A toy cannon uses a spring to project a 5.20-g soft rubber ball. The spring is o

Question

A toy cannon uses a spring to project a 5.20-g soft rubber ball. The spring is originally compressed by 4.93 cm and has a force constant of 7.98 N/m. When the cannon is fired, the ball moves 15.4 cm through the horizontal barrel of the cannon, and the barrel exerts a constant friction force of 0.031 9 N on the ball. With what speed does the projectile leave the barrel of the cannon? m/s At what point does the ball have maximum speed? cm (from its original position) What is this maximum speed? m/s

Explanation / Answer

BY Using Work Energy Theorem

- fd = 1/2mv^2 - 1/2 * k * d^2

-0.0319 * 0.154 = 1/2 * 5.20 * 10^-3 *v^2 - 1/2 * 7.98 * (0.0493)^2

v = 1.356 m/s

b)

work energy theorem

- fx = 1/2 * mb * vb^2 + 1/2 * (0.0493 - x)^2 - 1/2 *k * d^2

for vb to be 2m2x we diff. 2nd set dvb/dx = 0

-f = 0 + k(0.0493 - x)(-1)

0.0493 - x = f/r

x = 0.0493 - 0.0319 /7.98

x = 4.53 * 10^-2 m

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