91影视

Mass of the ball is$m=0.2\text{kg}$.

Speed is$v_{i,y}=8\text{m}/\text{s}$.

Upward speed is$v_{f,y}=7\text{m}/\text{s}$.

Contact time with the floor is,$螖F=0.5\text{ms(}0.5脳{10}^{-3}\text{s)}$.

Acceleration due to gravity is $g=9.8\text{m}/{\text{s}}^2$.

The change in momentum is given by:

$$\begin{gathered} \mathit{螖}\mathit{P}\mathbf{=}{\mathit{P}}_{\mathbf{f}}\mathbf{-}{\mathit{P}}_{\mathbf{i}} \\ \mathit{螖}\mathit{P}\mathbf{=}\mathit{m}{\mathit{v}}_{\mathbf{f}\mathbf{,}\mathbf{y}}\mathbf{-}\mathit{m}{\mathit{v}}_{\mathbf{i}\mathbf{,}\mathbf{y}} \\ \mathit{螖}\mathit{P}\mathbf{=}\mathit{m}\left(v_{f,y}-v_{i,y}\right) \end{gathered}$$

The average force exerted on the ball can be calculated by dividing the change in momentum by the time interval.

${\mathit{F}}_{\mathbf{a}\mathbf{v}\mathbf{g}}\mathbf{=}\frac{\mathbf{螖}\mathbf{P}}{\mathbf{螖}\mathbf{F}}$

(a)

Substitute the values to the first formula to find for the change in momentum.

$\begin{array}{rcl}螖P& =& m\left(v_{f,y}-v_{i,y}\right)\\ & =& (0.2kg)(-7\frac{m}{\sec }-8\frac{m}{\sec })\\ & =& 3\text{kg.m}/\text{s}\end{array}$

Use the second formula and substitute the values.

$$\begin{gathered} F_{avg}=\frac{螖P}{螖F} \\ {F}_{avg}=\frac{3\text{kg}路\text{m}/\text{s}}{5脳{10}^{-3}\text{s}} \\ {F}_{avg}=6000\text{N} \end{gathered}$$

Therefore, the average force is $F_{avg}=6000\text{N}$.

(b)

The magnitude of the gravitational force that the Earth exerts on the ball.

Ball's mass:$m=0.2kg$

Gravity strength on earth:$g=9.8\text{m}/{\text{s}}^2$

The gravitational force$F_{grav}=mg$

Substitute the values I the above formula.

$$\begin{gathered} F_{grav}=0.2脳9.8 \\ {F}_{grav}=2\text{N} \end{gathered}$$

Therefore, the gravitational force is 2 N.

(c)

From part (a) and (b):

$\begin{array}{rcl}\frac{\left|{\stackrel{鈫�}{F}}_{\text{floor}}\right|}{\left|{\stackrel{鈫�}{F}}_{\text{grav}}\right|}& =& \frac{6002}{2}\\ & =& 3000\end{array}$

So, the average magnitude of the force exerted on the ball by the floor is 3000 times the magnitude of the force exerted on the ball by the Earth.