Question

A football of mass 0.5kg moving with a velocity of 10m/s hits a pole and bounces back with a velocity of 5m/s . Find the change in momentum and the force exerted on the ball when the force acts for 0.02s.

Answer 1

Explanation:

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Answer 2

Answer

• Momentum of ball is changed by 7.5 kg m/s.
• A force of 375 N is exerted on the ball.

Explanation

Given:-

• Mass of football, m = 0.5 kg
• Initial velocity of football, u = 10 m/s
• Ball hits a pole and bounces back with certain velocity
• Final velocity of football, v = -5 m/s   [Negative because ball bounces back]
• time for which force acts, t = 0.02 s

To find:-

• Change in momentum of the ball, Δp =?
• Force exerted on the ball, F =?

Formulae required:-

• Formula for Change in momentum

        Δp = (Final p) - (Initial p) = m v - m u

• Formula for force

        F = Δp / t

Where, p is momentum, m is mass, u is initial velocity, v is final velocity, t is time.

Solution:-

Calculating the change in momentum of ball

→ Δp = (Final p) - (Initial p) = m v - m u

→ Δp = m v - m u

→ Δp = m ( v - u )

→ Δ p = 0.5 ( -5 -10 ) = -7.5 kg m/s

Therefore,

• The magnitude of change in momentum of the ball is 7.5 kg m/s.

Now, Calculating force exerted on the ball

→ F = Δp / t

→ F = (-7.5) / 0.02

→ F = -375 N

Therefore,

• A force of magnitude 375 N is exerted on the ball by the wall.