# Potential and Kinetic Energy?

I have a problem which states that Ep = Ek due to the conservation of energy.

A 5.2 kg pendulum bob is suspended from the ceiling by a 1.7 m long string. The pendulum is pulled to one side, such that the string makes a 33° angle from the vertical. Calculate the speed of the pendulum as it passes its lowest point.

mgh = (1/2)mv^2

(can subtract both masses from either side)

2(9,8)(.27) = v^2

= 2.3m/s

I thought that Potential and Kinetic energy are not equal to each other and equal the total energy in a system when added together. I would also expect that one of these energies by negative if they are to be put into an equation like this, any help, please?

I also have another question which says

mgh = (1/2)mv^2 + Fd

I don't get why work would be added to kinetic energy?

Thank you,

Alright, so basically all energies are equal to each other as long as they are in a closed system.

But for the second part why would

J = J + J

### 3 Answers

- 1 decade agoFavorite Answer
For the first question: Energy is energy. Energy is conserved in a closed system. That should explain enough right there. =-)

For the second question:

What's work measured in and what's the unit for energy? ;-)

Source(s): I had two semesters of calculus-based Physics. - Denis SLv 61 decade ago
Since you have displaced the mass from the equilibrium position you give it potential energy. The equation should read

PE(max)=KE(max)

The potential energy is max when the angle is +/-33°, where v=0.

The kinetic energy is max when the angle is 0°, where h=0.

You're right

Total Energy=PE+KE

It's only at the extremes when PE, KE=0 that you can easily derive what the values are.

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The second part looks like an air friction term where the F*d is actually taking energy away from the system. You start with mgh amount of energy and at the bottom of the pendulum swing the velocity is less than the max from above because there is a F*d term. It is some force acting to take away energy from the system.

- debydeteLv 71 decade ago
Actually the basic "law" for mechanical energy problems is "the net work done by all forces on an object (Except the force of gravity) = object's change in kinetic energy + object's change in potential energy".

Net Work = (Kf - Ki) + (Pf - Pi)

In your pendulum problem there are two forces on the pendulum bob; the force of gravity (its weight) and the tension, T , in the string. But T does no work as the pendulum swings because it is always perpendicular to the direction of motion. Therefore, the net work done on a pendulum is zero and you have;

0 = (Kf - Ki) + (Pf - Pi)

Kf +Pf = Ki + Pi (where i & f can be any two points along the pendulum's trajectory)

(1/2)MVf^2 + MgYf = (1/2)MVi^2 + MgYi

In your problem the initial height is Yi = L - LCos(33) = 1.7 - (1.7)(.84) = .27

And the initial velocity is Vi = 0

And the final height (at bottom of swing) is ; Yf =0

(1/2)Vf^2 + 0 = 0 + gYi

Vf = SqRt[2gYi]

= 2.3 m/s

Now there will be other problems where the net work is not zero and it has to be included in the calculations.