### All High School Physics Resources

## Example Questions

### Example Question #11 : Using Spring Equations

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

**Possible Answers:**

**Correct answer:**

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 ?

**Possible Answers:**

**Correct answer:**

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?

**Possible Answers:**

**Correct answer:**

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?

**Possible Answers:**

**Correct answer:**

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 ?

**Possible Answers:**

**Correct answer:**

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?

**Possible Answers:**

**Correct answer:**

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?

**Possible Answers:**

There is insufficient information to solve

**Correct answer:**

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?

**Possible Answers:**

**Correct answer:**

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

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

**Possible Answers:**

**Correct answer:**

There are two forces at work here: the force due to gravity and the restoring force of the spring. We can set these two forces equal to one another because the forces must be in equilibrium when the spring is compressed at its maximum point.

Expand this equation by using the formulas for gravitational and spring force, respectively.

Plug in our given values for the girl's mass, gravitational acceleration, and the spring constant. Using these values, we can solve for the displacement of the spring.