Question

A green hoop with mass mh = 2.4 kg and radius Rh = 0.14 m hangs from a string that goes over a blue solid disk pulley with mass md = 2.3 kg and radius Rd = 0.08 m. The other end of the string is attached to an orange block on a flat horizontal surface that slides without friction and has mass m = 3.6 kg (see Figure 1). The system is released from rest.

(a) What is magnitude of the linear acceleration of the hoop? (4pt)

(b) What is magnitude of the linear acceleration of the block? (1pt)

(c) What is the magnitude of the angular acceleration of the disk pulley? (1pt) (d) What is the tension in the string between the block and disk pulley? (1pt)

(e) What is the tension in the string between the hoop and disk pulley? (1pt) (f) What is the speed of the green hoop after it falls distance d = 1.49 m from rest. (2pt)

(g) Now use energy conservation principle to solve for the hoop’s speed in (f). (5pt)

(h) Now instead of the block, the other end of the string is attached to a massless axel through the center of an orange sphere that rolls without slipping and has mass m = 3.6 kg and radius R = 0.22 m (Figure 2). Use energy conservation principle to solve for the speed of the hoop after it falls distance d = 1.49 m from rest. Compare your answer with the result you got in (g) [or (f)] and briefly expain why they are different. (5pt)

Answer 1