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 5.06 cm and has a force constant of 7.98 N/m. When the cannon is fired, the ball moves 16.0 cm through the horizontal barrel of the cannon, and the barrel exerts a constant friction force of 0.031 7 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)

v = speed of projectile

f = frictional force = 0.0317 N

x = compression of spring = 0.0506 m

d = length of barrel = 0.16 m

k = spring constant = 7.98 N/m

using conservation of energy

Spring potential energy = work done by frictional force in barrel + kinetic energy

(0.5) k x2 = f d + (0.5) m v2

(0.5) (7.98) (0.0506)2 = (0.0317) (0.16) + (0.5) (0.00531) v2

v = 1.39 m/s

b)

ball has the maximum speed when the spring leaves contact with the projectile

so at x = 5.06 cm

c)

using conservation of energy

Spring potential energy = maximum kinetic energy

(0.5) k x2 = (0.5) m vmax2

(0.5) (7.98) (0.0506)2 = (0.5) (0.00531) vmax2

vmax = 1.96 m/s

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