1
$\begingroup$

The problem is as follows:

A ball of $1\,kg$ in mass is thrown with a speed of $-10\vec{j}\,\frac{m}{s}$ from a height of $15\,m$ to a horizontal floor. Find the modulus of the average force in $N$ that the ball receives from the floor during the impact with the ground which lasts $0.1\,s$ and dissipates $150\,J$. (You may use the value of gravity $g=10\,\frac{m}{s^2}$.

The alternatives given in my book are as follows:

$\begin{array}{ll} 1.&290\,N\\ 2.&300\,N\\ 3.&310\,N\\ 4.&320\,N\\ 5.&330\,N\\ \end{array}$

This problem has left me go in circles as I don't know exactly how should I treat or use the information to obtain the average force?. I'm assuming that there is a conservation of momentum but as I mentioned I don't know what to do?. Can somebody help me here?.

Supposedly the answer is $310\,N$. But the only thing that comes to my mind to find the average force is:

$\overline{\vec{F}}=m\frac{\Delta v}{\Delta t}$

Since there will be a conservation of mechanical energy at the impact it can be found using this analysis. But again I'm not sure how to get to the answer of $310\,N$. Can somebody help me here?.

$\endgroup$
  • $\begingroup$ So all you need is calculate $\Delta v=v_1-v_0$ where $\frac{mv_0^2}{2}=\frac{m(-10j\frac{m}{s})^2}{2}+mgh$ and $\frac{mv_0^2}{2}-150J=\frac{mv_1^2}{2}$ and $v_1,v_0$ have different signs. $|v_1|=10\frac{m}{s}$, ... $\endgroup$ – Alexey Burdin Dec 2 '19 at 11:24
1
$\begingroup$

Velocity before impact = $-20j$ m/s

Energy before impact = $0.5*(1)(20)^2 = 200$ J

Energy after impact = $50$ J

Velocity after impact = $10j $ m/s

Average Net Force = $\frac{10(1)- (-20)(1) }{0.1} = 300j $ N

Average Force of floor = Average Net force - Average Body Force

Hence average force of floor = $300 - (-10) = 310 N$

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.