Physics 321 -- Spring 2003

Homework #4, due Wednesday Feb. 5

1. (3) Marion & Thornton: problem 9-25.

2. (3) Marion & Thornton, problem 9-40.

Hint: Read pg. 364 carefully. The component of velocity parallel to the surface is unchanged by the collision. The perpendicular component is not only reversed, but is reduced according to the coefficient of restitution.

3. (4) Consider a one-dimensional (head-on) elastic collision between a particle of mass m₁ travelling initially with velocity u₁, incident on a particle of mass m₂ initially at rest.

a) Analyze this problem using the center of mass frame of reference. First, find the initial velocities in the CM frame, u₁’ and u₂’. Second, find the final velocities in the CM frame, v₁’ and v₂’. Third, transform those final velocities back to the lab frame to get v₁ and v₂. Draw pictures of the initial and final situations in the CM frame to make sure everything looks right.

b) Check that your answers obey conservation of momentum and kinetic energy in the lab frame. You could have done the whole problem in the lab frame to begin with, but the algebra is easier using the CM frame, and the physics is clearer.

4. (4) Marion & Thornton, problem 9-34.

Hint: There are solutions both for a>0 and a<0.

5. (5) Marion & Thornton, problem 9-41.

Once you have written down the two components of conservation of momentum and the relation between initial and final kinetic energy, how can you avoid getting lost in the algebra? Here is how I did it: Eliminate the unknown angle z by using cos²z+sin²z=1. Then choose either u₁ or T₀ as your given quantity, and get rid of the other one. After the dust settles, you should have two equations involving v₁ and v₂ in terms of u₁. Solve them, and plug back into your original momentum equations to find the angle z.

6. (2) Marion & Thornton, problem 9-42.

Hint: Use Newton’s 2^nd Law in the form F=dp/dt to figure out how much force it takes to get the chain moving. Then draw a free-body diagram so you don’t forget about gravity!

7. (4) Marion & Thornton, problem 9-19.

Hint: Use Newton’s 2^nd Law in the form F=dp/dt to figure out how much force it takes to stop the falling chain. Don’t forget about the part of the chain that is already laying on the table!