PHYSICS 231
2nd Midterm, November 8, 1996, 5:30 pm - 6:45 pm
Instructor: P. Q. Hung

Do all problems . READ them carefully. You have to EXPLAIN all your answers. DO NOT just write them down. ANSWERS WITHOUT EXPLANATION WILL BE GIVEN NO CREDIT.

Some formulas (not necessarily all useful):

,

,

,

,

,

,

,

kg, m.

I) A block of mass 2.0 kg slides along a frictionless table with a speed of 10 m/s. Directly in front of it, and moving in the same direction, is a block of mass 5.0 kg moving at 3.0 m/s. A massless spring with spring constant k = 1120 N/m is attached to the near side of , as shown in the Figure. When the blocks collide, what is the maximum compression of the spring? Hint: At the moment of maximum compression of the spring, the two blocks move as one. Find the velocity by noting that the collision is completely inelastic to this point. 25 pts.

Momentum conservation gives us:

Total Energy conservation gives us:

II) A 3.0 kg toy car has velocity m/s (i.e. along the x-axis). (a) What is the car's angular momentum and (b) the torque acting on the car about a point P with coordinates (2.0 m, 5.0 m, 0)? Hint: Find the position vector extending from point P to the location of the car as shown in the Figure. 25 pts.

a)

Let be the position vector of the toy car.

Then if is the vector from point P to , we have

b)