Question

Part C: Quantitative Problems when vf is not 0

8. A 7 kg. bowling ball traveling down a lane at 8 m/s hits a wall, and after 0.05 seconds
rebounds at the same speed.

a. Find (delta)v and m(delta)v.

b. With what impact force did the bowling ball hit the wall?

Answer 1

Answer:

(a)

$\triangle v=-8\ m/s\\\triangle mv=-56\ kg.m/s$

(b)

1120 N

Explanation:

Change in velocity, $\triangle v$ is given by subtracting the initial velocity from the final velocity and expressed as $\triangle v= v_f -v_i$

Where v represent the velocity and subscripts f and i represent final and initial respectively. Since the ball finally comes to rest, its final velocity is zero. Substituting 0 for final velocity and the given figure of 8 m/s for initial velocity then the change in velocity is given by

$\triangle v=0-8=-8\ m/s$

To find $m\triangle v$ then we substitute 7 kg for m and -8 m/s for $\triangle v$ therefore $\triangle\ v=7 Kg\times -8 m/s=-56\ Kg.m/s$

(b)

The impact force, F is given as the product of mass and acceleration. Here, acceleration is given by dividing the change in velocity by time ie

$a=\frac {\triangle v}{t}=\frac { v_f -v_i}{t}$

Substituting t with 0.05 s then $a=\frac {\triangle v}{t}=\frac { v_f -v_i}{t}=\frac {-8}{0.05}=-160 m/s^{2}$

Since F=ma then substituting m with 7 Kg we get that F=7*-160=-1120 N

Therefore, the impact force is equivalent to 1120 N