a 4.0 kg object moving at 6.0 m/s encounters a 20 n resistive force over a duration of 0.20s. the momentum change (magnitude only) experienced by this object is approximately ns.
The Correct Answer and Explanation is :
The correct answer is: 4.0 kg·m/s
To find the momentum change experienced by the object, we start by calculating the force acting on it, which is given as a resistive force of 20 N. According to Newton’s second law, the change in momentum (( \Delta p )) can also be defined in terms of the net force and the time over which the force acts:
[
\Delta p = F \cdot t
]
Where:
- ( F ) is the net force (in this case, the resistive force of 20 N),
- ( t ) is the time duration (0.20 s).
Step 1: Calculate the Change in Momentum
Using the formula:
[
\Delta p = 20 \, \text{N} \cdot 0.20 \, \text{s} = 4.0 \, \text{N} \cdot \text{s}
]
Since the resistive force is acting against the direction of the object’s motion, the change in momentum is in the opposite direction to the object’s initial momentum. Therefore, the magnitude of the momentum change is 4.0 kg·m/s.
Step 2: Understand the Context of Momentum Change
Momentum is defined as the product of an object’s mass (( m )) and its velocity (( v )):
[
p = m \cdot v
]
In this case, the mass of the object is 4.0 kg, and its initial velocity is 6.0 m/s, resulting in an initial momentum:
[
p_{initial} = 4.0 \, \text{kg} \cdot 6.0 \, \text{m/s} = 24.0 \, \text{kg} \cdot \text{m/s}
]
After the force acts on the object, the final momentum can be calculated by subtracting the change in momentum:
[
p_{final} = p_{initial} – \Delta p = 24.0 \, \text{kg} \cdot \text{m/s} – 4.0 \, \text{kg} \cdot \text{m/s} = 20.0 \, \text{kg} \cdot \text{m/s}
]
Conclusion
The magnitude of the momentum change experienced by the object is approximately 4.0 kg·m/s. This scenario illustrates the principle of momentum and how external forces can alter an object’s motion over time, demonstrating fundamental concepts in dynamics and the conservation of momentum.