# Between kinetic energy and potential energy, what type of energy increased in each of the...

## Question:

Between kinetic energy and potential energy, what type of energy increased in each of the following examples?

1. A car accelerating from 0 mph to 60 mph.

2. A baseball thrown by a pitcher.

3. A spring compressed by 10 cm.

4. A ball rolls down a hill.

5. The temperature of a gas is increased.

6. A book picked up off the floor and put on a table.

## Mechanical Energy:

The total energy needed to perform work can be categorized into two quantities: the kinetic energy, or the energy that an object has while in motion, and; the potential, or the energy an object gathers while being at rest and is constantly applied a certain force.

## Answer and Explanation:

Kinetic energy is the energy in motion; potential energy is the gathered energy while being at rest.

#### 1.

The object increases its velocity, so the kinetic energy is increased.

#### 2.

As the ball moves, it experiences a constant downward force due to gravity. Therefore, it experiences acceleration and an increase in velocity. Consequently, kinetic energy also increases.

#### 3.

The expression for a spring's potential energy is given by:

{eq}U = \frac{1}{2}k(\Delta x)^2 {/eq},

where x is the compression length.

From a certain length, we compressed it by 10 cm, which increases the {eq}\Delta x {/eq}, also increasing the potential energy.

#### 4.

Similar to item 2, the ball also experiences a constant downward force from gravity, therefore experiencing a constant downward acceleration, therefore causing an increase in velocity and consequently, kinetic energy.

#### 5.

Increasing a gas's temperature increases the energy between the molecules, causing them to move about. This motion signifies an increase in velocity, therefore it equates to kinetic energy.

#### 6.

Gravitational potential energy can also be written as:

{eq}U = mg\Delta h {/eq}.

Here, h is the height of the object from the ground. An increase of height from the surface equates to an increase in potential energy.