Question

A cue strikes a stationary pool ball, with an average force of \[32{\text{ N}}\] over a time of $14{\text{ms}}$. If the ball has mass $0.20{\text{ kg}}$, what speed does it have just after impact?

Answer 1

Hint: In this question, we are given the force applied over a specified time and the mass of the ball. The ball is initially at rest as it says stationary pool ball and we have to find the final speed of the ball after the collision between the ball and the cue stick.

Complete step by step answer:
When two objects collide with each other elastically and if their linear momentum kinetic energy remains conserved before and after the collision, then the collision is called elastic Collision. When two bodies collide elastically, they exchange their velocities. Otherwise, it is called inelastic collisions. Some kinetic energy is always lost in an inelastic collision.

Given, initial velocity $u = 0$, force applied $F = 32{\text{ N}}$, time $t = 14{\text{ ms}}$ and mass $m = 0.20{\text{ kg}}$. According to the definition of impulse, it can be defined as the product of the force and the duration of collision which is in turn equal to the change in the momentum.Therefore,
$F \times t = {p_f} - {p_i}$
Where $p$ is the momentum.
$ \Rightarrow F \times t = mv - mu$
Substituting the values we get
$ \Rightarrow 32 \times 14 \times {10^{ - 3}} = 2 \times {10^{ - 1}}(v - 0)$
Shifting the equation to make velocity the subject of the equation
$ \Rightarrow v = 16 \times 14 \times {10^{ - 2}}$
$ \therefore v = 2.24{\text{ m}}{{\text{s}}^{ - 1}}$

Therefore the velocity of the ball after being stroked by the cue stick is $2.24{\text{ m}}{{\text{s}}^{ - 1}}$.

Note: The combination of the force and collision duration is known as the impulse. The impulse can be calculated by multiplying the net force by the duration of the collision. (Alternatively, the impulse is equal to the area underneath the force vs. time curve for the collision such as those in the previous example). The impulse-momentum theorem states that the impulse applied to an object will be equal to the change in its momentum.