Please help with formulas for take home test due tomorrow.

[revit]

Homework Statement

The test has two parts. In Part A, you predict the results and give qualitative reasoning and in Part B, you actually calculate the values and verify if your predictions and the calculations are in agreement, and then give correct physics reasoning.

Consider three events: Event 1: A solid cylinder (blue) of mass M = 10 Kg. rolls about the center mass axis without slipping due to the hanging mass that is tied to the cylinder. The cylinder is tied to a solid mass m=20 Kg. by a string of negligible mass. The string runs over a freely rotating wheel as shown in the below figures. Assume that the rolling friction is almost zero and the radius of the smaller wheel is negligible when compared with the cylinder. The hanging mass is initially at a half meter height from the
ground. Radius of the cylinder r=25 cm.
Event 2: Instead of the cylinder a solid sphere of the same mass and the same radius rolls without slipping.
Event 3: Instead of the cylinder a solid box of the same mass slides without friction.
Part A: Predict the results and give physics reasoning to explain your prediction. (Points: 30)
1. Among the sphere, cylinder and the solid box, which one will have the highest value
acceleration and which one the smallest value. Why is it the way it is?
2. Which object will have the largest and the smallest velocities just before the hanging mass touches the ground and why?
3. How is the initial total energy of the system distributed as the hanging mass moves down in each of the events?Part B: Calculate the values. (Points: 30)
1. Calculate the accelerations of the sphere, cylinder and the solid box. Do these values agree with your predictions in part A. Give corrected reasoning.
2. Calculate the velocities of the cylinder, sphere and the box just before the hanging mass touches the ground. Do these values agree with your predictions and give corrected reasoning.
3. Now give the corrected reasoning for the distribution of the initial total energy.I have completed Part A but not sure which formulas to use for part B. Can you please help me out with the formulas?

Thanks

 

[tiny-tim]

welcome to pf!

hi revit! welcome to pf!

I have completed Part A but not sure which formulas to use for part B.

you'll always need the rolling constraint v = rω (and a = rα)

then use conservation of energy (sometimes that doesn't work, and you'll have to use torque = Iα instead)