Calculating Force Needed to Accelerate a 7.00g Pellet from Rest to 175 m/s

[airelemental135]

8. What average force is needed to accelerate a 7.00-gram pellet from rest to 175 m/s over a distance of 0.700 m along the barrel of a rifle?

9. A fisherman yanks a fish out of the water with an acceleration of 4.5 m/s^2 using very light fishing line that has a "test" value of 22 N. The fisherman unfortunately loses the fish as the line snaps. What can you say about the mass of the fish?

10. A 0.140-kg baseball traveling 45.0 m/s strikes the catcher's mitt, which, in bringing the ball to rest, recoils backward 11.0 cm. What was the average force applied by the ball on the glove?3

I tried doing number 8 on my own.

vfinal^2=vinitial^2 + 2ad
175m/s=0^2 + 2a(0.700m)
a= 125m/s
F=ma
F=(7.00g)(125 m/s)
F=875N

Is this correct>? How do you do the others?

 

[whozum]

You did 8 correct all the way to the last part, since you use MKS units, you need the mass in kilograms, 7 grams = 0.007kg.

Draw a force diagram for 9, should be all you need. Assume he pulsl the fish straight up

10 is done the same way as 8

 

[quicknote]

Your calculation for number 8 appears to be correct. To check your work, you can also use the equation F = mv^2/d, where m is the mass of the pellet, v is the final velocity, and d is the distance traveled. Plugging in the given values, we get F = (0.007 kg)(175 m/s)^2/0.700 m = 875 N, which matches your answer.

For number 9, we can use the equation F = ma, where F is the force, m is the mass, and a is the acceleration. Since the line snapped, the force applied by the fisherman (22 N) must have been greater than the maximum force the line could withstand. So we can say that the mass of the fish must have been greater than the mass that would produce a force of 22 N with an acceleration of 4.5 m/s^2. The exact mass cannot be determined without more information.

For number 10, we can use the equation F = ma, where F is the force, m is the mass, and a is the acceleration. In this case, the acceleration is caused by the ball striking the catcher's mitt and coming to rest, so we can use the given values to find the force. F = (0.140 kg)(45 m/s)/0.11 m = 57.3 N. So the average force applied by the ball on the glove was 57.3 N.