Answer to Question #224506 in Mechanics | Relativity for Adib

Question

Sturridge scores from a free kick by kicking a stationary football with a force of 40N. If the ball has a mass of 0.4kg and his foot is in contact with the ball for 0.1s calculate:

1) The change in momentum of the ball (its impulse).

2) The speed the ball moves away with

Answer 1

Explanations & Calculations

• Change in momentum, force, time & impulse is involved in this question. They interconnected according to the equation

$\qquad\qquad \begin{aligned} \small F&=\small \frac{\Delta p}{\Delta t}=\frac{mv-mu}{\Delta t}=\frac{m(v-u)}{\Delta t} \end{aligned}$

• When there is an unbalanced force acting on an object its momentum is changed.

1)

• Rearranging the equation yeilds,

$\qquad\qquad \begin{aligned} \small F\times\Delta t &=\small m(v-u) \end{aligned}$ which describes the impuls or the change in momentum.

• Then the impulse will be,

$\qquad\qquad \begin{aligned} \small I&=\small F\times \Delta t\\ &=\small 40\,N\times0.1\,s\\ &=\small \bold{4\,Ns} \end{aligned}$

2)

• This impulse causes the momentum change in the ball & since it starts from rest, its initial momentum is zero. Therefore, $\small u = 0\, ms^{-1}$ in the above equation which eases getting a value for the final velocity: $\small v$. Then,

$\qquad\qquad \begin{aligned} \small 4\,Ns&=\small m(v-0)\\ \small v&=\small \frac{4}{m}=\frac{4\,kgms^{-2}.s}{0.4\,kg}\\ &=\small \bold{10\,ms^{-1}} \end{aligned}$

• This is the speed just after the ball loses contact with the players foot which causes it to move away.