Question

A solid sphere of mass 2.50 kg and radius 0.120 m is at rest at the top of a ramp inclined 15.0°. It rolls to the bottom without slipping. The upper end of the ramp is 1.20 m higher than the lower end. Find the sphere’s total kinetic energy when it reaches the bottom.

Answer 1

Answer:

KE= 30 J

Explanation:

Given that

m= 2.5 kg

r= 0.12 m

θ = 15°

h= 1.2 m

As we know that solid sphere rolls without slipping.It means that

v= ω r

v=Linear velocity

ω=Angular speed

r=radius

The total kinetic energy KE

$KE=\dfrac{1}{2}mv^2+\dfrac{1}{2}I\omega^2$

Moment of inertia of solid sphere I

$I=\dfrac{2}{5}mr^2$

Now from energy conservation

Energy at top = Energy at bottom

The potential energy at top = m g h

Potential energy at bottom = 0

Kinetic energy at top = 0

Kinetic energy at bottom = KE

m g h + 0 = 0 + KE

KE= 2.5 x 10 x 1.2                 ( take g =10 m/s²)

KE= 30 J