Question

21. A frictionless roller coaster car is released from rest on the track at a height of 50 m. How fast is the car going at the top of a circular loop with a radius- 12 m? (a) 19.8 m/s (b) 20.8 m/s (c) 21.7 m/s (d) 22.6 m/s (e) 23.6 m/s 7 22. A bullet (mass-0.0050 kg) is fired into a suspended block of wood (m-5.0 kg). Initially the wood is not moving. The bullet lodges in the wood. Recoil of the wood causes it to swing (rising 0.020 m vertically. What was the initial speed of the bullet? (a) 280 m/s (b) 410 m/s (c) 520 m/s (d) 627 m/s (e) 750 m/s h 0.020 m 18. A hockey player uses her stick to exert a constant horizontal force F on a hockey puck of mass M that was initially at rest on level ice. She applies this constant force through a distance D. What is the speed of the hockey puck when it leaves her stick? (a) 2FD/M (b) MD/F (d) [FD/(2M)] (e) (2FD/M) 19. A particle of mass m is initially at rest and compressed a distance d against a horizontal spring of spring constant k. When the particle is released it slides along the horizontal surface without friction. How fast does the particle slide when it is no longer compressed against the spring? (a) kd (b) kd/2 (c) mv (d) k/d (e) None of the above.

Answer 1

Conservation of energy mg times 50 = mg times 24 + 1/2 mv^2 v = squareroot 2 times (50 - 24) g v = squareroot 2 times 26 times 9.21 22.6 m/s v = 22.6 m/s (22) Conservation of momentum m_4 = (m + m) v v = mu/m + m Now using conservation of energy 1/2 (m + m) v^2 = (m + m) gh v^2 = 2 gh v^2 = 2 gh (mu/m + m)^2 = 2 gh = > 4 = squareroot gh times (m + m/m) u = squareroot 2 times 9.21 times 0.02 times (0.005 + 5/0.005) = 627 m/s