Pendulum Problem: Potential energy equals? kinetic energy


by smeiste
Tags: energy, equals, kinetic, pendulum, potential
smeiste
smeiste is offline
#1
Oct16-11, 09:36 PM
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
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PeterO
PeterO is offline
#2
Oct17-11, 07:00 AM
HW Helper
P: 2,316
Quote Quote by smeiste View Post
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.
smeiste
smeiste is offline
#3
Oct17-11, 12:41 PM
P: 36
Thank you so much!


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