A stone of mass 20g is release from a catapult whose rubber has been stretched through 4cm, if the force constant of the rubber is 200N/M .calculate the velocity with which the stone leaves the catapult.
F = 200N/m * 0.04m = 8 N.
W = F*d = 8*0.04 = 0.32 J.
Work = change in KE:
W = 0.5M*V^2 = 0.32.
0.01*V^2 = 0.32,
V =
the energy stored in the rubber is ... 1/2 k x^2 ... 1/2 * 200 * .04^2 Joules
with no losses (friction, etc.) , the stored energy becomes the stone's K.E
1/2 k x^2 = 1/2 m v^2 = 1/2 * .02 kg * v^2
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answer
1/2KE^2=1/2mv^2
1/2*200*(0.05)^2=1/2*0.02*v^2
V^2=25
V=5m/s