A toy cannon uses a spring to project a 5.20-g soft rubber ball. The spring is o

Question

A toy cannon uses a spring to project a 5.20-g soft rubber ball. The spring is originally compressed by 4.99 cm and has a force constant of 8.09 N/m. When the cannon is fired, the ball moves 15.9 cm through the horizontal barrel of the cannon, and the barrel exerts a constant friction force of 0.032 2 N on 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) work done by spring + work done by cannon friction = change in KE

kx^2 /2 + (- fd) = mv^2 /2 - 0

(8.09 x (0.0499^2) /2) - ( 0.032 x 0.159) = 5.20 x 10^-3 x v^2 /2

v = 1.38 m/s

b) when spring is just compressed by x= 0

d = 4.99 cm

c) 8.09 x 0.0499^2 /2 - 0.032 x 0.0499 = 0.0052 x v^2 /2

v = 1.81 m/s

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