# Pendulum Problem: Potential energy equals? kinetic energy

by smeiste
Tags: energy, equals, kinetic, pendulum, potential
 P: 36 1. The problem statement, all variables and given/known data A pendulum consists of an object of mass m = 1.65 kg swinging on a massless string of length l. The object has a speed of 1.97 m/s when it passes through its lowest point. If the speed of the object is 0.87 m/s when the string is at 70° below the horizontal, what is the length of the string? Correct answer: 2.64 m (to 3 sig figs) 2. Relevant equations Ep = mgh Ek = 1/2mv^2 3. The attempt at a solution I tried the equation: mg(length(1-cos20°)) = 1/2mv^2 and this did not work.. it worked when I had the length and needed the velocity? 1. The problem statement, all variables and given/known data 2. Relevant equations 3. The attempt at a solution
HW Helper
P: 2,315
 Quote by smeiste 1. The problem statement, all variables and given/known data A pendulum consists of an object of mass m = 1.65 kg swinging on a massless string of length l. The object has a speed of 1.97 m/s when it passes through its lowest point. If the speed of the object is 0.87 m/s when the string is at 70° below the horizontal, what is the length of the string? Correct answer: 2.64 m (to 3 sig figs) 2. Relevant equations Ep = mgh Ek = 1/2mv^2 3. The attempt at a solution I tried the equation: mg(length(1-cos20°)) = 1/2mv^2 and this did not work.. it worked when I had the length and needed the velocity? 1. The problem statement, all variables and given/known data 2. Relevant equations 3. The attempt at a solution
Using your two speeds, you can calculate the kinetic energy at the bottom, and when in the 70 degree position [or indeed 20 degree as you are starting to use]
The reduction in kinetic energy will be accompanied by an equivalent increase in Potential energy - so you know the gain in height.

A bit of trig on the triangle formed should yield the pendulum length you are after.
 P: 36 Thank you so much!

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