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A 1.0 kg ball drops vertically onto the floor with a speed of 25 m/s. It rebounds with an initial speed of 10 m/s. The impulse action on the ball during contact will be
- a)15 N - s
- b)25 N - s
- c)35 N - s
- d)45 N - s
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A 1.0 kg ball drops vertically onto the floor with a speed of 25 m/s. ...
Impulse = change in momentum
= mv2 - mv1
= 1 (10) - 1 (-25) = 35 N - s
Most Upvoted Answer
A 1.0 kg ball drops vertically onto the floor with a speed of 25 m/s. ...
Impulse and Momentum
To understand the solution to this problem, we need to have a clear understanding of impulse and momentum.
- Impulse: Impulse is the product of the force applied to an object and the time interval over which the force is applied. It can be calculated using the equation:
Impulse = Force × Time
- Momentum: Momentum is the product of an object's mass and velocity. It can be calculated using the equation:
Momentum = Mass × Velocity
- Conservation of Momentum: According to the law of conservation of momentum, the total momentum of a system remains constant if no external forces act on it.
Given Parameters
- Mass of the ball (m) = 1.0 kg
- Initial velocity of the ball (u) = 25 m/s
- Final velocity of the ball (v) = -10 m/s (since it rebounds in the opposite direction)
Calculating the Change in Momentum
The change in momentum of the ball can be calculated using the equation:
Change in Momentum = Final Momentum - Initial Momentum
- Initial Momentum = Mass × Initial Velocity = m × u
- Final Momentum = Mass × Final Velocity = m × v
Substituting the given values:
- Initial Momentum = 1.0 kg × 25 m/s = 25 kg·m/s
- Final Momentum = 1.0 kg × (-10 m/s) = -10 kg·m/s
- Change in Momentum = (-10 kg·m/s) - (25 kg·m/s)
Change in Momentum = -35 kg·m/s
Calculating the Impulse
The impulse on the ball during contact can be calculated by equating it to the change in momentum. Therefore:
Impulse = Change in Momentum
Substituting the value of the change in momentum:
Impulse = -35 kg·m/s
Since impulse is a vector quantity, we consider its magnitude. Therefore, the magnitude of the impulse is 35 N·s.
Answer Explanation
The correct answer is option C) 35 N·s. The impulse acting on the ball during contact is 35 N·s.
To understand the solution to this problem, we need to have a clear understanding of impulse and momentum.
- Impulse: Impulse is the product of the force applied to an object and the time interval over which the force is applied. It can be calculated using the equation:
Impulse = Force × Time
- Momentum: Momentum is the product of an object's mass and velocity. It can be calculated using the equation:
Momentum = Mass × Velocity
- Conservation of Momentum: According to the law of conservation of momentum, the total momentum of a system remains constant if no external forces act on it.
Given Parameters
- Mass of the ball (m) = 1.0 kg
- Initial velocity of the ball (u) = 25 m/s
- Final velocity of the ball (v) = -10 m/s (since it rebounds in the opposite direction)
Calculating the Change in Momentum
The change in momentum of the ball can be calculated using the equation:
Change in Momentum = Final Momentum - Initial Momentum
- Initial Momentum = Mass × Initial Velocity = m × u
- Final Momentum = Mass × Final Velocity = m × v
Substituting the given values:
- Initial Momentum = 1.0 kg × 25 m/s = 25 kg·m/s
- Final Momentum = 1.0 kg × (-10 m/s) = -10 kg·m/s
- Change in Momentum = (-10 kg·m/s) - (25 kg·m/s)
Change in Momentum = -35 kg·m/s
Calculating the Impulse
The impulse on the ball during contact can be calculated by equating it to the change in momentum. Therefore:
Impulse = Change in Momentum
Substituting the value of the change in momentum:
Impulse = -35 kg·m/s
Since impulse is a vector quantity, we consider its magnitude. Therefore, the magnitude of the impulse is 35 N·s.
Answer Explanation
The correct answer is option C) 35 N·s. The impulse acting on the ball during contact is 35 N·s.
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