A toy cannon uses a spring to project a 5.28 g soft rubber ball. The spring is o

Question

A toy cannon uses a spring to project a 5.28 g soft rubber ball. The spring is originally compressed by 5.05 cm and has a force constant of 7.94 N/m. When the cannon is fired, the ball moves 15.0 cm through the horizontal barrel of the cannon, and there is a constant frictional force of 0.0318 N between the barrel and 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

Explanation / Answer

here,

mass , m = 5.28 g = 0.00528 kg

x = 0.0505 m

spring constant , K = 7.94 N/m

uk = 0.0318

a)

let the projectile leave the barrel of the cannon at a speed v

using conservation of energy

0.5 * k * x^2 - uk * m * g *l = 0.5 * m * v^2

0.5 * 7.94 * 0.0505^2 - 0.0318 * 0.00528 * 9.81 * 0.15 = 0.5 * 0.00528 * v^2

solving for v

v = 1.93 m/s

b)

the ball have maximum speed at the position when it leaves the spring

c)

let the maximum speed be v'

using conservation of energy

0.5 * k * x^2 - uk * m * g *x = 0.5 * m * v'^2

0.5 * 7.94 * 0.0505^2 - 0.0318 * 0.00528 * 9.81 * 0.0505 = 0.5 * 0.00528 * v'^2

solving for v'

v' = 1.95 m/s

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