Question

You are on in-line skates at the top of a small hill. Your potential energy is equal to 1,000 J. The last time you checked, your mass was 60.0 kg.

What is my weight in newtons?
What is the height of the hill?
If you start rolling down this hill, your potential energy will be converted to kinetic energy. At the bottom of the hill, your kinetic energy will be equal to your potential energy at the top.
What is your speed at the bottom of the hill?

Answer 1

Your weight is 588 N. The height of the hill is approximately 1.69 m. Your speed at the bottom of the hill is approximately 7.75 m/s.

Step-by-step explanation:

The weight of an object can be calculated using the formula:

Weight = mass × acceleration due to gravity

Given that your mass is 60.0 kg, we can calculate your weight:

Weight = 60.0 kg × 9.8 m/s² = 588 N

To find the height of the hill, we can use the formula for potential energy:

Potential energy = mass × gravity × height

Since potential energy is equal to 1000 J and the mass is 60.0 kg, we can solve for the height:

1000 J = 60.0 kg × 9.8 m/s² × height

Height = 1000 J / (60.0 kg × 9.8 m/s²) ≈ 1.69 m

Finally, to find your speed at the bottom of the hill, we can use the conservation of energy:

Potential energy at the top = Kinetic energy at the bottom

1000 J = (1/2) × mass × velocity²

Since potential energy and kinetic energy are equal, we can solve for the velocity:

1000 J = (1/2) × 60.0 kg × velocity²

Velocity = sqrt(1000 J / (1/2) × 60 kg) ≈ 7.75 m/s