Problem Set 8

Physics 5200

Due 6 Apr. 1999

1. (3 points) A uniform billiard ball of mass m and radius a is hit and initially slides across the table with velocity v₀. Due to friction, the ball begins to roll. What is its velocity when it begins pure rolling? The coefficient of friction is m.

   
   

2. (2 points) A uniform disk or radius a and mass m begins rolling down a plane inclined at an angle q. What are v_cm, w, and x_cm as functions of time? The disk never slides. Hint: Although there may be a force parallel to the plane at the point of contact, since the disk doesn't slide, energy is conserved.
   
   
3. (2 points) If an object is falling subjet to a drag force of the form
   F_drag = -c₁v - c₂v|v|,
   show that the terminal velocity (speed) is
   v_t = [(mg/c₂) + (c₁/2c₂)²]^1/2 - (c₁/2c₂).
   Hint: Get rid of the absolute value in the drag force, and make sure that you get the signs correct on the two terms.
   
   

4. (3 points) A metal block of mass m slides on a horizontal surface that has been lubricated with a heavy oil so that the vlock suffers a viscous resistance that varies as the 3/2 power of the speed:
   F(v) = -cv^3/2
   If the initial spped of the block is v₀ at x=0, show that the block cannot travel farther than 2mv₀^1/2/c.