Chapters 10 and 12 Written Homework

Be sure to show all your work, particularly for odd-numbered questions. If you end up looking at a solution please cite the source of your information. 10 – 26: The angular acceleration of a wheel, as a function of time, is 𝛼 = 4.2𝑑2 βˆ’ 9.0𝑑, where 𝛼 is in π‘Ÿπ‘Žπ‘‘/𝑠2 and 𝑑 in seconds. If the wheel starts from rest (πœƒ = 0, πœ” = 0, at 𝑑 = 0):

  1. a) Determine a formula for the angular velocity πœ” as a function of time.
  2. b) Determine a formula for the angular position πœƒ as a function of time.
  3. c) Evaluate πœ” and πœƒ at 𝑑 = 2.0 𝑠.

10 – 51: An Atwood machine consists of two masses, π‘šπ΄ = 65 π‘˜π‘” and π‘šπ΅ = 75 π‘˜π‘”, connected by a massless inelastic cord that passes over a pulley free to rotate (as shown below). The pulley is a solid cylinder of radius

𝑅 = 0.45 π‘š and mass 6.0 π‘˜π‘”.

  1. a) Determine the acceleration of each mass.
  1. b) What percent error would be made if the moment of inertia of the pulley is ignored?

Hint: The tensions 𝑭𝑻𝑨 and 𝑭𝑻𝑩 are not

  • equal. (The Atwood machine was discussed in
  • example 4-13, assuming I = 0 for the pulley.)

There is one more question on the next page.

12 – 17: A traffic light hangs from a pole as shown below. The uniform aluminum pole 𝐴𝐡 is 7.20 π‘š long and has a mass of 12.0 π‘˜π‘”. The mass of the traffic light is 21.5 π‘˜π‘”.

  1. d) Determine the tension in the horizontal massless cable 𝐢𝐷.
  2. e) Determine the vertical and horizontal components of the force exerted by the pivot 𝐴 on the aluminum pole