Question

A 4-lb ball B is traveling around in a circle of radius r1 = 3 ft with a speed (vB)1 = 6 ft/s. If the attached cord is pulled down through the hole with a constant speed vr = 2 ft/s, determine how much time is required for the ball to reach a speed of 12 ft/s. How far r2 is the ball from the hole when this occurs? Neglect friction and the size of the ball.

Answer 1

t= 0.75 s

Step-by-step explanation:

Here given that there is no any external torque that is why it angular momentum will be conserve.

Initial angular momentum= m V₁ r₁

Final angular momentum= m V₂ r₂

So

m V₁ r₁ = m V₂ r₂

Now by putting the values

m V₁ r₁ = m V₂ r₂

V₁ r₁ = V₂ r₂

6 x 3 = 12 x r₂

r₂ = 1.5 ft

So the time t

t = r₂ / Vr

t= 1.5 / 2

t= 0.75 s