Slopes, Pulleys & Sliding Things

1) A snowboarder slides straight down a 25° incline. It’s a beautiful day, sunny, with no air resistance and no friction. What is his acceleration?

2) The snowboarder takes another run down the 25° incline, but this time the snow has a coefficient of kinetic friction equal to 0.15. How fast will he be moving after he slides 60.0 m down the slope? He starts from rest.

3) Imagine you’re dragging a child on a sled by pulling on a rope that makes a 29° angle with the ground. The coefficient of kinetic friction between the sled and the snow is 0.095, the child has a mass of 30.0 kg. You’re moving at a constant velocity. How hard are you pulling on the rope?

4) Two boxes are connected by a rope. The boxes are both sitting on a frictionless floor. Mass #1 equals 14.0 kg and mass #2 equals 6.50 kg. Pull on mass #2 with a force of 55.0 N. How fast will the boxes accelerate? What is the tension in the rope?

5) Two more boxes are connected by a rope, and both are resting on a frictionless table. The box on the left has a mass of 15.5 kg and the box on the right has a mass of 22.0 kg. The box on the right is connected to a third box that hangs off the edge of the table, and the rope that connects them is draped over a frictionless pulley. The third box has a mass of 8.50 kg. How fast will the boxes accelerate? What is the tension in each of the two ropes?

6) Box #1 (mass₁ = 3.2 kg) sits on a flat surface. It is connected by a rope to box #2 (mass₂ = 4.5 kg) which rests on a 50° slope. The rope between them runs over a rusty pulley that is not frictionless, and it is the friction caused by the pulley that keeps the boxes from sliding. If the coefficient of static friction between box and surface is 0.13 what is the friction caused by the pulley?

7) Here’s one without numbers. Two masses M and m are connected by a massless rope hung over a frictionless pulley. Mass M is on the right and m is on the left. M is greater than m. Find the acceleration of M and the tension in the rope.