1. Consider a modified Atwood machine, with a mass sitting on an inclined plane connected by a string which stretches over a pulley connected to a hanging mass. See picture. Friction is ignored.

a) Draw a free body diagram for both block 1 and block 2.

b) Apply Newton's second law to both block 1 and block 2.

c) If the angle is 30o , and the mass of block 2 is 10 kg while the mass of block 1 is 15 kg, find the tension in the rope.

2. Consider the following system with a 2 kg mass sitting on a table, connected to both 1 kg and 3 kg masses by strings which go over two separate pulleys and are pulling on the 2 kg mass in opposite directions.

a) What static friction coefficient would be required between the 2 kg mass and the table to stop the masses from accelerating?

b) If the masses are in motion, what kinetic friction coefficient would be required between the 2 kg mass and the table to ensure the masses move at a constant velocity?

c) Find the tension in both pieces of string for the case of zero friction.

3. Tarzan is running towards a cliff, ready to swing down rescue Jane from some poisonous snakes, and make it back up to a tree on the other side. For now, we are going to assume energy is conserved and ignore momentum. (We'll come back to this problem later!) If the height of the cliff is 10 m, the height of the tree on which Tarzan hopes to land is 7 m, the mass of Tarzan is 100 kg and the mass of Jane is 50 kg. What velocity does Tarzan have to be running to rescue Jane?