Question

A hollow, spherical shell with mass 3.00 kg rolls without slipping down a 37.0 ∘ slope. Find the acceleration.

Answer 1

Sol::
Given:

Mass(m)= 3 kg
Angle= 37°

We have
F= ma
= (force due to gravity along slope) - (force due to friction)
=>ma = mgsinθ - Ff .....................(1)

Now
Torque = I*α= (Ff)(r)

Iα = (Ff)(r)....................................... (2)

Since the sphere doesn't slip,

[(2/3)*mr²]*(a/r) = (Ff)(r)

Ff = (2/3)*ma................................... [3]

Substituting Ff into [1]

ma = mgsinθ - 2ma/3
a = (3/5)gsinθ
a = (3/5)(9.8)(sin37°)
= 3.538 m/s²
≈ 3.54 m/s²

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