Question 1: A 50-gram ruler is suspended from two strings, attached at 10cm and 80cm. (See figure) A mass m = 150 g is suspended from the 30cm point. The ruler is in equilibrium. What are the tensions in the two strings?
Question 2: A mass, pulley, and lever are arranged as shown in figure. The mass of the lever and the pulley are negligible compared to M. The lever has a pivot on the left end. What is the force F required to hold the mass in position?
Question 3: A chain hoist uses two coaxial pulleys, with radii R1 and R2, on which is looped a chain as shown in figure. The pulley wheels are toothed (like bicycle chainrings) so that the chain cannot slip on the wheels. Assume that the two sections of chain supporting the mass m are both approximately vertical.
(a) What force F shown in figure is required to move the mass m upwards at constant speed?
(b) Find the force F, in pounds, required to lift m = 2000 lbs if R1 = 25 cm and R2 = 20 cm.
Question 4: If you stack two uniform rectangular blocks of width L on the edge of a table as shown in figure, what is the maximum possible overhang x?
Question 5: A well-meaning relative gives you a huge bucket of homegrown plums. They taste horribly sour, but you don't want to just throw them away so you are making them into jam. The recipe calls for 16 pounds of pitted plums, and you don't have a scale. You do have a meterstick, some string, some plastic bags of negligible mass, and a 5-pound bag of sugar. Explain exactly how to weigh out the necessary quantity of plums.
Question 6: A ladder of mass m is leaning against a frictionless wall, as shown in figure. The coefficient of friction of the floor is µ. What is the minimum angle θ at which the ladder can remain in equilibrium?
Question 7: A lab cart, track, pulley, and hanging mass are arranged as shown in figure. The track and pulley are frictionless. If the weight of the cart is three times the weight of the hanging mass, what should be the angle of the track (measured from horizontal) so that the system is in equilibrium?
Question 8: A non-uniform bar is suspended by two spring scales, as shown in figure. The left scale reads 120 N, and the right scale reads 40 N. What is the total weight of the bar and how far from the left end is the center of mass?
Question 9: The uniform bar shown in figure has mass m. It is supported at the left end. Find the force F.
Question 10: A metal block is placed on a smooth wooden ramp. The coefficient of static friction between block and ramp is µ. If the angle of the ramp is slowly increased, at what angle will the block begin to slide?
Question 11: A chicken is sitting on a clothesline as shown in the figure. Find the tension in the clothesline?
