Question

A roller coaster cart with a mass of 200 kg is at rest on its track at a height of 5 m above the ground.

Later the same 200 kg cart reaches a lower part of the track and is traveling at a velocity of 6.0 m/s.
How high the cart above the ground when its speed is 6.0 m/s?

Answer 1

The height of the cart above the ground when its speed is 6.0 m/s is 1.83 m.

Step-by-step explanation:

To determine the height of the roller coaster above the ground when its speed is 6.0 m/s, we can use the principle of conservation of energy. At the higher part of the track, the roller coaster has potential energy equal to its mass multiplied by the acceleration due to gravity (PE = mgh). At the lower part of the track, it has both potential energy and kinetic energy, which is equal to (PE + KE = mgh + 1/2 mv^2). Since the roller coaster is at rest at the higher part, its potential energy is given by (PE = mgh), and at the lower part, its kinetic energy is given by (KE = 1/2 mv^2).

Setting the potential energy at the higher part equal to the sum of the potential and kinetic energy at the lower part, we can solve for the height (h) using the equation: mgh = mgh + 1/2 mv^2. Since the mass of the roller coaster cancels out, we can simplify the equation to: gh = gh + 1/2 v^2. Solving for h:

h = 1/2 v^2/g = 1/2 * (6.0 m/s)^2 / 9.8 m/s^2 = 1.83 m.