91Ó°ÊÓ

The mass of each snowball,$\mathrm{m}=0.250\mathrm{kg}$.

The speed of each snowball,$\mathrm{v}=4.00\mathrm{m}/\mathrm{s}$.

The duration of impact,role="math" localid="1661243323595" ${\mathrm{t}}_{\mathrm{d}}=10\mathrm{ms}\left(\frac{1×{10}^{-3}\mathrm{s}}{1\mathrm{ms}}\right)=1.0×{10}^{-2}\mathrm{s}$.

The time for repetition of impact is,${\mathrm{t}}_{\mathrm{d}}=50.0\mathrm{ms}\left(\frac{1×{10}^{-3}\mathrm{s}}{1\mathrm{ms}}\right)=5.00×{10}^{-2}\mathrm{s}$.

The maximum force of impact is, ${\mathrm{F}}_{\max }=200\mathrm{N}$.

The impulse during each impact can be calculated from the graph using the area under the curve. The average force can be calculated using the equation relating impulse and time. To calculate the average force for many impacts, we assume the number of impacts as ‘N’ and solve the equation of average force. Use the formula given as.

$$\begin{gathered} \mathrm{J}=∆\mathrm{P} \\ ∆\mathrm{P}=\mathrm{m}×\left({\mathrm{v}}_2-{\mathrm{v}}_1\right) \\ \mathrm{J}={\mathrm{F}}_{\mathrm{avg}}×\mathrm{t} \end{gathered}$$

The impulse of each impact can be calculated from the area under the F(t) curve.

As it is triangular

$$\begin{gathered} \mathrm{Area}=\frac{1}{2}\mathrm{base}×\mathrm{height} \\ \mathrm{J}=\frac{1}{2}×{\mathrm{t}}_{\mathrm{d}}×{\mathrm{F}}_{\max } \\ =\frac{1}{2}×10×{10}^{-3}\mathrm{s}×200\mathrm{N} \\ =1.00\mathrm{N}·\mathrm{s} \end{gathered}$$

The average force is given by

$$\begin{gathered} {\mathrm{F}}_{\mathrm{avg}}=\frac{\mathrm{J}}{{\mathrm{t}}_{\mathrm{d}}} \\ =\frac{1.00\mathrm{N}·\mathrm{s}}{10×{10}^{-3}\mathrm{s}} \\ =100\mathrm{N} \end{gathered}$$

Let us assume the number of impacts is N . So, the time interval is

$\mathrm{t}=\mathrm{N}×{\mathrm{t}}_{\mathrm{r}}$

And the total impulse is

${\mathrm{J}}_{\mathrm{total}}=\mathrm{N}×1.0\mathrm{N}·\mathrm{s}$

So, the average force for many impacts is

$$\begin{gathered} {\mathrm{F}}_{\mathrm{avg}}=\frac{{\mathrm{J}}_{\mathrm{total}}}{\mathrm{t}} \\ =\frac{\mathrm{N}×1.0\mathrm{N}·\mathrm{s}}{\mathrm{N}×5×{10}^{-2}\mathrm{s}} \\ =20.0\mathrm{N} \end{gathered}$$