A toy cannon uses a spring to project a 5.25-g soft rubber ball. The spring is o

Question

A toy cannon uses a spring to project a 5.25-g soft rubber ball. The spring is originally compressed by 5.03 cm and has a force constant of 8.08 N/m. When the cannon is fired, the ball moves 14.2 cm through the horizontal barrel of the cannon, and the barrel exerts a constant friction force of 0.031 2 N on the ball. With what speed does the projectile leave the barrel of the cannon? At what point does the ball have maximum speed? What is the sign of the acceleration an instant before the velocity reaches a maximum and an instant after the velocity reaches its maximum? cm (from its original position) What is this maximum speed?

Explanation / Answer

Here ,

m = 0.00525 Kg

x = 0.0503 m

k = 8.08 N/m

d = 14.2 cm = 0.142 m

f = 0.0312 N

a) let the final speed is v

Using work energy theorum

0.5 *m * v^2 = 0.5 * k * x^2 - f * d

0.5 * 0.00525 * v^2 = 0.5 * 8.08 * 0.0503^2 - 0.0312 * 0.142

solving for v

v =1.49 m/s

the speed having projectile is 1.49 m/s

b) for the maximum speed ,

k * x= f

8.08 * x = 0.0312

x = 3.86 *10^-3 m = 0.38 cm

from starting point , del x = 5.03 - 0.38 = 4.65 cm

maximum speed is at the position 4.65 cm from the original position

c) for the maximum speed v

Using work energy theorum

0.5 * 0.00525 * v^2 = 0.5 * 8.08 * (0.0503^2 - (3.86 *10^-3)^2) - 0.0312 * 0.0465

solving for v

v = 1.82 m/s

the maximum speed is 1.82 m/s

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