JBug asked in Science & MathematicsPhysics · 9 years ago

# A 2.0-kg solid cylinder and 2.5-kg solid sphere are released from rest at the top of a ramp and allowed to...?

A 2.0-kg solid cylinder and 2.5-kg solid sphere are released from rest at the top of a ramp and allowed to roll without slipping. The ramp is 0.79 m high and 5.0 m long.

Which object do you expect to have the greater speed at the bottom of the ramp?

cylinder or sphere?

Verify your answer to part A by calculating the speed of the cylinder and of the sphere when they reach the bottom of the ramp.

Relevance
• 9 years ago

For the cylinder

As there is no slipping,

The kinetic energy due to rotation is half of the linear kinetic energy.

M g h = 0.5 M U² + 0.5 (0.5 M R²) U² / R²

g h = 0.5* U² + 0.5*0.5 U²

9.8* 0.79 = 0.5* U² + 0.5*0.5 U²

Uc = 3.21 m/s

---------------------------------------------------------

For the sphere

As there is no slipping,

The kinetic energy due to rotation is two fifth of the linear kinetic energy.

M g h = 0.5 M U² + 0.5 (0.4 M R²) U² / R²

g h = 0.5* U² + 0.5*0.4 U²

9.8* 0.79 = 0.5* U² + 0.5*0.4 U²

Us = 3.33 m/s

======================================

Since Us > Uc sphere reaches first at the bottom of the ramp .

======================================