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 β 26: The angular acceleration of a wheel, as a function of time, is πΌ = 4.2π‘2 β 9.0π‘, where πΌ is in πππ/π 2 and π‘ in seconds. If the wheel starts from rest (π = 0, π = 0, at π‘ = 0):
- a) Determine a formula for the angular velocity π as a function of time.
- b) Determine a formula for the angular position π as a function of time.
- c) Evaluate π and π at π‘ = 2.0 π .
10 β 51: An Atwood machine consists of two masses, ππ΄ = 65 ππ and ππ΅ = 75 ππ, 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
π = 0.45 π and mass 6.0 ππ.
- 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 ππ»π¨ and ππ»π© 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 β 17: A traffic light hangs from a pole as shown below. The uniform aluminum pole π΄π΅ is 7.20 π long and has a mass of 12.0 ππ. The mass of the traffic light is 21.5 ππ.
- d) Determine the tension in the horizontal massless cable πΆπ·.
- e) Determine the vertical and horizontal components of the force exerted by the pivot π΄ on the aluminum pole