A toy cannon uses a spring to project a 5.23 g soft rubber ball. The spring is o

Question

A toy cannon uses a spring to project a 5.23 g soft rubber ball. The spring is originally compressed by 4.91 cm and has a force constant of 8.06 N/m. When the cannon is fired, the ball moves 14.8 cm through the horizontal barrel of the cannon, and there is a constant frictional force of 0.0316 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?
m/s

Explanation / Answer

a)

According to law of conservation of energy:

initial energy = final energy

0.5*K*x^2 = f*.16 +0.5*m*v^2

0.5*8.06*.0491^2 = 0.0316*0.148 +0.5*.00523*v^2

v =1.39 m/s

b)

At x= 4.91 cm the ball will has maximum speed and is

c)

0.5*8.06*.0491^2 = 0.5*.00523*v^2

V=1.93 m/s

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