Question

Part B: Quantitative

Problems when Vf = 0

4. A 7 kg. bowling ball traveling down a test track at 8 m/s hits a pile of
dirt, and comes to a halt after 0.01 seconds.

a. Find Av and mav.

b. With what impact force did the bowling ball hit the pile of dirt?

Answer 1

Answer:

(a)

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

(b)

5600 N

Explanation:

Change in velocity, $\triangle v$ is expressed as

$\triangle v= v_f -v_i$

Where v represent the velocity and subscripts f and i represent final and initial respectively. Given that the ball finally comes to rest, its final velocity is taken as 0. 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 the change in momentum, $m\triangle v$ 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 equivalent to ma where m is the mass of the ball and a is the 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 $a=\frac {\triangle v}{t}=\frac { v_f -v_i}{t}=\frac {-8}{0.01}=-800 m/s^{2}$

Since F=ma then substituting m with 7 Kg we get that F=7*-800=-5600 N

Therefore, the impact force is equivalent to 5600 N