Conceptual Questions:
1. What can you say about the velocity of a moving body in dynamic equilibrium? (CQ-5.1)
2. What kind of equilibrium describes a box at rest on the floor? (CQ-5.8)
3. For an object in equilibrium (no accelerations), what two principles allow one to figure outthe relationships between all the forces involved? Draw a situation subject to torques and other forces and illustrate your answer. (CQ-5.15)
Numerical Problems: answers link to a help page.
1. A bucket of water with total mass 23 kg is attached to a rope, which in turn is wound around a 0.05 m radius cylinder at the top of a well. A crank with a turning radius of 0.25 m is attached to the end of the cylinder. What force directed perpendicular to the crank handle is required to raise the bucket at constant speed? (assume the rope's mass is negligible, that the cylinder turns on frictionless bearings, and that g = 9.8 m/s2) (P-5.3)
2. Tasha weighs 200 N and wants to use a 4.0 m board that weighs 100 N as a seesaw. Her friends are busy, so Tasha seesaws by herself by putting the support at the center of gravity when she sits on one end of the board. How far is she from the support point? (P-5.5)
3. A 100 N uniform ladder, 8 m long, rests against a smooth vertical wall. The coefficient of static friction between ladder and floor is 0.40. What minimum angle can the ladder make with the floor before it slips? (P-5.20)
4. A meter stick is supported by a knife edge at the 50 cm mark. Doug hangs masses of 0.40 and 0.60 kg from the 20 cm and 80 cm marks, respectively. Where should Doug hang a third mass of 0.30 kg to keep the stick balanced? (P-5.16)
5. An 800 N billboard worker stands on a 4 m scaffold supported by vertical ropes at each end. If the scaffold weighs 500 N and the worker stands 1 m from one end, what is the tension in the rope nearest the worker? (P-5.17)
6. A uniform, horizontal beam of length 6 m and weight 120 N is attached at one end to a wall by a pin connection (so that it may rotate). A cable attached to the wall above the pin supports the opposite end. The cable makes an angle of 60ø with the horizontal. What is the tension in the cable needed to maintain the beam in equilibrium? (P-5.18)
7. A copper wire of length 2 meters, cross sectional area 7.1 x10-6 m2 and Young's modulus 11 x1010 N/m2 has a 200 kg load hung on it. What is its increase in length? (g = 9.8 m/s2) (P-5.47)
8. When water freezes, its volume increses by 9.05%. What force per unit area will freezing water exert on a closed container? Water/ice has a bulk modulus of 2.2 x109 N/m2. (P-5.56)