# A box slides down a frictionless, 10-meter, 30o incline. Calculate the gravitational potential...

## Question:

A box slides down a frictionless, 10-meter, 30o incline.

a. Calculate the gravitational potential energy at both the beginning and end of the motion.

b. Calculate the work done by GRAVITY as the box slides down the incline.

c. Compare this to the overall change in gravitational potential energy.

d.What conclusions can you draw from this?

## Energy Conservation Principle:

The energy conservation principle refers to a physical law that states that if no external forces are working on the system, the total energy of the system will conserve. The system may suffer energy transformations, but the total energy will always remain equal throughout time.

#### Part a):

In order to calculate the potential energy, we must first determine the height of the incline. We use trigonometric functions in order to determine the height of the incline:

known information:

• Angle of the incline: {eq}\theta=30^\circ {/eq}
• Distance on the incline: {eq}d=10\ m {/eq}
• Assuming a mass value of: {eq}m=1\ kg {/eq}

We proceed to solve for height:

{eq}\sin\theta=\dfrac{h}{d}\\ h=\d\sin\theta\\ h=10\sin30\\ h= 5\ m {/eq}

We proceed to calculate the total potential energy at the beginning of the motion.

{eq}U_{ei}=mgh\\ U_{ei}=1\times 9.8\times 5\\ U_{ei}=49\ J {/eq}

At the end of the incline, all of the potential energy will have converted to kinetic energy. As the height is zero, the potential energy at the end of the incline is of zero.

#### Part b):

The work done by the force of gravity will correspond to the horizontal component of the weight of the box over the incline. The total work on the system will be equal to the product of the horizontal component of the weight times the total distance the box slides over the incline.

{eq}W=mg\sin30\times d\\ W=1\times9.8\sin 30\times 10\\ W= 49\ J {/eq}

#### Part c):

The total work done by the gravitational force is equal to the change in the potential energy of the system. The work done by the gravitational force is what makes the object gain kinetic energy, but at the same time lose potential energy.

#### Part d):

We can conclude that thanks to the gravitational force, the energy is able to conserve within the system. Also, the work done by the force of gravity is what makes the object transform the total potential energy into kinetic energy. 