Force, Work, and Torque

  1. Suppose a 22kg weight is suspended from two cables anchored into the ceiling. One cable is 3m long and the other is 7m long, and they are fastened 9m apart in the ceiling. Nothing is moving.

    1. At what angles are cables hanging relative to the ceiling?
    2. What is the tension (force) along each cable?

  2. Suppose a paddle-boarder plans on crossing the Colorado river. They are on the south shore at a point where the river is \(200\)ft wide and flowing westward at about 1.5ft/s. They want to travel directly across the river, so they know they must paddle in a direction pointed slightly upstream. Suppose they know they can paddle at about 5ft/s.

    1. In what direction should they paddle?
    2. How long will it take them to cross the river?
  3. Suppose a 12kg cannonball is fired at an initial speed of 180m/s at an angle of inclination of 30°. If the cannon is on level ground and fires over level ground, how far away does the cannonball hit and what’s its speed at impact.
  4. Suppose you’re pushing a 19kg shopping cart. Well, maybe not “pushing,” because you’re just leaning on the handle while you walk along. You exert a force of 300N on the cart, at an angle of 40° below horizontal. After pushing the cart 50m, how much work did you do?

  5. Suppose you’re using a 0.2m long wrench to tighten a bolt, and you can apply 43N of force on the wrench handle.

    1. Suppose you apply a force directly orthogonal to the wrench. How much torque do you generate?
    2. Suppose you have a bad grip and can only apply the force at an angle of 70° relative to wrench handle. How much torque do you generate?
    3. Suppose you have a really bad grip, having to reach into a tight space to turn the wrench. You apply the force at an angle of 70° relative to wrench handle, and 20° off the plane in which the bolt should rotate. How much torque do you generate in the direction the bolt tightens?