Question

A cricket ball of mass 150g is moving with a velocity of 25m/s and is hit by a bat, so that the ball is turned back with a velocity of 20m/s. The force of the blow acts for 0.01s on the ball. Find the average force exerted by the bat on the ball.

Answer 1

Answer :

Mass of ball = 150g = 0.15kg

Initial velocity = 25m/s

Final velocity = -20m/s

[Negative sign shows opposite direction.]

Time interval = 0.01s

We have to find average force exerted by the bat on ball$.$

◈ Newton's second law of motion :

As per this law, Force is defined as the rate of change of linear momentum.

Momentum is defined as the product of mass and velocity.

Mathematically,

• F = m(v - u) / t

◕ F denotes force

◕ m denotes mass

◕ v denotes final velocity

◕ u denotes initial velocity

◕ t denotes time

Let's calculate ☃

➝ F = m(v - u) / t

➝ F = 0.15(-20-25) / 0.01

➝ F = 0.15(-45) / 0.01

➝ F = -675N

Average force |F| = 675 N

Answer 2

Given ,

Mass of ball (m) = 150 g or 0.15 kg

Initial velocity (u) = 25 m/s

Final velocity (v) = -20 m/s

Time (t) = 0.01 sec

As we know that ,

The Newton's second law of motion states that the rate of change of momentum is directly proportional to the force applied

Mathematically ,

$\sf \mapsto F \propto \frac{P}{t} \\ \\ \sf \mapsto F = \frac{Δp}{t} \\ \\ F = \frac{m(v - u)}{t}$

Thus ,

F = 0.15(-20 - 25)/0.01

F = 15 × (-45)

F = -675 N

Therefore ,

• The average force exerted by the bat on the ball is 675 N