Question

We are going to calculate the amount of potential energy that the roller coaster has. Using PE = mgh, calculate the potential energy if the mass of the roller coaster is 1,650 kg and it is carrying six 100-kg people. The height of the roller coaster in step 1 is 13.1 meters. Remember g = 9.8 m / s 2.

2. Now find the step number where the box on the part is completely blue, which means that the total energy is completely kinetic. What step number is this? Calculate the kinetic energy of the roller coaster knowing the mass from question 1 and the speed is 16 m / s. Use the equation KE = 1/2 mv 2.
3. According to the law of conservation of energy, energy cannot be created or destroyed. Comparing your answers for the numbers 1 and 2, is energy being conserved? (It's okay if your numbers are a little off)
4. Explain why in step 4 there are both potential energy and kinetic energy. Why is there more potential energy than kinetic energy in this step?

Answer 1

The roller coaster's potential energy is calculated using the mass, gravitational acceleration, and height. The step where kinetic energy is maximum is typically at the lowest point of the descent. The energy values calculated indicate that energy is being conserved according to the law of conservation of energy.

Step-by-step explanation:

1. To calculate the gravitational potential energy (PE) of the roller coaster, we use the formula PE = mgh, where m is the mass, g is the acceleration due to gravity (9.8 m/s2), and h is the height. The total mass of the roller coaster and its passengers is 1,650 kg + (6 × 100 kg) = 2,250 kg. At 13.1 meters high, the potential energy is PE = 2,250 kg × 9.8 m/s2 × 13.1 m = 289,035 Joules.

2. To find the step where the total energy is completely kinetic, we would need to refer to the provided roller coaster energy graph or the point in the roller coaster ride where it reaches the lowest point after the first descent. At this step, all potential energy has been converted to kinetic energy (KE). Using the formula KE = 1/2 mv2, with the roller coaster's mass of 2,250 kg and a speed of 16 m/s, the kinetic energy is KE = 1/2 × 2,250 kg × (16 m/s)2 = 288,000 Joules.

3. According to the law of conservation of energy, energy cannot be created or destroyed, only transformed. Comparing the potential energy calculated in step 1 to the kinetic energy calculated in step 2, they are very close in value, confirming that energy is being conserved, considering negligible energy losses like air resistance or mechanical friction.

4. In step 4, there is both potential energy and kinetic energy because the roller coaster is neither at its highest point (where it would have maximum potential energy and no kinetic energy) nor at its lowest point (where it would have maximum kinetic energy and no potential energy). There is more potential energy than kinetic energy at this step because the roller coaster is on its way up to another rise after descending from a previous one, converting some of its kinetic energy back into potential energy as it slows down.