A 10,000N car is on a roller coaster. at the top of the tallest hill (position 1) the reaches a hieght 36m above the lowest point on the roller coaster (position 2). after accelerating down the hill the roller coaster makes another (position 3) climb that rises 20m about the lowest point calculate the gravitational potentional energy at positions 1 and 3. also calculate the velocity at postition 2.

Question

A 10,000N car is on a roller coaster. at the top of the tallest hill (position 1) the reaches a hieght 36m above the lowest point on the roller coaster (position 2). after accelerating down the hill the roller coaster makes another (position 3) climb that rises 20m about the lowest point calculate the gravitational potentional energy at positions 1 and 3. also calculate the velocity at postition 2.

Answer 1

To calculate the gravitational potential energy at positions 1 and 3, we can use the formula:

Gravitational Potential Energy = mass × gravitational acceleration × height

Given that the force acting on the car is 10,000 N, and assuming the gravitational acceleration is approximately 9.8 m/s², we can calculate the mass of the car using Newton's second law:

Force = mass × acceleration

10,000 N = mass × 9.8 m/s²

Solving for mass, we find:

mass = 10,000 N / 9.8 m/s²

Now that we have the mass, we can calculate the gravitational potential energy at position 1 and position 3.

1. Position 1 (top of the tallest hill, 36 m above the lowest point):
Gravitational Potential Energy₁ = mass × gravitational acceleration × height₁

Gravitational Potential Energy₁ = mass × 9.8 m/s² × 36 m

2. Position 3 (the second climb, 20 m above the lowest point):
Gravitational Potential Energy₃ = mass × gravitational acceleration × height₃

Gravitational Potential Energy₃ = mass × 9.8 m/s² × 20 m

To calculate the velocity at position 2, we can use the conservation of energy. The initial potential energy at position 1 will be fully converted to kinetic energy at position 2 due to the absence of any other external energy sources (such as friction).

Since potential energy is given by:

Potential Energy = mass × gravitational acceleration × height

And kinetic energy is given by:

Kinetic Energy = 1/2 × mass × velocity²

At position 2, all the gravitational potential energy has been converted into kinetic energy, so we can equate the two:

Gravitational Potential Energy₁ = Kinetic Energy₂

mass × gravitational acceleration × height₁ = 1/2 × mass × velocity²

Simplifying the equation, we find:

velocity² = 2 × gravitational acceleration × height₁

Finally, we can calculate the velocity at position 2 by taking the square root of both sides:

velocity = √(2 × gravitational acceleration × height₁)

Now you have the formulas and steps to calculate the gravitational potential energy at positions 1 and 3, as well as the velocity at position 2.