Answer:
a. v = 7.5 m/s
b. w = 50 rad/s
c. 46.667 rad
Explanation:
Using the equations of energy in the motion to determine the speed, angular speed and the angle
Ep = m * g * h
, ⇒ h = 7m * sin 35
Ep = 1.5kg * 9.8m/s^2 * 7 m * sin 35
Ep= 59.02 J
Ek = ½ * m * v^2 , ⇒Ek = ½ *1.5 kg* v^2
Ew = ½ * I * ω^2 For a solid sphere I = 2/5 * m * r^2 ⇒ I = 2/5 * 1.5 * 0.15^2 = 0.0135
ω = v/0.15, ω^2 = v^2/0.0225
Ek = ½ * 0.0135 * v^2/0.0225
Ek = 0.3 * v^2
Total E = 0.75 * v^2 + 0.3 * v^2
E = 1.05 * v^2
59.02 J = 1.05 * v^2
v = √56.2 = 7.5 m/s
ω = 7.5 / 0.15 = 50 rad/s
C= 2 * π * 0.15 = 0.3 * π
θ =[ 7 /(0.3 * π) ] * (2 π)
θ= 46.667 rad