A stagecoach is pursued by bandits. The stagecoach is traveling at a top speed o
ID: 1399464 • Letter: A
Question
A stagecoach is pursued by bandits. The stagecoach is traveling at a top speed of 2.68 m/s when one of its wheels came loose (suspected sabotage). How far up a hill (incline) with grade of 35° will the wheel travel if it were near the bottom of the hill when it was detached from the stagecoach? Assume that the wheel has a total mass of 10.87 kg and the all the spokes make up of the total mass. Also, the diameter of the wheel is 0.9144 meters and you may assume that the length of the spokes is equal to the radius of the wheel. Ignore the contribution of the hub of the wheel. 1. Make Two sketches of the problem. Sketch #1 showing the wheel at the base of the hill (incline)AND Sketch. #2 showing the wheel at the point along the incline where it stopped moving ? 2. Use the equations on your equation sheets to calculate the moment of inertia ofthe wheel ? 3. Calculate the total energy of the wheel at the base of the hill ? 4. Calculate the total energy of the wheel at the point on the hill when the wheel stopped moving ? 5. Use energy conservation principles to calculate the distance traveled along hill (incline). ?
Explanation / Answer
1) I hope this part you can do.
2) Let M is the mass and R is the radius of wheel.
Moment of inertia of the wheel, I = M*R^2
3) At the base of the hill potential energy is zero.
Total energy = KEi
= KE_linear + KE_rotational
= 0.5*M*v^2 + 0.5*I*w^2
= 0.5*M*v^2 + 0.5*M*R^2*w^2
= 0.5*M*v^2 + 0.5*M*(R*w)^2
= M*v^2
4) At the point where the whell stopped moving, its kinetic energy is zero.
Let L is the length of the along incline.
h = L/sin(30)
Total energy = M*g*h
= M*g*L/sin(35)
5) initail mechaincal energy = final mechaincal energy
M*v^2 = M*g*L/sin(35)
L = v^2*sin(35)/g
= 2.68^2*sin(35)/9.8
= 0.42 m <<<<<----------Answer
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