A toy cannon uses a spring to project a 5.32-g soft rubber ball. The spring is o

Question

A toy cannon uses a spring to project a 5.32-g soft rubber ball. The spring is originally compressed by 5.02 cm and has a force constant of 8.09 N/m. When the cannon is fired, the ball moves 15.8 cm through the horizontal barrel of the cannon, and the barrel exerts a constant friction force of 0.032 7 N on the ball (a) With what speed does the projectile leave the barrel of the cannon? 1.37 m/s (b) At what point does the ball have maximum speed? cm (from its original position) (c) What is this maximum speed? 1.96 Note that the initial potential energy of the spring is now found in several different forms. Make certain you can list each of them before writing down an energy equation. m/s Need Help?ReadWatch

Explanation / Answer

here,

mass , m = 0.00532 kg

compression , x = 5.02 cm = 0.0502 m

K = 8.09 N/m

s = 15.8 cm = 0.158 m

frictional force ,ff = 0.0327 N

a)

1.37 m/s

b)

the ball has maximum speed when the spring is at equilibrium position

5.02 cm from the initial position

c)

let the maximum speed be v

work done by fritcional force = initial potential energy of spring - final kinetic energy

ff * x = 0.5 * K * x^2 - 0.5 * m *v^2

0.0327 * 0.0502 = 0.5 * 8.09 * 0.0502^2 - 0.5 * 0.00532 * v^2

solving for v

v= 1.79 m/s

the maximum speed is 1.79 m/s

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