# Trading KE for PE and back again

1. Feb 22, 2016

### David Bell

Being a Mechanical Engineer, we solve one of the easiest classical physics problems, the child's swing. It is very easy to solve heights and velocity questions. At the top of the swinging motion there is no KE and all PE. At the bottom it is all KE and no PE. But, here is the question:

WHAT ARE WE TALKING ABOUT? What is PE and KE? But more to the point: What is the transfer mechanism between KE and PE? How does energy change/convert between the energy of motion (KE) and the energy of position (PE)?

David

2. Feb 22, 2016

### drvrm

well transformation of energy takes place in nature as well as in our daily life. its the conceptual analysis which leads to the answer. i think you do an exercise of the free body diagram of the forces acting on the swing and the translation /displacement of the swing ; then try to calculate the work done by the forces or against the forces - you should get the answer about mechanism of transfer.

3. Feb 22, 2016

### jbriggs444

What are PE and KE? They are, to some extent, just bookkeeping entries. They are computed numeric quantities that are a convenient way of summarizing one aspect of a physical system. You might imagine them as analogous to the way a FICA credit score summarizes your credit report.

Kinetic energy is the quantity computed by $KE = \frac{1}{2}mv^2$. It is the energy that a body possesses by virtue of its motion. For an object propelled by a constant force, it turns out to be equal to the force propelling the object multiplied by the distance (in that same direction) over which that force acts. Force multiplied by distance is called "work". The fact that the change in kinetic energy is equal to work done is the "work energy theorem".

Some forces (gravity, electrostatic repulsion, ideal springs, compressed air) are "conservative". If you move an object against these forces and then allow it to rebound, the force on the forward stroke and the force on the return stroke will be equal and opposite. More technically, the work done by a conservative force on the forward stroke will be equal to the work done on the return stroke, even when the forward path and the return path are not identical. All that matters is the starting and ending positions, not the path by which they are reached.

Since the work done (and, hence, the kinetic energy produced) going between two points is always the same, we can give this quantity a name, "potential energy". We pick an arbitrary fixed ending point and make "potential energy" a function of the starting point alone. Potential energy is then the kinetic energy that an object would gain when moving from the given starting point to the agreed upon reference point when subject to the conservative force alone.

It is then no surprise that potential energy transfers to kinetic energy. It does so by definition. The mechanism is nothing more than the application of whatever conservative force one is talking about.

Last edited: Feb 22, 2016
4. Feb 22, 2016

### Staff: Mentor

5. Feb 24, 2016

### geir arge norway

I liked your question very much.

Work done by the gravitational force is about taking energy into or out of the gravitational field.

When a force does work upon an object, there must be a displacement of the point where the force attacks the object. If the force is directed the same way as the displacement, energy is transferred into the object. If the force is directed towards the direction of the displacement, energy is transferred out of the object.

In your example we can look at the situation when the child on the swing is lifted. The gravitational force is downwards, the displacement is upwards. Energy is taken out of the child and into the gravitational field. It will be stored in the field until the child is released. (At the same time the adult pushing the child, transfer energy into the child. We can say that energy flows from the adult through the child and into the gravitational field).

Now we look at what happens to the energy when the child is released.The gravitational force is acting downwards, that is in the same direction as the displacement, and energy is transferred into the child again and out of the gravitational field. (The rope is also pulling the child, but the pull is at right angle to the displacement, so it neither transfers energy into nor out of the child.)

In this analysis nothing has been said about what sort of energy it is talk about. That is not necessary. It is the transfer that is important to understand.

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6. Feb 24, 2016

### Staff: Mentor

It starts with Newton's 2nd law, F = ma. In your pendulum problem, take the dot product of the force balance with the velocity vector and integrate with respect to time.

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