- #1

kidgt23

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## Homework Statement

An 8.5 gram slug is fired East from a 0.357 magnum hand gun held 1.5 meters above the ground. The muzzle velocity (as the projectile leaves the gun) is 1400 ft/sec. The bullet is accelerated at a constant rate as it travels through the 10 cm long barrel. After leaving the barrel, the gun powder force drops to 0.

2 a) [2] What force does the exploding powder exhaust apply to accelerate the slug?

2 b) [2] What horizontal force is put on the shooters arm by the gun? Sketch a graph of this force as a function of time. (assume the gun is held fixed)

## Homework Equations

u = initial velocity

v = u + at

v

^{2}= u

^{2}+ 2ad

F = ma

## The Attempt at a Solution

a)

Converting to SI units:

1400 ft/sec x 12in/ft = 16800 in/s

16800 in/s x 0.0254m/in = 426.72 m/s

8.5 grams = 0.0085 kg

10 cm = 0.1 m

assuming u = 0 m/s

426.72

^{2}= 0 + 2(0.1)(a)

a = 910449.7920 m/s

^{2}(what the hell?)

F = ma

F = 0.085(910449.7920)

= 7739 N

b) Due to Newton's third law, the force exerted by the gun (7739 N) should be the same as on the man's arm.

My values are very odd, so I feel like what I've done is incorrect however I can't think of how this is wrong. Thanks for your help.