# High School Physics : Using Spring Equations

## Example Questions

### Example Question #11 : Using Spring Equations

force is used to stretch a spring . What is the spring constant?

Explanation:

The formula for the force required to stretch or compress a spring is:

We are given the force and the distance, allowing us to solve for the spring constant.

### Example Question #11 : Using Spring Equations

What is the potential energy stored in a spring that is stretched  and has a spring constant of ?

Explanation:

Spring potential energy is given by the equation:

We are given the spring constant and the distance that the spring is stretched. Using these values, we can find the energy stored in the spring.

### Example Question #12 : Using Spring Equations

A spring with a spring constant of  has a mass of  attached to one end. It is stretched a distance of . How much force is required to restore the spring to its equilibrium position?

Explanation:

The formula for the restoring force of a spring is:

Essentially, the restoring force is equal and opposite to the force required to stretch the spring. Note that the mass has no place in this calculation. We are given the spring constant and displacement, allowing us to calculate the force.

### Example Question #14 : Using Spring Equations

A spring with a spring constant of  is compressed . What is the potential energy in the spring?

Explanation:

The formula for potential energy in a spring is:

We are given the values for the spring constant and displacement, allowing us to calculate the potential energy.

### Example Question #15 : Using Spring Equations

How much force is required to compress a spring if it has a spring constant of  ?

Explanation:

The formula for compression force in a spring is:

We are given the value for the spring constant and the displacement, allowing us to solve for the force required.

### Example Question #16 : Using Spring Equations

A spring is stretched  in the horizontal direction. If the spring requires  of force to restore it to its original position, what is the spring constant?

Explanation:

To solve this problem, use Hooke's law.

We know the force of the spring and the distance it is displaced. Using these values, we can solve for the spring constant.

### Example Question #13 : Using Spring Equations

A spring with a spring constant of is compressed . A object is placed at the end of the compressed spring and the spring is released. What is the maximum velocity of the object?

There is insufficient information to solve

Explanation:

For this problem, use the law of conservation of energy. Assuming no other forces are acting upon the object the initial spring potential energy will be equal to the maximum final kinetic energy.

Expand this equality with the formulas for each type of energy.

We are given the spring constant and displacement, allowing us to complete the left side of the equation. We are also able to plug in the mass to the left side of the equation.

Solve to isolate and solve for the velocity variable.

### Example Question #26 : Harmonic Motion

How much potential energy is generated by a spring with a spring constant of  if it is stretched from equilibrium?

Explanation:

Spring potential energy is equal to half of the spring constant times the compression/stretching distance squared:

Using the given values for the spring constant and displacement, we can solve for the energy.

### Example Question #14 : Using Spring Equations

girl bounces on a massless pogo stick. If the spring constant for the stick is , what is the maximum compression of the spring?