Calculating Pendulum Speed: 20cm Length, 10 Degree Angle at Top - Solution

[zee]

I have no idea how to do this problem. What equation do I use?

The pendulum on my clock is 20 cm long. At the top of the swing, it makes an angle of 10 degrees with the vertical. What is the speed of the pendulum at the bottom of the swing?

The answer is 0.24 m/s, but how?

Thank you.

 

[Integral]

Use consevation of energy. The intial angle will give you the information you need to find the height for the potential energy.

 

[sporkstorms]

Conservation of energy can be a tricky thing to learn to use at first, so here's a couple of hints.

Conservation of energy tells us that K (kinetic energy) + U (potential energy) = E (total energy).

Put the origin of the coordinate system where the pendulum is at the bottom of its arc. Why do we do this? Well, what can you say about the system when the pendulum is at the origin? Its height is zero, so the potential energy (due to gravity) is also zero.

Since E = K + U, always (when energy is conserved), at this point you know E = K + 0 = K. All energy of the pendulum is kinetic.

Using this line of thinking, when is E = U?

Once you figure that out, and start writing the equaions, the problem will practically solve itself.