1) A solid sphere of mass 0.595 kg rolls without slipping along a horizontal sur

Question

1) A solid sphere of mass 0.595 kg rolls without slipping along a horizontal surface with a translational speed of 5.49 m/s. It comes to an incline that makes an angle of 39° with the horizontal surface. Ignoring energy losses due to friction, to what vertical height above the horizontal surface does the sphere rise on the incline?

2)The string in a yo-yo is wound around an axle of radius 0.529 cm. The yo-yo has both rotational and translational motion, like a rolling object, and has mass 0.204 kg and outer radius 1.96 cm. Starting from rest, it rotates and falls a distance of 1.50 m (the length of the string). Assume for simplicity that the yo-yo is a uniform circular disk and that the string is thin compared to the radius of the axle.

Explanation / Answer

Since you are only permitted to ask one question per post on Cramster, I can only answer one, so I will answer the first question for you. Please repost the second question for that to be answered.

At the bottom of the ramp, the sphere has both rotational and translational KE. At the top of the ramp it will have only PE

The equation becomes

KEr + KEt = PE

.5(I2) + .5mv2 = mgh

The moment of inertia of a sphere is 2/5MR2 and = v/r

By substitution, we get

.5(2/5)mr2v2/rr + .5mv2 = mgh

Simplify (where m cancels)

.7v2 = gh

.7(5.49)2 = (9.8)h

h = 2.15 m

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