A sphere, a cylinder and hoop with 1.0 m radius and 10 kg mass were released fro

Question

A sphere, a cylinder and hoop with 1.0 m radius and 10 kg mass were released from 45m high ramp with 30° from the horizontal. All of the objects were released at the same time and the velocity is measured at the bottom. a) What are the potential energies of the three different shape objects? (Hint: P.E. =mgh) I used the equation and did 10kgx 9.8m/s2x45m and I got 4410 is that correct? b)What are the kinetic energies of the three objects at the bottom? (Hint: K.E. = ½ m V2 + ½ I 2) b) What are the velocities of the three objects at the bottom? The sphere has the maximum velocity, because of the coefficient in moment of inertia is small.

I did part A and was wondering if it was correct however I can figure out part b and c can someone please help

Explanation / Answer

Part a)

The potential energy is mgh = 10*9.8*45 = 4410 J

b) K.E. = ½ m V2 + ½ I 2

V= r*

KE = ½ m V2 + ½ I (V/R)^2

FOR cylinder . I = mR^2/2

FOR Sphere I = 2/5 mR^2

FOR hoop , I = mR^2

KE cylinder = mR^2

KE Cylinder = ½ m V2 + ½ I (V/R)^2 = ½ m V2 + ½ mR^2/2* (V/R)^2 = (3/4)* mV^2

KE Sphere = ½ m V2 + ½ I (V/R)^2 = ½ m V2 + ½ 2/5*mR^2* (V/R)^2 = (7/10)*mV^2

KE Hoop = ½ m V2 + ½ I (V/R)^2 = ½ m V2 + ½ mR^2* (V/R)^2 = mV^2

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