Q. 63

Expert-verified
Found in: Page 290

### Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

Book edition 4th
Author(s) Randall D. Knight
Pages 1240 pages
ISBN 9780133942651

# A 20 g ball is fired horizontally with speed v0 toward a 100 g ball hanging motionless from a 1.0-m-long string. The balls undergo a head-on, perfectly elastic collision, after which the 100 g ball swings out to a maximum angle . What was v0?

The speed v0 of the ball was 7.9 m/s.

See the step by step solution

## Step 1. We need to find out the speed v0 of the ball.

Mass of the ball moving with speed v0 = 20 g

Mass of the motionless ball = 100 g

Length of the string = 1 m

The collision of the ball is an elastic collision which means mechanical energy is conserved.

## Step 2. Calculating the final velocity of the large ball and applying the law of conservation of energy and momentum.

As per the formula for final velocity after elastic collision, final velocity of the large ball vf.2 :

(vi.1 is the initial velocity of the smaller ball)

It is given that vi.1 = v0

Therefore,

When collision occurs, The large ball reaches to a height y as shown in figure.

When large ball reaches the height, its Kinetic energy gets converted into potential energy.

Using Law of conservation of Energy,

Kinetic Energy = Potential Energy

Height, y can be calculated as