2. consider an object (say a solid sphere) of mass m, radius r, and moment of in

Question

2. consider an object (say a solid sphere) of mass m, radius r, and moment of inertia l at the top of a ramp, as shown above. The object is released from rest and allowed to roll to the bottom, a vertical height h below the starting point. What is the object's speed on reaching the bottom? (use energy conservation) 3M 2M 2L. object A object B object C 3. Use the Universal Law of Gravitation to determine the total force exerted on object B by objects A and C. Calculate the acceleration of object B.

Explanation / Answer

part a )

using energy conservation

Ui + KEi = Uf + KEf

initially KEi = 0

and at the bottom of ramp = Uf = 0

and kinetic energy has rotatinal kinetic energy and translational kinetic energy

mgh = mv^2/2 + Iw^2/2

we know w = v/r

I = 2/5 *mr^2 (for solid sphere I = 2/5 * mr^2)

mgh = mv^2/2 + 1/2 * 2/5 * mr^2 * v^2/r^2

gh = v^2/2 + 1/5 * mv^2

gh = 7v^2/10

v = sqrt(10gh/7)

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