# Conservation of mechanical energy of pendulum

## Homework Statement

Consider a pendulum bob swinging. The bob follows a circular path which indicates that gravity is not the only force acting upon it.

Identify the additional force; does it affect the equation K + U = 1/2 mv2 + mgh? why or why not?

## The Attempt at a Solution

First i cannot figure out if the additional first it is talking about is the force of tension, or the force of friction on the bob by the air.

I want to say its tension but i cant figure out what to say about how tension would affect the equation or not.

If i say it is the friction force due to the air then i can say it doesnt affect the equation for a very long time because it would take the pendulum bob many oscillations before the force of friciton due to the air finally stopped the pendulum.

Any input on this would be very helpful.
Thank you :)

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ehild
Homework Helper
This question is a bit weird. There are two forces on each simple pendulum: gravity and tension. If it moves in a vertical plane, or follows some other trajectory on the surface of a sphere of radius equal to its length, depends on the initial velocity and position vectors.

The pendulum can move along a horizontal circle if the resultant force is equal to the centripetal force needed for that orbit.

ehild

I think it was referring to the pendulum moving vertically.

So tension sounds like it is the other force the question is looking for.

Can you give any insight as to why tension affects or doesnt affect the conservation of mechanical energy?

Thanks for the help :)

I think it was referring to the pendulum moving vertically.

So tension sounds like it is the other force the question is looking for.

Can you give any insight as to why tension affects or doesnt affect the conservation of mechanical energy?

Thanks for the help :)
The short answer is that it doesn't, as the tension force provides no additional kind of potential energy, U.

As for the longer answer, I may have rambled a bit, but here's my shot at it:

Well, forces like tension and the normal force are reaction forces. That means that they only act when there's something acting against them. If you let the object go, and don't let any other force act on it, nothing will happen. It will not gain any kinetic energy.

And that's what potential energy is all about. Potential energy measures how much work a conservative force (Such as a gravitational pull or electrical repulsion/attraction or a stretched/compressed spring) can do.

A tension or normal force cannot perform work on its own. It can only redirect the way energy goes. Whatever kinetic energy the pendulum bob gains comes at the expense of its gravitational potential energy, and not its "tension potential energy." And that's despite the fact that the tension force is the one making it oscillate horizontally.

Thank you RoyalCat. That was a great explanation :)

I appreciate it.