- #1
kidgt23
- 4
- 0
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
v2 = u2 + 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
426.722 = 0 + 2(0.1)(a)
a = 910449.7920 m/s2 (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.