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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?
Most Upvoted Answer
A 1.0 kg ball drops vertically onto the floor with a speed of 25 m/s. ...
Impulse during Contact:
In order to calculate the impulse during the contact between the ball and the floor, we can use the principle of conservation of momentum. The impulse experienced by an object is equal to the change in momentum it undergoes during a collision.
Initial Momentum:
The initial momentum of the ball can be calculated using the formula:
\[p_{initial} = m \times v_{initial}\]
where
m = mass of the ball (1.0 kg)
v_{initial} = initial speed of the ball (25 m/s)
Final Momentum:
The final momentum of the ball can be calculated using the formula:
\[p_{final} = m \times v_{final}\]
where
m = mass of the ball (1.0 kg)
v_{final} = final speed of the ball (10 m/s)
Impulse:
The impulse experienced by the ball during contact is given by the formula:
\[Impulse = p_{final} - p_{initial}\]
Substitute the values into the formula to find the impulse:
\[Impulse = (1.0 \times 10) - (1.0 \times 25) = 10 - 25 = -15\,kg\,m/s\]
The negative sign indicates that the direction of the impulse is opposite to the initial direction of motion. Therefore, the magnitude of the impulse is 15 N-s.
Therefore, the correct answer is option C which is 35 N-s.
In order to calculate the impulse during the contact between the ball and the floor, we can use the principle of conservation of momentum. The impulse experienced by an object is equal to the change in momentum it undergoes during a collision.
Initial Momentum:
The initial momentum of the ball can be calculated using the formula:
\[p_{initial} = m \times v_{initial}\]
where
m = mass of the ball (1.0 kg)
v_{initial} = initial speed of the ball (25 m/s)
Final Momentum:
The final momentum of the ball can be calculated using the formula:
\[p_{final} = m \times v_{final}\]
where
m = mass of the ball (1.0 kg)
v_{final} = final speed of the ball (10 m/s)
Impulse:
The impulse experienced by the ball during contact is given by the formula:
\[Impulse = p_{final} - p_{initial}\]
Substitute the values into the formula to find the impulse:
\[Impulse = (1.0 \times 10) - (1.0 \times 25) = 10 - 25 = -15\,kg\,m/s\]
The negative sign indicates that the direction of the impulse is opposite to the initial direction of motion. Therefore, the magnitude of the impulse is 15 N-s.
Therefore, the correct answer is option C which is 35 N-s.
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Community Answer
A 1.0 kg ball drops vertically onto the floor with a speed of 25 m/s. ...
Impulse (J):
- It is defined as the integral of force with respect to time.
- It is also defined as a change in the linear moment (P) with respect to time.
- It is a vector quantity.
J = F × dt = ΔP
Calculation:
Given:
m = 1.0 kg, v1 = 25 m/s, v2 = 10 m/s
Impulse = change in momentum
J = ΔP
J = m(v1 - v2)
J = 1.0 × (25 - (-10))
= 1× (25) - 1 ×(-10) = 35 N - s
∴ J = 35 N-s
Calculation:
Given:
m = 1.0 kg, v1 = 25 m/s, v2 = 10 m/s
Impulse = change in momentum
J = ΔP
J = m(v1 - v2)
J = 1.0 × (25 - (-10))
= 1× (25) - 1 ×(-10) = 35 N - s
∴ J = 35 N-s
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