HINTS FOR PROBLEM SET #12

Problem Set #12 – Problem 1

There are 3 collisions that you need to consider.

The first collision is when A hits B.  Use one prime to denote the velocities of A and B after this first collision.

The second collision is when B hits C.  Use two primes to denote the velocities of B and C after this second collision.

The third collision is when A hits B again.  Use three primes to denote the velocities of A and B after this third collision.

Find vB prime (the velocity of B after the first collision) using the conservation of momentum for the system of A and B.

This gives vB prime = 1.6 m/s

Now apply conservation of momentum for the system of B and C for the second collision. 

This gives vB double prime = 0.32 m/s

Now apply conservation of momentum for the system of A and B for the third collision. 

This gives vB triple prime = 0.3842 m/s

To get the coefficient of restitution between any two of the three cars, use the relative velocity equation for the first collision between A and B. 

This gives e = 0.6.

Problem Set #12 – Problem 2

This is a straight forward, if tedious problem.

For part (a), to find the angular momentum of the system about O, find the angular momentum of each of the three particles about O and add them up.

For part (b), to find the position vector of the mass center, plug into the formula given in the chapter.

For part (c), to find the linear momentum of the system about O, find the linear momentum of each of the three particles about O and add them up. 

For part (d), to find the angular momentum of the system about the mass center, G, find the angular momentum of each of the three particles about G and add them up.  This calculation is the hardest.  You will need to get  r cross mv for each particle. 

The r in this equation is the position vector from G to the particle, not the position vector from O to the particle.

The v in this equation can be the absolute velocity. It does not have to be the velocity relative to the mass center, G.  (Do you understand why?)

For part (e), to verify the equation that is presented, you just plug in what you found in parts (a) – (d).  

Is it equal?

(Note: You will need to get the velocity of the mass center. Use the linear momentum you found in part (c) and divide it by the total mass.)

Problem Set #12 – Problem 3

Since there are no external forces acting during the impact, momentum is conserved. 

Appling the conservation of momentum to the system of A, B and C, we can get two scalar equations. 

The only unknowns are the magnitudes of the velocity of B and the velocity of A after the collision. (Since the directions are given.)

So you can solve the two equations in two unknowns.