Question

1. a 2 n force acts on a 10 kg mass. if the momentum of the mass changes by 120 kg·m/s, determine the time over which this force acts.

Explanation:

Step1: Recall the impulse - momentum theorem

The impulse - momentum theorem states that the impulse \(J\) acting on an object is equal to the change in momentum \(\Delta p\) of the object. Mathematically, \(J=\Delta p\). Also, impulse \(J\) is defined as the product of force \(F\) and the time interval \(\Delta t\) over which the force acts, i.e., \(J = F\times\Delta t\).

Step2: Rearrange the formula to solve for time

From \(F\times\Delta t=\Delta p\), we can solve for \(\Delta t\) by dividing both sides of the equation by \(F\). So, \(\Delta t=\frac{\Delta p}{F}\).

Step3: Substitute the given values

We are given that \(F = 2\space N\) and \(\Delta p=120\space kg\cdot m/s\). Substituting these values into the formula for \(\Delta t\), we get \(\Delta t=\frac{120}{2}\).

Step4: Calculate the time

\(\frac{120}{2} = 60\space s\).

Answer:

The time over which the force acts is \(60\) seconds.