# College Physics : Spring Force

## Example Questions

### Example Question #43 : Mechanics

A  bowling ball is dropped from a height of  onto a spring. If the spring is to compressed  before halting the ball, what is the spring constant  of the spring?

Explanation:

This questions requires an understanding of the conversion of gravitational potential energy to potential energy stored in the compression of a spring. The ball's initial potential energy is  where  is the mass of the ball,  is the acceleration due to gravity, and  is the height of the ball. The energy stored in a compressed spring is  where  is the potential energy,  is the spring constant (typically given in ) and  is the compression of the spring. By setting the gravitational potential energy equal to the energy stored in the spring, we can solve for the spring constant :

### Example Question #44 : Mechanics

A block with mass  is attached to a vertically hanging spring with negligible mass and spring constant  and is allowed to reach a new equilibrium position. Approximately how far does the spring stretch from its initial equilibrium position?

Explanation:

The new equilibrium position will be where the spring force is opposite in direction and equal in magnitude to the gravitational force on the mass. This occurs where where is the displacement of the spring from equilibrium. Solving for , we get .

### Example Question #45 : Mechanics

Supposed that an object attached to a spring with a spring constant of  is displaced by a certain amount. The elastic potential energy contained within the spring is . What is the magnitude of the force acting on the object from the spring at this instant?