Determine the tension in the horizontal massless cable 𝐶𝐷. Determine the vertical and horizontal components of the force exerted by the pivot 𝐴 on the aluminum pole.

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 cite the source of your information.

10 – 26: The angular acceleration of a wheel, as a function of time, is 𝛼 = 4.2𝑡2 −9.0𝑡, where 𝛼 is in 𝑟𝑎𝑑/𝑠2 and 𝑡 in seconds. If the wheel starts from rest (𝜃 = 0,𝜔 = 0, at 𝑡 = 0):

a) Determine a formula for the angular velocity 𝜔 as a function of time.

b) Determine a formula for the angular position 𝜃 as a function of time.

c) Evaluate 𝜔 and 𝜃 at 𝑡 = 2.0 𝑠.

10 – 51: An Atwood machine consists of two masses, 𝑚𝐴 = 65 𝑘𝑔 and 𝑚𝐵 = 75 𝑘𝑔, 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 𝑚 and mass 6.0 𝑘𝑔.

a) Determine the acceleration of each mass.

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 𝐴𝐵 is 7.20 𝑚 long and has a mass of 12.0 𝑘𝑔. The mass of the traffic light is 21.5 𝑘𝑔.

d) Determine the tension in the horizontal massless cable 𝐶𝐷.

e) Determine the vertical and horizontal components of the force exerted by the pivot 𝐴 on the aluminum pole