A toy cannon uses a spring to project a 5.30 g soft rubber ball. The spring is o

Question

A toy cannon uses a spring to project a 5.30 g soft rubber ball. The spring is originally compressed by 5.00 cm and has a force constant of 8.00 N/m. When it is fired, the ball moves 15.0 cm through the barrel of the cannon that is angled upwards at 40.0 degrees, and a constant frictional force of 0.0320 N exists between barrel and 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 the starting position) (c) What is this maximum speed?

Please Note that the barrel of the cannon is angled upwards at 40.0 degrees and not horizontal.

Explanation / Answer

a) Energy of spring - frictional energy -mgh = 1/2 mv^2

1/2 * kx^2 - F * 0.15 - 0.0053*9.8*0.15*sin(40) = 1/2 *0.0053*v^2

1/2 * 8*0.05^2 - 0.0320 * 0.15 - 0.0053*9.8*0.15*sin(40) = 1/2 *0.0053*v^2

v = 0.27 m/sec

b) Maximum speed will be that moment when the spring is completely unstretched.

c) The speed will be when the body has moved 5 cm:

1/2 * kx^2 - F * 0.05 - 0.0053*9.8*0.05*sin(40) = 1/2 *0.0053*v^2

v = 1.59 m/sec

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