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

[john merrick]

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?

 

[PeroK]

Is it safe to assume that the final velocity is zero? Isn't it better to calculate than to assume?

 

[PeroK]

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.

 

[john merrick]

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.

 

[PeroK]

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.

 

[john merrick]

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.

 

[haruspex]

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.

 

[john merrick]

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.

 

[Lnewqban]

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.