Question

Use the law of conservation of energy (assume no friction nor air resistance) to determine the kinetic and potential energy at the various marked positions along the roller coaster track below: KE= ME PER KE PE=20 000J KE=25 000J PE= mgh PE=_ KE= KE KE=OJ PE-7 500J PE=5 000J PE- D Ε. Voc KE=/m 12 KE- PEN KE=_ PE=__ KE=40 000J PE=OJ What is the total mechanical energy of the roller coaster throughout the ride? Explain how you determined ME.​

Answer 1

The law of conservation of energy dictates that the total mechanical energy of the roller coaster is constant throughout the ride, calculated as the sum of kinetic and potential energy. It remains unchanged from the initial total mechanical energy provided at the start of the ride due to the absence of external work from friction or air resistance.

Step-by-step explanation:

The total mechanical energy of the roller coaster throughout the ride can be determined using the law of conservation of energy. This fundamental principle of physics tells us that in an isolated system (one where no energy is lost to the environment through friction or air resistance), the total mechanical energy (ME) remains constant throughout the roller coaster's journey.

The total mechanical energy is the sum of kinetic energy (KE) and potential energy (PE), expressed as ME = KE + PE. At the start of the ride, the roller coaster has a certain amount of mechanical energy due to its position and motion, which might be entirely potential energy if it starts from rest at the top of the first hill.

As the roller coaster moves, energy is transitioned between kinetic and potential forms, but the total mechanical energy remains the same. For instance, as the roller coaster descends, gravitational potential energy is converted to kinetic energy, increasing the speed of the coaster, and as it ascends, kinetic energy is converted back to potential energy, which slows it down. By examining specified points along the track with known KE and PE values, we can deduce that the initial total mechanical energy is consistent at all points.

In conclusion, to determine the total ME of the roller coaster, one simply needs to use the initial total energy values provided at the start of the ride, as this total will be conserved throughout the ride.

Answer 2

Part A

1) At the starting point, we have;

PE = 40,000 J

2) PE = 0 J, KE = 40,000 J

3) KE = 20,000 J

4) PE = 15,000 J

5) KE = 32,500 J

6) KE = 40,000 J, PE = 0 J

7) KE = 35,000 J

8) KE = 40,000 J, PE = 0 J

Part B

The total Mechanical Energy = ME = 40,000 J

At the final point, we have;

ME = KE + PE = 40,000 J + 0 J = 40,000 J

Step-by-step explanation:

Part A

By the law of conservation of energy, we have;

ME = PE + KE

Where;

ME = The total Mechanical Energy of the system

PE = The Potential Energy of the system

KE = The Kinetic Energy of the system

Where there is no friction, we have;

At the final stage, KE = 40,000 J. PE = 0 J

Therefore, ME = PE + KE = 40,000 J + 0 J = 40,000 J

1) At the starting point, we have;

KE = 0 J, therefore, PE = ME - KE = 40,000 J - 0 J = 40,000 J

2) At the bottom of the roller coaster, at the same level the PE is taken as PE = 0 J at the final stage, we have;

PE = 0 J, therefore, KE = ME - PE = 40,000 J - 0 J = 40,000 J

3) Where PE = 20,000 J, KE = ME - PE = 40,000 J - 20,000 J = 20,000 J

4) Where KE = 25,000 J, PE = ME - KE = 40,000 J - 25,000 J = 15,000 J

5) Where PE = 7,500 J, KE = ME - PE = 40,000 J - 7,500 J = 32,500 J

6) At the bottom KE = 40,000 J, PE = 0 J

7) Where PE = 5,000 J, KE = ME - PE = 40,000 J - 5,000 J = 35,000 J

8) KE = 40,000 J, PE = 0 J

Part B

The given that there is no friction nor air resistance, the total Mechanical Energy, ME, is constant and equal to the sum of the Potential Energy, PE and the Kinetic Energy, KE, as follows;

ME = KE + PE

At the final point, we have;

ME = 40,000 J + 0 J = 40,000 J

The total Mechanical Energy = ME = 40,000 J