A toy cannon uses a spring to project a 5.21-g soft rubber ball. The spring is o

Question

A toy cannon uses a spring to project a 5.21-g soft rubber ball. The spring is originally compressed by 5.01 cm and has a force constant of 7.94 N/m. When the cannon is fired, the ball moves 15.5 cm through the horizontal barrel of the cannon, and the barrel exerts a constant friction force of 0.031 9 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) Applying work - energy theorem,

work done by spring + work done by spring = change in KE

(7.94)(0.0501^2)/2 - (0.0319 x 0.155) = 0.00521 v^2 / 2 - 0

v = 1.39 m/s

(b) at equilibrium position,

Fnet= kx - f= 0

x = 0.0319 / 7.94 = 0.004 m

(c) (7.94 x 0.0501^2 / 2) - (7.94 x 0.004^2 / 2) - (0.0319 x 0.004) = 0.00521v^2 /2

v = 1.94 m/s

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