Physics,urgent?

Question

A solid sphere of uniform density (mass = 4.40 kg) starts from rest and rolls down a ramp (H = 1.19 m, θ = 17.1 deg). Find the speed of the sphere's CM when it reaches the bottom of the ramp.

Answer 1

Solid sphere mass m = 4.40 kg

Height of ramp H = 1.19 m

Inclined angle θ = 17.1º

Solid sphere starts from rest.

So initial velocity v_i = 0

Speed of the sphere when it reaches the bottom of the ramp v_f = ?

From above figure

AC = s = solid sphere traveling distance

BC = H = Height of ramp H = 1.19

From ABC right angled triangle

AC = BC/sin17.1

s = 1.19/0.294

s = 4.047 m

v_f - v_i = 2as

a =  acceleration due to gravity in ramp direction= gsinθ

v_f - v_i = 2gsinθs

v_f - 0 = 2(9.8)(sin17.1)(4.047)

v_f = 23.32 m/s

Speed of the sphere when it reaches the bottom of the ramp is 23.32 m/s