What magnitude impulse will give a 2.0kg object a momentum change of magnitude +50 kgm/s?
The correct answer and explanation is :
Answer:
The impulse ( J ) is given by the equation:
[
J = \Delta p
]
where ( \Delta p ) is the change in momentum. Given that the momentum change is ( +50 ) kg·m/s, we find:
[
J = 50 \text{ kg·m/s}
]
Thus, the magnitude of the impulse required is 50 N·s.
Explanation:
Impulse is defined as the product of force and the time interval during which the force acts:
[
J = F \cdot t
]
Alternatively, impulse can be understood as the change in momentum:
[
J = \Delta p = m \Delta v
]
where:
- ( m ) is the mass of the object,
- ( \Delta v ) is the change in velocity,
- ( \Delta p ) is the change in momentum.
In this case, the object has a mass of ( m = 2.0 ) kg, and we are given that the momentum change is ( \Delta p = +50 ) kg·m/s. Since impulse is equal to the change in momentum, the impulse magnitude is directly 50 N·s.
This means that any force ( F ) applied over a time interval ( t ) that results in an impulse of 50 N·s will cause this change in momentum. The force could be large over a short time or smaller over a longer time.
For example:
- A force of 50 N acting for 1 second:
[
J = 50 N \times 1 s = 50 N·s
] - A force of 25 N acting for 2 seconds:
[
J = 25 N \times 2 s = 50 N·s
]
Both scenarios would produce the required impulse.
Thus, an impulse of 50 N·s will always result in a +50 kg·m/s change in momentum, regardless of how it is applied.
