# Why does Conservation of Energy and Net Forces produce different answers?

• tkegis
In summary, the motorcycle can travel a maximum height of 500m if launched straight up, or it can travel a maximum height of 125m if launched along a curve.
tkegis

## Homework Statement

Motorcycle in a vertical loop.
Traveling at 50 m/s.
Assume g=10 m/s^2
Find the maximum height of the loop. h=?

## Homework Equations

F(net) = F(cent) + F(grav)
F(cent) = mv^2/r
F(grav) = mg

(change) KE = (change) PE
KE = 1/2 mv^2
PE = mgh

## The Attempt at a Solution

F(net) solution gives me 500m

F(cent) = F(grav)
mv^2/r = mg
v^2 = gr
v^2/g = r
r = 250m
the height is 500m

Conservation of Energy solution gives me 125m
KE = PE
1/2mv^2 = mgh
(v^2)/(2g) = h
125m = hI found this in an MCAT practice book and they said the correct answer was 500m.
Why does the conservation of energy formula not work here?

Last edited:
You haven't made the question very clear. Does the motorcycle end up going straight up? Or is it constrained to circular motion on some sort of track? If it is going straight up, your energy solution applies - all of the initial kinetic energy is converted to mgh potential energy. If on the circular track, at the top the motorcycle is moving horizontally so much of its energy is still kinetic and your energy solution does not apply. The centripetal force solution applies if the motorcycle is moving in circular motion at just the right speed to exert zero force on the track at the point of maximum height.

Vertical loop = circular motion

Assuming friction is negligible.
A ball falling down straight or parabolic will reach the ground at the same time.
Does the path taken matter?
Wouldn't the horizontal energy be converted to the vertical to reach the maximum height whether it's launched straight up or along a curve?

You are not using the Law of conservation of energy correctly. The motorcycle must have a non-zero speed at the highest point in order that the centrifugal force compensates gravity. You assume that the speed of the motorcycle is zero in your "conservation of energy equation".

EDIT:

Also your "net forces" equation involves a speed, but that is not what is given in the problem. Also, think how the height is related to the radius of a vertical loop.

50 m/s is the speed given.
The height would be twice the radius.

A height of 125m seems more realistic than 500m.
Can't argue the physics though. :)

Thank you both.

## 1. Why do we use conservation of energy and net forces separately?

Conservation of energy and net forces are two different principles used in physics to analyze the motion of objects. Conservation of energy deals with the total energy of a system, while net forces deal with the individual forces acting on an object. They are used separately because they provide different information and are used in different situations.

## 2. How do conservation of energy and net forces produce different answers?

Conservation of energy and net forces produce different answers because they are based on different principles. Conservation of energy states that the total energy of a system remains constant, while net forces take into account the individual forces acting on an object. This means that while the total energy of a system may be conserved, the forces acting on an object may still change its motion.

## 3. Which one should I use to analyze the motion of an object?

The choice between using conservation of energy and net forces depends on the situation. If you are interested in the overall energy of a system or if the forces acting on an object are constant, then conservation of energy is more suitable. However, if the forces acting on an object are changing, then net forces should be used to analyze its motion.

## 4. Can conservation of energy and net forces be used together?

Yes, conservation of energy and net forces can be used together in certain situations. For example, in a system where the forces acting on an object are constant, both principles can be used to analyze its motion. However, it is important to note that they provide different information and should not be used interchangeably.

## 5. How do conservation of energy and net forces relate to each other?

Conservation of energy and net forces are related in the sense that they both describe the motion of objects. However, they use different approaches and provide different information. While conservation of energy focuses on the total energy of a system, net forces focus on the individual forces acting on an object. Therefore, they should be used in conjunction with each other to get a complete understanding of the motion of an object.

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