# How do I find the modulus of the average force a sphere gets from collisioning with the ground?

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?.

• 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. $|v_1|=10\frac{m}{s}$, ... – Alexey Burdin Dec 2 '19 at 11:24

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 = $$300 - (-10) = 310 N$$