1.A 1.5 kg mass rests atop a spring with spring constant 500 N/m. The spring is

Question

1.A 1.5 kg mass rests atop a spring with spring constant 500 N/m. The spring is compressed a distance 25 cm and released. to what height wil the ball ascend?

2. Bill who weighs 280 pounds is rollerblading 6.0 m/s in a straight line and catches a 1.0 pound ball thrown back to him by his friend Jill who is skating in front of Bill. If the catch reduces Bill's speed to 5.9 m/s, how fast was the ball moving just before Bill caught it?

3.A string is wrapped around a pulley with a radius of 2.0 cm. The pulley is initially at rest. A constant force of 50 N is applied to the string, causing the pulley to rotate and the string to unwind. If the string unwinds 1.2 m in 4.9 s, what is the moment of inertia of the pulley?

Explanation / Answer

1. Using energy conservation,

kx^2 / 2 = mgh

500 (0.25^2) /2 = 1.5 x 9.81 x h

h = 1.06 m

2. using momentum conservation,

280 x 6 + 1 x v = (280 +1) x 5.9

v = - 22.1 m/s

Speed of ball = 22.1 m/s

3. 1.2 m in 4.9s

using h = ut + at^2 /2

1.2 = 0 + a(4.9^2)/2

a = 0.10 m/s^2

torque = r x F = I x alpha

0.02 x 50 = I x (0.10 / 0.02)

I = 0.2 kg m^2

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