Question

A toy cannon uses a spring to project a 5.39-g soft rubber ball. The spring is originally compressed by 5.04 cm and has a force constant of 8.10 N/m. When the cannon is fired, the ball moves 15.6 cm through the horizontal barrel of the cannon, and the barrel exerts a constant friction force of 0.032 5 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

Answer 1

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A toy cannon uses a spring to project a 5.39-g soft rubber ball. The spring is originally compressed by 4.93 cm and has a force constant of 7.96 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 0.031 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   

A nonconservative force is simply a force that changes the total amount of mechanical energy in a system. Friction is the only nonconservative force here. Energy must be conserved in this problem, so the following expression must be true. ME0 = MEf + Wnc Where ME0 is the initial mechanical energy, MEf is the final mechanical energy, and Wnc is the work done by nonconservative forces. We are dealing with spring potential energy and translational kinetic energy, so: ME = 1/2 k x^2 + 1/2 m v^2 Our work done by friction is the force of friction multiplied by the distance it travels through the barrel. Wnc = F d This makes our conservation equation: 1/2 k x0^2 + 1/2 m v0^2 = 1/2 k xf^2 + 1/2 m vf^2 + F d We know that xf and v0 both are zero so the equation simplifies to: 1/2 k x0^2 = 1/2 m vf^2 + F d 0.5(7.96)(0.0493)^2=0.5(0.00539)vf^2 + 0.0319(0.159) vf^2=1.707 Vf =1.3067 m/sec