Physics 71 S5B Problem Set Chapter 5 Deadline: 09July2010 Solve the following problems individually. Use whole sheets of yellow paper. 1. EQUILIBRIUM. For the systems in equilibrium in the figure below, find the unknown tensions and masses.
2. ACCELERATING. Two climbers on an icy (frictionless) slope, tied together by a 30-m rope, are in the predicament shown in the figure below. At time t = 0, the speed of each is zero, but the top climber, Paul (mass 52 kg), has taken one step too many and his friend Jay (mass 74 kg) has dropped his pick. (a) Find the tension in the rope as Paul falls and his speed just before he hits the ground. (b) If Paul unhooks his rope after hitting the ground, find Jay's speed as he hits the ground.
3. FRICTION. In the figure, m1 = 4 kg. The coefficient of static friction between the block and the incline is 0.4. (a) Find the range of possible values for m2 for which the system will be in static equilibrium. (b) What is the frictional force on the 4-kg block if m2 =1kg? (c) If m2 = 5 kg, and the coefficient of kinetic friction between the inclined plane and the 4-kg block is Âľk = 0.24. Find the acceleration of the masses and the tension in the cord.
4. CIRCULAR MOTION. Mass m1 moves with speed v in a circular path of radius R on a frictionless horizontal table (see figure below). It is attached to a string that passes through a frictionless hole in the center of the table. A second mass m2 is attached to the other end of the string. Derive an expression for R in terms of m1, m2, and v.