Question

A toy cannon uses a spring to project a 5.24-g soft rubber ball. The spring is originally compressed by 5.01 cm and has a force constant of 8.08 N/m. When the cannon is fired, the ball moves 15.8 cm through the horizontal barrel of the cannon, and the barrel exerts a constant friction force of 0.031 0 N on the ball.With what speed does the projectile leave the barrel of the cannon?

Answer 1

Speed will be equal to 1.40 m/sec

Step-by-step explanation:

Mass of the rubber ball m = 5.24 kg = 0.00524 kg

Spring is compressed by 5.01 cm

So x = 5.01 cm = 0.0501 m

Spring constant k = 8.08 N/m

Frictional force f = 0.031 N

Distance moved by ball d = 15.8 cm = 0.158 m

Energy gained by spring

`KE=(1)/(2)kx^2=(1)/(2)* 8.08* 0.0501^2=0.0101J`

Energy lost due to friction

`W=Fd=0.031* 0.158=0.0048J`

So remained energy to move the ball = 0.0101 - 0.0048 = 0.0052 J

This energy will be kinetic energy

`(1)/(2)mv^2=0.0052`

`(1)/(2)* 0.00524* v^2=0.0052`

v = 1.40 m/sec