A 1200 kg frictionless roller coaster starts from rest at a height of 23 m. What is its kinetic energy when it goes over a hill that is 13 m high?
Whatever the potential energy at 13m is. The height at 23m is not relevant to the question.
To find the kinetic energy of the roller coaster, we need to calculate its speed at the top of the hill using the principle of conservation of energy.
First, let's find the potential energy of the roller coaster at the starting point and at the top of the hill. The potential energy can be calculated using the formula:
Potential Energy = mass * gravity * height
The mass of the roller coaster is given as 1200 kg, gravity is approximately 9.8 m/s^2, and the height at the starting point is 23 m. Substituting these values into the formula, we find:
Potential Energy at starting point = 1200 kg * 9.8 m/s^2 * 23 m
Now, let's find the potential energy at the top of the hill. The height at the top of the hill is given as 13 m:
Potential Energy at top of hill = 1200 kg * 9.8 m/s^2 * 13 m
Next, we can use the principle of conservation of energy to find the kinetic energy of the roller coaster at the top of the hill. According to this principle, the total mechanical energy (the sum of potential energy and kinetic energy) remains constant throughout the roller coaster's motion. Therefore, we can equate the potential energy at the starting point to the sum of the potential energy and kinetic energy at the top of the hill:
Potential Energy at starting point = Potential Energy at top of hill + Kinetic Energy at top of hill
Now, rearranging the equation to solve for the kinetic energy at the top of the hill:
Kinetic Energy at top of hill = Potential Energy at starting point - Potential Energy at top of hill
Substituting the values we calculated earlier:
Kinetic Energy at top of hill = (1200 kg * 9.8 m/s^2 * 23 m) - (1200 kg * 9.8 m/s^2 * 13 m)
Now, we can simplify the equation to find the answer.