Solving the Pendulum Problem: Find Speed at Bottom of Path

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In summary, the conversation discusses finding the speed of a bob of a pendulum with a length of 1.2m when released from a 40 degree angle from the vertical. The equations for potential and kinetic energy are mentioned, and the conversation leads to solving for the velocity at the bottom of the path. The final solution is approximately 2.35 m/s.
  • #1
bfr
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Homework Statement



The bob of a pendulum 1.2m long is pulled aside so the string is 40 degrees from the vertical. When the bob is released, with what speed will it pass through the bottom of its path?

Homework Equations



PE=mgh
KE=(mv^2)/2

The Attempt at a Solution



Well, I started out with cos 40=x/1.2 and found x to be approximately .92, but I don't exactly know where to go from there.
 
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  • #2
Well, you wrote down the expressions for KE and PE. What do you think you should do with them? Think conservation.
 
  • #3
Wait...PE+KE is always a constant, right? So when the bob is first released at 40 degrees, it as zero kinetic energy, and PE=mgh=9.8(1.2-.92)~=2.75, where .92 is the solution to "cos 40=x/1.2". So, at the bottom of its path, it's height will be zero...right? Which leaves me with m(9.8)(0)+.5(m)(v^2)=2.75. Can I just eliminate "m" from the equation and solve from there?
 
  • #4
You're close.

bfr said:
PE=mgh=9.8(1.2-.92)~=2.75

There should be an m on the right hand side. You've only accounted for the gh.

Which leaves me with m(9.8)(0)+.5(m)(v^2)=2.75. Can I just eliminate "m" from the equation and solve from there?

You can eliminate the m, but only after you make the correction on the right side of the equation. Do you see what I'm talking about?
 
  • #5
Oh, yeah...thanks!

So m(9.8)(0)+.5(m)(v^2)=2.75m -> .5v^2=2.75 -> v~=2.35 ?
 
  • #6
Yes, that's it.
 

1. What is the Pendulum Problem?

The Pendulum Problem is a physics problem that involves finding the speed of a pendulum at the bottom of its path.

2. What factors affect the speed of a pendulum at the bottom of its path?

The speed of a pendulum at the bottom of its path is affected by the length of the pendulum, the mass of the pendulum bob, and the angle at which the pendulum is released.

3. How can the speed of a pendulum at the bottom of its path be calculated?

The speed of a pendulum at the bottom of its path can be calculated using the equation v = √(2gh), where v is the speed, g is the gravitational acceleration, and h is the height of the pendulum at the bottom of its path.

4. What is the significance of solving the Pendulum Problem?

Solving the Pendulum Problem allows us to understand the principles of conservation of energy and motion, as well as apply these principles to real-life scenarios.

5. Are there any real-world applications of the Pendulum Problem?

Yes, the Pendulum Problem has many real-world applications, such as in the design of clocks, amusement park rides, and seismometers for measuring earthquakes.

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