Q. 63

Expert-verifiedFound in: Page 290

Book edition
4th

Author(s)
Randall D. Knight

Pages
1240 pages

ISBN
9780133942651

A 20 g ball is fired horizontally with speed v_{0} 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 v_{0}?

The speed v_{0} of the ball was 7.9 m/s.

Mass of the ball moving with speed v_{0 }= 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.

As per the formula for final velocity after elastic collision, final velocity of the large ball v_{f.2} :

(v_{i.1} is the initial velocity of the smaller ball)

It is given that v_{i.1} = v_{0}

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

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