# Work-Energy: Finding Contact Force at Lowest Point

• johnchen25
In summary, the conversation discusses a problem involving a skater sliding down a parabolic track with known height and a quadratic equation in terms of x and y. The goal is to find the contact force between the skater's wheels and the track at the lowest point, neglecting friction. The solution involves considering the motion as purely horizontal and identifying the force involved.
johnchen25

## Homework Statement

Suppose a skater is sliding down a parabolic track of known height of 12 meters. You are also given the quadratic equation of the track in terms of x and y, which are in meters. Neglecting friction, how would you find the contact force between his wheels and the track at the lowest point (the minimum of the quadratic equation)?

y = (12/121) x^2

## The Attempt at a Solution

I'm not sure how to attack this problem. Any help would be greatly appreciated!

At the lowest quadratic minimum, the motion is purely horizontal.
What force(s) are involved?
It appears to me to be a very simple problem with only one force . . .

Yeah, it seemed too simple to be correct...

## 1. How do I calculate the contact force at the lowest point in a work-energy problem?

The contact force at the lowest point can be calculated by using the work-energy theorem, which states that the work done by the contact force is equal to the change in kinetic energy of the object. Therefore, the contact force can be found by taking the difference between the initial and final kinetic energies of the object.

## 2. Do I need to consider any other forces besides the contact force in a work-energy problem?

Yes, in a work-energy problem, it is important to consider all the forces acting on the object, including gravitational force, normal force, and any other external forces. This is because the total work done on the object is equal to the sum of work done by all these forces.

## 3. Can the contact force at the lowest point be negative?

Yes, the contact force at the lowest point can be negative if the object is losing kinetic energy. This can happen if the contact force is acting in the opposite direction of the object's motion, resulting in negative work being done on the object.

## 4. What happens to the contact force at the lowest point if the object changes direction?

If the object changes direction at the lowest point, the contact force will also change direction. This is because the contact force is always perpendicular to the surface of contact, and as the object changes direction, the surface of contact also changes.

## 5. Can the work-energy theorem be used to find the contact force at any point in a work-energy problem?

No, the work-energy theorem can only be used to find the contact force at the lowest point in a work-energy problem. This is because the theorem assumes that the work done by all the forces acting on the object is constant, which is only true at the lowest point.

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