A 30 kg launching machine fires a 250 gram projectile horizontally at 100 m/s. T

Question

A 30 kg launching machine fires a 250 gram projectile horizontally at 100 m/s. This causes the machine to slide 1.122 meters before coming to a rest.

a)      What is the machine%u2019s initial velocity?

b)      How long did it take to go the 1.122 meters?

c)      What was the momentum of the machine?

d)     What was the force necessary to move this machine?

e)      What was its acceleration during this time?

f)       What is the coefficient of kinetic friction?

g)      What surfaces are likely to cause this friction?

IF this was on the moon, and all else was the same, how far would this machine slide?

Explanation / Answer

conserving momentum :
m1v1 = m2v2
=> v2 = (250*100/1000)/30 =0.8333333333333 m/s answer(a)

v^2 = u^2 -2ad
=> 0 = 0.8333333333333*0.8333333333333 -2*a*1.122
=> a = 0.3094672212319 m/s2

v = u -at
=> o = 0.8333333333333 - 0.309467221231*t
=> t = 2.69280 s answer(b)

momentum = 30*0.8333333333333 = 24.99999999999 kgm/s answer(c)

f = rate of change of momentum = 24.99999999999/2.69280 = 9.28401663695 N answer(d)

a = 0.3094672212319 m/s2 answer(e)

friction coeffecient = F/mg = 9.28401663695/(30*9.8) = 0.031578287881 answer(f)

thus must be smooth surface (g)

on moon gravity is 1.6249 m/s2

v^2 = u^2 -2ad
=> 0 = 0.8333333333333*0.8333333333333 -2*1.6249*0.031578287881*d
=> d = 6.76693950 m answer

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