You are on roller blades on top of a small hill. Your PE is 1,000.0 Joules. The last time you check your mass was 60.0 kg. What is the height of the hill?

if you start skating down this hill, your poetntial energy will be converted to kinetic. At the bottom of the hill, the kinetic energy will be equal ot your potential energy at the top. What will be your speed at the bottom of the hill? What is a Joule?

1 Joule is a unit of energy or work. It equals 1 Newton*meter or 1 kg*m^2/s^2. They all mean the same thing.

When you use physics equations with length measured in meters, time in seconds and mass in kg, you will end up with work and energy with units of joules. It is important to know that.

If 1 kg is moving at 1 m/s, its kinetic energy (K.E.) is 0.5 joules, since
K.E. = (1/2) M V^2.

To answer your other questions,
the height of the hill is
H = 1000 J/(M*g) = 1.70 meters. That is a very small "hill" !

If the kinetic energy at the bottom is 1000 J, then
(1/2)M*V^2 = 1000
V^2 = 33.33
V = 5.77 m/s
The fastest sprinters can run at about 10 m/s

To find the height of the hill, we can use the formula for potential energy: PE = mgh, where PE is the potential energy, m is the mass, g is the acceleration due to gravity, and h is the height.

Given that the potential energy (PE) is 1,000.0 Joules and the mass (m) is 60.0 kg, we can rearrange the formula to solve for the height (h):

PE = mgh

Rearranging the formula, we have:

h = PE / (mg)

Now let's plug in the values:

h = 1,000.0 J / (60.0 kg * 9.8 m/s^2)

h ≈ 1.70 meters

So, the height of the hill is approximately 1.70 meters.

Now, let's move on to the speed at the bottom of the hill. The potential energy at the top of the hill is converted into kinetic energy at the bottom. The formula for kinetic energy is KE = 1/2 mv^2, where KE is the kinetic energy and v is the velocity.

Since the potential energy at the bottom is equal to the potential energy at the top (1,000.0 Joules), we can equate the two formulas:

PE = KE

mgh = 1/2 mv^2

Simplifying the equation, we get:

gh = 1/2 v^2

v^2 = 2gh

Taking the square root of both sides:

v = sqrt(2gh)

Now we can plug in the values we know:

v = sqrt(2 * 9.8 m/s^2 * 1.70 m)

v ≈ 7.62 m/s

So at the bottom of the hill, your speed will be approximately 7.62 m/s.

Lastly, a Joule (J) is a unit of energy in the International System of Units (SI). It represents the amount of work done when a force of one newton is applied over a distance of one meter. The Joule is named after the English physicist James Prescott Joule, who discovered the relationship between work and energy.

Thank you so much, now I can try to help my child with her 12 problems. I needed that refresher.

Did I do these one correctly?

A baby carriage is sitting on top of a hill that is 21 m high. The carriage with the baby wieghs 12N. Calculate the energy?

PE= mgh
PE= 12N(21m)
PE= 252 Nm or do i multiply by 9.8m/s^2?

no, the N includes the g. 12N = mg

Newton moves 1kg, not 1km!

A Joule is the energy used to apply i Newton for 1 meter. J = Nm

A Newton is the force needed to accelerate 1 km at the rate of 1m/s^2. That is, to increase its velocity by 1m/s every second.

PE = mgh
1000 = 60*9.8*h
h = 1.7m (small hill indeed!)

KE = 1/2 mv^2
1000 = 1/2 * 60 * v^2
v^2 = 33.333
v = 5.77m/s