Question

Please answer the correct question and I will give you 50 points

1) Consider a ring, sphere and solid cyclinder all with the same mass. They are all held at the top of an inclined plane which is at 20° to the horizontal. The top of the inclined plane is 1 m high. The shapes are released simultaneously and allowed to roll down the inclined plane. Assume the objects roll without slipping and that they are all made from the same material. Assume the coefficient of static friction between the objects and plane to be 0.3.
A ) calculate the tangential (linear) Velocity of each shapes-
B) determine the linear acceleration(a)
C) which shapes have the greater moment of inertia ?
D) How long will it take each shape to reach the bottom of the Slope ?

E) workout what order they would get to the bottom of the Slope.


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Answer 1

A) The tangential (linear) velocity of each shape is:

For the ring: v = rω = 2.41 m/s.

For the sphere: v = rω = 1.57 m/s.

For the solid cylinder: v = rω = 2.41 m/s.

B) The linear acceleration of each shape is:

For the ring: α = 2gsinθ/(3r(1 + 0.3) + 2R) = 1.191 m/s^2.

For the sphere: α = 2gsinθ/(5r(1 + 0.3)) = 1.176 m/s^2.

For the solid cylinder: α = 2gsinθ/(3r(1 + 0.3) + 2R) = 1.228 m/s^2.

C) The solid cylinder has the greatest moment of inertia.

D) The time taken for each shape to reach the bottom of the slope is:

For the ring: t = 0.576 s.

For the sphere: t = 0.197 s.

For the solid cylinder: t = 0.576 s.

E) The sphere will reach the bottom of the slope first, followed by the ring and the solid cylinder.