Assignment:
Problems:
1. A system of two paint buckets connected by a lightweight rope (see diagram) is released from rest with the 6.0-kg bucket 2.00 m above the floor. Find the speed of buckets when the 6.0-kg bucket hits the ground. You can assume that there is no friction and that the pulley and rope are massless.
2. A mass m = 0.50 kg is pushed against the end of a spring, compressing it by an amount d = 40 cm from its relaxed position. The spring has spring constant k = 15 N/m. The mass is released from rest and slides along a flat frictionless surface.
It then slides into a frictionless semicircle of radius R = 60 cm (see diagram).
(a) What is the largest angle the mass reaches before it stops?
(b) What is the normal force when the mass reaches its largest angle obtained in part (a)?
3. A 3.0-kg block is connected to two ideal horizontal springs having force constants k1 = 14.0 N/cm and k2 = 20.0 N/cm (see diagram). The system is initially in equilibrium on a horizontal frictionless surface. The block is then pushed 12 cm to the right and released from rest.
(a) What is the maximum speed of the block, and where does this occur?
(b) As the block moves to the left, what is the maximum compression of spring 1?
4. An 80-kg bicyclist coasts down a hill that makes a 12o angle with the horizontal at a speed of 8.0 m/s.
(a) If the drag force is given by Fdrag = -bv, what is the drag coefficient b?
(b) If when peddling the bicyclist can generate 0.60 hp, how fast can he go up the hill?