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 the cannon is fired, the ball moves 15.0 cm through the horizontal barrel of the cannon, and the barrel exerts a constant friction force of 0.032 N on the ball.

A) With what speed does the projectile leave the barrel of the cannon?
B) At what point does the ball have max speed?
C) What is the maximum speed?

Answer 1

To determine the speed at which the projectile leaves the barrel of the toy cannon, the spring potential energy and the work done by friction are considered. The maximum speed of the projectile is reached just before work due to friction begins, which is when the ball is still in contact with the spring, but not yet moving along the barrel.

Step-by-step explanation:

To solve the problem, we need to apply concepts from mechanics, specifically, energy transformation and work done by a force. We can calculate the speed of the ball as it leaves the barrel of the toy cannon using the work-energy theorem, which states that the work done on an object is equal to its change in kinetic energy.

Part A: Speed of the Projectile Exiting the Barrel

The spring potential energy (PEspring) is converted into kinetic energy (KE) and work done against friction (Wfriction) as follows: