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?

(a)

(b)

1120 N

Explanation:

Change in velocity, is given by subtracting the initial velocity from the final velocity and expressed as

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

To find then we substitute 7 kg for m and -8 m/s for therefore

(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

Substituting t with 0.05 s then

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

given data:

determine the horse power (h.p) = ?

force applied to move the box(f) = 10 pounds,

box lifted from a distance         (d) = 3 feet

time taken to lift                         (t) = 10 sec,

the horse power is defined as amount of work required to move a load. the horse power is equal to 550 foot-pound per second

                  1 h.p   = 550 foot-pound/second

it can also be defined as the the load that need to be move a body for certain distance in a certain amount of time.

mathematically,

                      h.p = (force × distance)/ time

                            = (10 × 3)/ 10

                            = 30/10

                            = 3 foot -pound/sec

hence, the horse power is needed to move the box is 3 foot-pound/second

important note: 1 h.p = 550 foot-pound/second = 746 watts

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