Work, power, and energy

In summary: Then, using the formula PE=mgh, we can calculate the potential energy at the top of the first hill (PE=mgh=4727*9.8*34.1=1572154.6 J) and at the bottom of the drop (PE=mgh=4727*9.8*12.2=570793.6 J). Therefore, the difference in potential energy is 1001361 J, which is converted into kinetic energy as the train drops. In summary, the work required to get an empty train of cars from
  • #1
4. At Six Flags in Massachusetts, a ride called the Cyclone is a giant roller coaster that ascends a 34.1m hill and then drops 21.9m before ascending the next hill. The train of cars has a mass of 4727kg.

a. how much work is required to get an empty train of cars from the ground to the top of the first hill?

b. what power must be generated to bring the train to the top of the first hill in 30.0s?

c. how much PE is converted into KE from the top of the first hill to the bottom of the 21.9m drop?

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4. For this problem I used w=f*d but I needed to find out the force to find the work. So I did f=m*aà f=(4727)*-10(gravity) -47270. Then I just plugged in the force for the work equation and found out that the work required is -1611907 j .For part b I just used the power equation (work/time) therefore (5388.78*34.1)/(30) and you get the answer 6125.2466. For part c i don't know what to do
 
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  • #2
rottentreats64 said:
4. At Six Flags in Massachusetts, a ride called the Cyclone is a giant roller coaster that ascends a 34.1m hill and then drops 21.9m before ascending the next hill. The train of cars has a mass of 4727kg.

a. how much work is required to get an empty train of cars from the ground to the top of the first hill?

b. what power must be generated to bring the train to the top of the first hill in 30.0s?

c. how much PE is converted into KE from the top of the first hill to the bottom of the 21.9m drop?

-----------------------------------------------------------------------------
4. For this problem I used w=f*d but I needed to find out the force to find the work. So I did f=m*aà f=(4727)*-10(gravity) -47270. Then I just plugged in the force for the work equation and found out that the work required is -1611907 j .For part b I just used the power equation (work/time) therefore (5388.78*34.1)/(30) and you get the answer 6125.2466. For part c i don't know what to do

If you are going to round off g to 10 you are going to have to round it off to 1.6e6 J.

For part c, what is the height difference between the two points? What is the PE of a mass at height h relative to another point?

AM
 
  • #3


I can provide a more detailed and precise response to this content. Work, power, and energy are all related concepts that describe the physical processes involved in moving objects. Work is defined as the force applied to an object multiplied by the distance it is moved. In this case, the work required to get the empty train of cars from the ground to the top of the first hill can be calculated by multiplying the force of gravity (4727 kg * 10 m/s^2) by the distance of 34.1m, resulting in a work of -1611907 joules (J). The negative sign indicates that work is being done against the force of gravity.

Power, on the other hand, is the rate at which work is done or energy is transferred. It is calculated by dividing work by time. In this scenario, the power required to bring the train to the top of the first hill in 30.0 seconds is 6125.2466 watts (W).

Finally, energy is the ability to do work and is measured in joules (J). In this case, potential energy (PE) is converted into kinetic energy (KE) as the train descends from the top of the first hill to the bottom of the 21.9m drop. The amount of PE converted into KE can be calculated by subtracting the PE at the top of the first hill (mgh = 4727 kg * 9.8 m/s^2 * 34.1m = 1611907 J) from the KE at the bottom of the drop (1/2mv^2 = 1/2 * 4727 kg * (2gh)^2 = 998774.8 J), resulting in a difference of 612132.2 J.

In conclusion, work, power, and energy are all important concepts in understanding the physical processes involved in moving objects. By using these equations and understanding their relationship, we can better analyze and predict the movements of objects, such as the train on the Cyclone roller coaster at Six Flags.
 

What is work?

Work is the transfer of energy from one object to another by the application of a force. In other words, work is done when a force acts on an object to move it in the direction of the force. The amount of work done is equal to the force applied multiplied by the distance the object moves.

What is power?

Power is the rate at which work is done or energy is transferred. It is measured in watts (W) and is equal to the amount of work done divided by the time it takes to do the work. In other words, power is a measure of how quickly work is being done.

What are the different types of energy?

The different types of energy include kinetic energy, potential energy, thermal energy, chemical energy, nuclear energy, and electromagnetic energy. Kinetic energy is the energy of motion, while potential energy is the energy an object has due to its position or condition. Thermal energy is the energy associated with the movement of particles in a substance, while chemical energy is the energy stored in chemical bonds. Nuclear energy is the energy released from the splitting or combining of atomic nuclei, and electromagnetic energy is the energy carried by electromagnetic waves such as light.

What is the law of conservation of energy?

The law of conservation of energy states that energy cannot be created or destroyed, but it can be transformed from one form to another. This means that the total amount of energy in a closed system remains constant over time. For example, if an object falls from a height, its potential energy is converted into kinetic energy as it gains speed.

How are work, power, and energy related?

Work, power, and energy are all related concepts. Work is a measure of energy transfer, and power is a measure of how quickly work is being done. Energy is the ability to do work or cause change. The relationship between work, power, and energy can be represented by the equation: work (J) = power (W) x time (s). In other words, work is equal to power multiplied by time. This equation can also be rearranged to find power (P) or time (t) if the other two values are known.

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