Question

A hoop and a disk, both of 0.40- m radius and 3.0- kg mass, are released from the top of an inclined plane 2.7 m high and 9.0 m long. What is the speed of each when it reaches the bottom? Assume that they both roll without slipping. What is the speed of the hoop?

What is the speed of the disk?

Answer 1

Here,

let the speed of the hoop is v1

Using conservation of energy

initial mechanical energy = final mechanical energy

0.50 * m * v^2 + 0.50 I * w^2 = mgh

0.50 *m * v^2 + 0.50 * m * r^2 * (v/r)^2 = mgh

1 * v^2 = 9.8 * 2.7

v = 5.14 m/s

the speed of the hoop is 5.14 m/s

for the speed of the disk

Using conservation of energy

initial mechanical energy = final mechanical energy

0.50 * m * v^2 + 0.50 I * w^2 = mgh

0.50 *m * v^2 + 0.50 * 0.50 m * r^2 * (v/r)^2 = mgh

0.75 * v^2 = 9.8 * 2.7

v = 5.94 m/s

the speed of the hoop is 5.94 m/s m/s