A toy cannon uses a spring to project a 5.31 g soft rubber ball. The spring is o

Question

A toy cannon uses a spring to project a 5.31 g soft rubber ball. The spring is originally compressed by 4.91 cm and has a force constant of 8.01 N/m. When the cannon is fired, the ball moves 15.5 cm through the horizontal barrel of the cannon, and there is a constant frictional force of 0.0317 N between the barrel and the ball. (a) With what speed does the projectile leave the barrel of the cannon? m/s (b) At what point does the ball have maximum speed? cm (from its original position) (c) What is this maximum speed?

Explanation / Answer

a)

1/2*kx^2 = F*d + 1/2*mv^2

1/2*8.01*0.0491^2 = .0317*0.155 + 1/2*0.0631*v^2

v = 0.3877 m/s

b)

Max. speed is when F*d = 0 or when d = 0, i.e just at the beginning inside the barrel.

c)

Putting = 0 in above calculations, we get v = 0.5532 m/s

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