial momentum of the ball at rest before the collision and adding vectors.

The procedures and questions for this experiment are as follows:

1. Draw a line joining X (the point of collision) with the point of contact of mass 1. Draw another line joining X with the point of contact of mass 2. The length of these two lines represents the final momentum vectors of mass 1 and mass 2.

2. Measure the angles between these momentum lines and draw a scale vector diagram to represent the sum of the two final momentum vectors. For addition of vectors, join them head to tail. Find the resultant momentum.



P(total) = P(total)(after collision)

m1v1 + m2v2 = m1v1(after) + m2v2(after)

since masses are equal:

v1 + v2 = v1 (after) + v2 (after)

--> momentum is proportional to velocity, proportional to distance

For v1, I rolled one of the balls down the ramp alone and got the distance it landed on the bottom of the table and said that the length of this line represented the initial momentum vector for mass 1. I am also guessing that the inital momentum for mass 2 is zero because it is at rest.


I am completely stuck...is the sum of the distance the balls of mass 1 and 2 travel the total momentum after they collide?? If someone could tell me ANY useful information that I should know, that would be grrrrrrrreat.

 

[astrorob]

but I am having trouble finding the initial momentum of the ball at rest before the collision

If the ball's initially at rest (velocity = 0) and momentum is mass x velocity, what does that mean the momentum is equal to initially?

 

[sodr2]

zero. ok, so what about the initial momentum of the ball colliding the ball at rest before collision?

 

[astrorob]

Are you not given anymore information?

In this case proving momentum is conserved is possible, but i don't see how you'd find the exact value of it.

To prove it's conserved you don't have to calculate the initial momentum. We use those proportionality relationships you described above, that is to say;

note: ' signifies the ball after collision.

We start with our momentum conservation equation:

p1 = p1' + p2'

or equivalently

mv1 = mv1' + mv2'

since the mass of the balls is the same for each we can eliminate the mass by dividing through

v1 = v1' + v2'

Now, speed equals distance over time, but our time is a constant also. We can eliminate that to give

d1 = d1' + d2'

where d is the horizontal displacement. d1 represents the horizontal displacement when rolling the ball off the ramp without the secondary collision ball.

 

[sodr2]

Ok, thankyou very much for your help. I get it now.