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A rubber ball of mass 0.05 kg is thrown against a wall. It strikes the wall normally with a velocity of 25 m/s and rebounds with the same speed in the opposite direction. Calculate the impulse of the force exerted by the wall on the ball.?
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A rubber ball of mass 0.05 kg is thrown against a wall. It strikes the...
Explanation:
When the rubber ball strikes the wall, it exerts a force on the wall and the wall exerts an equal and opposite force on the ball. This is known as the law of action and reaction.
Formula:
The impulse of a force is defined as the product of the force and the time for which it acts. Mathematically, it is given by the formula:
Impulse = Force x Time
Calculation:
Given,
Mass of the ball, m = 0.05 kg
Initial velocity of the ball, u = 25 m/s
Final velocity of the ball, v = -25 m/s (opposite direction)
The change in velocity of the ball, Δv = v - u = -25 - 25 = -50 m/s
By using the formula of impulse, we can calculate the force exerted by the wall on the ball.
Impulse = Force x Time
Δp = FΔt (where Δp is the change in momentum)
The momentum of the ball before the collision is,
p = m x u = 0.05 x 25 = 1.25 kg m/s
The momentum of the ball after the collision is,
p' = m x v = 0.05 x (-25) = -1.25 kg m/s
The change in momentum of the ball is,
Δp = p' - p = (-1.25) - 1.25 = -2.5 kg m/s
As the collision time is very short, we can assume that the force exerted by the wall on the ball is constant. Therefore, we can write,
Impulse = Force x Time = Δp
Force x Time = -2.5
The time for which the force acts can be calculated by using the formula of time,
Time = distance / velocity
As the ball rebounds with the same speed, the distance covered by the ball is twice the distance between the ball and the wall.
Distance = 2u x t = 2 x 25 x t = 50t
Time = Distance / Velocity = 50t / 25 = 2t
Substituting the value of time in the equation of impulse, we get
Force x 2t = -2.5
Force = -1.25/t
As the force is equal to the rate of change of momentum, the negative sign indicates that the force is in the opposite direction to the velocity of the ball.
Therefore, the impulse of the force exerted by the wall on the ball is -2.5 Ns.
Conclusion:
The impulse of the force exerted by the wall on the ball is -2.5 Ns. When the ball strikes the wall, it experiences a force in the opposite direction, which causes a change in its momentum. The time for which the force acts can be calculated by using the formula of time. This helps in calculating the force exerted by the wall on the ball.
When the rubber ball strikes the wall, it exerts a force on the wall and the wall exerts an equal and opposite force on the ball. This is known as the law of action and reaction.
Formula:
The impulse of a force is defined as the product of the force and the time for which it acts. Mathematically, it is given by the formula:
Impulse = Force x Time
Calculation:
Given,
Mass of the ball, m = 0.05 kg
Initial velocity of the ball, u = 25 m/s
Final velocity of the ball, v = -25 m/s (opposite direction)
The change in velocity of the ball, Δv = v - u = -25 - 25 = -50 m/s
By using the formula of impulse, we can calculate the force exerted by the wall on the ball.
Impulse = Force x Time
Δp = FΔt (where Δp is the change in momentum)
The momentum of the ball before the collision is,
p = m x u = 0.05 x 25 = 1.25 kg m/s
The momentum of the ball after the collision is,
p' = m x v = 0.05 x (-25) = -1.25 kg m/s
The change in momentum of the ball is,
Δp = p' - p = (-1.25) - 1.25 = -2.5 kg m/s
As the collision time is very short, we can assume that the force exerted by the wall on the ball is constant. Therefore, we can write,
Impulse = Force x Time = Δp
Force x Time = -2.5
The time for which the force acts can be calculated by using the formula of time,
Time = distance / velocity
As the ball rebounds with the same speed, the distance covered by the ball is twice the distance between the ball and the wall.
Distance = 2u x t = 2 x 25 x t = 50t
Time = Distance / Velocity = 50t / 25 = 2t
Substituting the value of time in the equation of impulse, we get
Force x 2t = -2.5
Force = -1.25/t
As the force is equal to the rate of change of momentum, the negative sign indicates that the force is in the opposite direction to the velocity of the ball.
Therefore, the impulse of the force exerted by the wall on the ball is -2.5 Ns.
Conclusion:
The impulse of the force exerted by the wall on the ball is -2.5 Ns. When the ball strikes the wall, it experiences a force in the opposite direction, which causes a change in its momentum. The time for which the force acts can be calculated by using the formula of time. This helps in calculating the force exerted by the wall on the ball.
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A rubber ball of mass 0.05 kg is thrown against a wall. It strikes the wall normally with a velocity of 25 m/s and rebounds with the same speed in the opposite direction. Calculate the impulse of the force exerted by the wall on the ball.?
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A rubber ball of mass 0.05 kg is thrown against a wall. It strikes the wall normally with a velocity of 25 m/s and rebounds with the same speed in the opposite direction. Calculate the impulse of the force exerted by the wall on the ball.? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about A rubber ball of mass 0.05 kg is thrown against a wall. It strikes the wall normally with a velocity of 25 m/s and rebounds with the same speed in the opposite direction. Calculate the impulse of the force exerted by the wall on the ball.? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rubber ball of mass 0.05 kg is thrown against a wall. It strikes the wall normally with a velocity of 25 m/s and rebounds with the same speed in the opposite direction. Calculate the impulse of the force exerted by the wall on the ball.?.
A rubber ball of mass 0.05 kg is thrown against a wall. It strikes the wall normally with a velocity of 25 m/s and rebounds with the same speed in the opposite direction. Calculate the impulse of the force exerted by the wall on the ball.? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about A rubber ball of mass 0.05 kg is thrown against a wall. It strikes the wall normally with a velocity of 25 m/s and rebounds with the same speed in the opposite direction. Calculate the impulse of the force exerted by the wall on the ball.? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rubber ball of mass 0.05 kg is thrown against a wall. It strikes the wall normally with a velocity of 25 m/s and rebounds with the same speed in the opposite direction. Calculate the impulse of the force exerted by the wall on the ball.?.
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