Question

1) A rope of negligible mass passes over a uniform cylindrical pulley of 1.50 kg mass and 0.090 m radius. The bearings of the pulley have negligible friction, and the rope does not slip on the pulley. On one end of the rope hangs a 3.00 kg bunch of bananas, and on the other end hangs a 4.50 kg monkey. Calculate the downward acceleration of the monkey and the tension in both ends of the rope.

2) A 200 g sphere of ? = 25 cm radius and a 300 g cylinder of identical radius roll without slipping down a 30° slope, starting from a vertical height of 1.2 m.

a) Using conservation of energy, calculate for each of these objects their translational speed when they reach the bottom of the slope

b) Calculate the linear acceleration of each as they roll down the slope. (HINT: 1) Σ ? = ?? for motion parallel to the plane, where the forces are the relevant component of gravity and the static friction of the plane acting on the rim of the ball or cylinder, making it roll; 2) ? = ??, where the torque is provided by that same static friction force. The linear acceleration ? and the angular acceleration ? are related, in the case for rolling without slipping, by ? = ??)

c) Calculate the time required for each to reach the bottom

Answer 1