Question

A solid circular plate has a mass of 0.25 kg and a radius of a 0.30 m. It starts rolling from rest at the top of a hill 10 m long and inclined at 30 degrees to the horizontal. What will the speed of the plate be at the bottom of the hill if it rolls without slipping? Think of the plate as a short solid cylinder.

A 2.7 m/s

B 6.9 m/s

C 8.1 m/s

D 3.3 m/s

E 10.4 m/s

Answer 1

Gravitational acceleration = g = 9.81 m/s²

Mass of the plate = M = 0.25 kg

Radius of the plate = R = 0.3 m

Moment of inertia of the plate = I = MR²/2

Length of the incline = L = 10 m

Angle of incline = = 30^o

Height lost by the plate when it reaches the bottom = H

H = LSin

H = (10)Sin(30)

H = 5 m

Speed of the plate at the bottom = V

Angular speed of the plate at the bottom = = V/R

The initial potential energy of the plate is converted into the kinetic energy of the plate.

V = 8.1 m/s

Speed of the plate at the bottom of the hill if it rolls without slipping = 8.1 m/s