The spring of a spring gun has force constant k =400 N/m and negligible mass. Th
ID: 1268811 • Letter: T
Question
The spring of a spring gun has force constant k =400 N/m and negligible mass. The spring is compressed 6.00 cm and a ball with mass 0.0300 kg isplaced in the horizontal barrel against the compressed spring. Thespring is then released, and the ball is propelled out the barrelof the gun. The barrel is 6.00 cm long, so the ball leaves the barrel at the same point that it loses contact with the spring. The gun is held so the barrel is horizontal. For the situation in part (b), at whatposition along the barrel does the ball have the greatest speed? (In this case, the maximum speed does not occur at the end of the barrel.) What is that greatest speed?
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Explanation / Answer
the ball will have greast speed at just after the spring is relaeased from compressed position
that is at 6 cm
given data
mass m1 = 0.0300 kg
intial speed of the ball V1 =0
spring constant K = 400 N/m
compression x1 = 6 cm =0.06 m
x2=0
from the conservation of energy principle
0.5Kx1^2+0.5mv1^2 =0.5kx2^2 + 0.5 mv2^2
0.5*400*0.06^2 = 0.5*0.0300*V2^2
V2 = 6.928 m/s = 6.93 m/s
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