A ball of mass 0.5 kg moving with a velocity of 2 m/sec strikes a wall normally and bounces back with the same speed. If the time of contact between the ball and the wall is one millisecond, the average force exerted by the wall on the ball is
Question
A ball of mass 0.5 kg moving with a velocity of 2 m/sec strikes a wall normally and bounces back with the same speed. If the time of contact between the ball and the wall is one millisecond, the average force exerted by the wall on the ball is
Solution 1
Sure, let's solve the problem step by step.
Step 1: Given information
- Mass of the ball (m) = 0.5 kg
- Initial velocity of the ball (u) = 2 m/s
- Final velocity of the ball (v) = -2 m/s (since it bounces back with the same speed)
- Time of contact (t) = 1 millisecond = 0.001 seconds
Step 2: Calculate the change in velocity The change in velocity (Δv) can be calculated using the formula: Δv = v - u
Substituting the values: Δv = (-2 m/s) - (2 m/s) Δv = -4 m/s
Step 3: Calculate the acceleration Acceleration (a) can be calculated using the formula: a = Δv / t
Substituting the values: a = (-4 m/s) / (0.001 s) a = -4000 m/s^2
Step 4: Calculate the average force The average force (F) exerted by the wall on the ball can be calculated using Newton's second law of motion: F = m * a
Substituting the values: F = (0.5 kg) * (-4000 m/s^2) F = -2000 N
Therefore, the average force exerted by the wall on the ball is -2000 Newtons.
Solution 2
Sure, let's solve the problem step by step.
Step 1: Given information
- Mass of the ball (m) = 0.5 kg
- Initial velocity of the ball (u) = 2 m/s
- Final velocity of the ball (v) = -2 m/s (since it bounces back with the same speed)
- Time of contact (t) = 1 millisecond = 0.001 seconds
Step 2: Calculate the change in velocity The change in velocity (Δv) can be calculated using the formula: Δv = v - u
Substituting the values: Δv = (-2 m/s) - (2 m/s) Δv = -4 m/s
Step 3: Calculate the acceleration Acceleration (a) can be calculated using the formula: a = Δv / t
Substituting the values: a = (-4 m/s) / (0.001 s) a = -4000 m/s^2
Step 4: Calculate the average force The average force (F) exerted by the wall on the ball can be calculated using Newton's second law of motion: F = m * a
Substituting the values: F = (0.5 kg) * (-4000 m/s^2) F = -2000 N
Therefore, the average force exerted by the wall on the ball is -2000 Newtons.
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