A rubber ball of mass 0.4 kg hits the ground at an angle of 30 degree with the ground and rebounds at the same angle without any change in speed. If the speed of ball is 1m/s and the period of contact between the ball and floor is 0.4s , find the average force exerted by the ball on the ground?

Question

Answer

Problem:

A rubber ball of mass 0.4 kg hits the ground at an angle of 30 degree with the ground and rebounds at the same angle without any change in speed. If the speed of ball is 1m/s and the period of contact between the ball and floor is 0.4s , find the average force exerted by the ball on the ground?

Solution:

Given, mass of the ball m = 0.4 kg, angle of incidence θ = 30°, angle of reflection φ = 30°, speed of the ball v = 1 m/s, time of contact between ball and floor t = 0.4 s.

Step 1: Calculate the initial and final velocities of the ball

Initial velocity of the ball, u = v (as there is no vertical component of velocity)

Final velocity of the ball, w = v (as there is no change in speed)

Step 2: Calculate the vertical component of velocity

Vertical component of velocity, Vy = usinθ = vsinθ = 1 × sin30° = 0.5 m/s

Step 3: Calculate the time taken by the ball to reach maximum height

Time taken by the ball to reach maximum height, t1 = Vy/g where g is acceleration due to gravity (9.8 m/s²)

t1 = 0.5/9.8 = 0.051 s

Step 4: Calculate the maximum height reached by the ball

Maximum height reached by the ball, H = Vyt1 - 0.5gt1²

H = (0.5)(0.5)(0.051) - 0.5(9.8)(0.051)² = 0.013 m

Step 5: Calculate the average force exerted by the ball on the ground

The average force exerted by the ball on the ground is given by the formula F = (mΔv)/t where Δv is the change in velocity of the ball during the time of contact with the ground.

Δv = 2w (as the ball rebounds without any change in speed)

Δv = 2(0.5) = 1 m/s

Therefore, F = (0.4 × 1)/0.4 = 1 N

Step 6: Conclusion

The average force exerted by the ball on the ground is 1 N.

Answer

1N

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