Understanding the Work-Energy Theorem: Solving the Roller Coaster Problem

In summary, the net work done on a roller coaster by a given force is equal to the change in kinetic energy of the roller coaster.
  • #1
john merrick
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Homework Statement
If it takes a force of 3943 N [parallel to the track] to pull the roller coaster up to point A, and it is pulled along 105 m of track, find the work done on the roller coaster.
Relevant Equations
E=1/2mv^2
height to point A is 65m. no friction. comes to rest at point A. total mass of the roller coaster is 650 kg.
the work-energy theorem states that the net work done on an object is equal to the change in kinetic energy of the object. kinetic energy is E=1/2mv^2. initial velocity is zero(problem doesn't say that but i think it is safe to assume). final velocity is zero. therefore the net work on the roller coaster is zero. is this correct?
 
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  • #2
Is it safe to assume that the final velocity is zero? Isn't it better to calculate than to assume?
 
  • #3
john merrick said:
therefore the net work on the roller coaster is zero. is this correct?
If the rollercoaster starts and ends at rest, then the total (net) work done on it (by all forces combined) is zero. So, yes.
 
  • #4
PeroK said:
Is it safe to assume that the final velocity is zero? Isn't it better to calculate than to assume?
question states that roller coaster comes to rest.
 
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  • #5
john merrick said:
question states that roller coaster comes to rest.
Okay, so the question setter has done all the work for you! I wonder what is the purpose of a question like this?

If I was setting the question, I would get you to calculate the required force, assuming we know the mass of the rollercoaster and the length and height of the tower. At least that question would have a purpose.
 
  • #6
PeroK said:
Okay, so the question setter has done all the work for you! I wonder what is the purpose of a question like this?

If I was setting the question, I would get you to calculate the required force, assuming we know the mass of the rollercoaster and the length and height of the tower. At least that question would have a purpose.
that is what I'm thinking. but this is just one of the questions... there is another 4 or 5 questions related to this roller coaster problem. i only put up the information necessary to answer question 1.
 
  • #7
john merrick said:
find the work done on the roller coaster.
There is a difference between the work done on a body by a given force and the net work done on the body by all forces.
The change in KE is the net work done.
It is not clear to me which is being asked for in this question.
 
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  • #8
haruspex said:
There is a difference between the work done on a body by a given force and the net work done on the body by all forces.
The change in KE is the net work done.
It is not clear to me which is being asked for in this question.
you are right i think what they want is the work done on the roller coaster by a given force( you pulling it) i'll put both answers.
 
  • #9
john merrick said:
you are right i think what they want is the work done on the roller coaster by a given force( you pulling it) i'll put both answers.
It seems to me that the error of this problem is to use the given relevant equation.
There is a force adding potential energy to the roller coaster, rather than a force slowing it down to a stop in its way up to point A.
 

1. How is work done on a roller coaster?

Work is done on a roller coaster when the force of gravity acts on the mass of the roller coaster cars, causing them to move up and down along the track. This movement requires energy, which is provided by the initial potential energy of the cars at the top of the first hill.

2. What factors affect the amount of work done on a roller coaster?

The amount of work done on a roller coaster is affected by the height of the hills, the speed of the cars, the mass of the cars, and the force of friction between the cars and the track. Additionally, the design of the track and the shape of the hills can also impact the amount of work done.

3. How does work affect the speed of a roller coaster?

The work done on a roller coaster is directly related to the change in speed of the cars. As the cars move up and down the hills, they gain and lose potential energy, which is converted into kinetic energy. This results in changes in speed throughout the ride.

4. Can the amount of work done on a roller coaster be calculated?

Yes, the amount of work done on a roller coaster can be calculated using the formula W = Fd, where W is work, F is the force applied, and d is the distance over which the force is applied. In the case of a roller coaster, the force of gravity is the main force acting on the cars, and the distance is the height of the hills.

5. How does work done on a roller coaster relate to the conservation of energy?

The work done on a roller coaster is a result of the conversion between potential and kinetic energy. According to the law of conservation of energy, energy cannot be created or destroyed, only transferred from one form to another. Therefore, the total amount of energy on a roller coaster remains constant, but it is constantly changing between potential and kinetic energy as the cars move along the track.

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