Question

You are at the edge of a diving board that is 9 meters above the water. If you weigh 500 Newtons, what is your potential energy?

Answer 1

4500 J

Explanation:

First, let's define some equations and derivations.

Our potential energy formula is:

Where m is mass (in kg), g is the gravitational constant (in m/s²), and h is height (in m).

We also know that mg is equal to the weight of an object (in N), from Newton's 2nd Law of Motion: F = ma (Force is equal to [constant] mass times acceleration).

Therefore, we can simply substitute force into the equation:

Where F is the force (in N) and h is still height (in m).

Now we can calculate the amount of potential energy in our system, measured in joules.

Substitute in the given variables, F = 500 N and h = 9 m:

Using simple Pre-Algebra rules, we find that:

This tells us that the we have 4500 joules of potential energy when I am 9 meters above the water on the edge of the diving board.

Answer 2

4500 J

Step-by-step explanation:

First, let's define some equations and derivations.

Our potential energy formula is:

• 
  `\displaystyle U = mgh`

Where m is mass (in kg), g is the gravitational constant (in m/s²), and h is height (in m).

We also know that mg is equal to the weight of an object (in N), from Newton's 2nd Law of Motion: F = ma (Force is equal to [constant] mass times acceleration).

Therefore, we can simply substitute force into the equation:

• 
  `\displaystyle U = Fh`

Where F is the force (in N) and h is still height (in m).

Now we can calculate the amount of potential energy in our system, measured in joules.

Substitute in the given variables, F = 500 N and h = 9 m:

• 
  `\displaystyle U = (500 \ N)(9 \ m)`

Using simple Pre-Algebra rules, we find that:

• 
  `\displaystyle U = 4500 \ J`

This tells us that the we have 4500 joules of potential energy when I am 9 meters above the water on the edge of the diving board.