Question

1. to impart the greatest momentum to an object, should you exert the largest force possible, extend that force for as long a time as possible, or both? explain.

Explanation:

According to the impulse - momentum theorem, the impulse \(J\) (which is equal to the change in momentum \(\Delta p\)) is given by \(J = F\Delta t\), where \(F\) is the force and \(\Delta t\) is the time interval over which the force acts. To maximize \(J\) (and thus \(\Delta p\)), we need to maximize both \(F\) and \(\Delta t\) because if we only maximize one (say \(F\)) while keeping the other (\(\Delta t\)) small, the product \(F\Delta t\) will not be as large as when both are maximized. For example, if \(F_1 = 10\space N\) and \(\Delta t_1=1\space s\), \(J_1 = 10\times1= 10\space N\cdot s\). If \(F_2 = 5\space N\) and \(\Delta t_2 = 3\space s\), \(J_2=5\times3 = 15\space N\cdot s\). But if \(F_3=8\space N\) and \(\Delta t_3 = 4\space s\), \(J_3=8\times4=32\space N\cdot s\) (a larger value than the previous two cases where only one quantity was relatively large).

Answer:

Both. Because according to the impulse - momentum theorem \(J=\Delta p = F\Delta t\), maximizing both the force \(F\) and the time interval \(\Delta t\) over which the force acts will maximize the impulse \(J\) (and thus the change in momentum \(\Delta p\)) imparted to the object.