SOLUTION: A pendulum has a string with the length 1.2 m. You hold it at an angle of 22 degrees to the vertical and release it. The pendulum bob has a mass of 2.0 kg. What is the potential e

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Question 1206077: A pendulum has a string with the length 1.2 m. You hold it at an angle of 22 degrees to the vertical and release it. The pendulum bob has a mass of 2.0 kg.
What is the potential energy before it is released?___J. What will be the velocity of the pendulum through the bottom of its swing? ___m/s.
Note:- Use g = 10 m/s^2. Use geometry to determine the height when released.
Found 3 solutions by mananth, ikleyn, math_tutor2020:
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website!
(1.2-h)= cos 22 deg*1.2
1.2 -h = 1.1126
h= 1.2- 1.1126
h= 0.0874 m
PE = m*g*h
PE = 2*10*0.0874
Potential energy =1.748 J

At the bottom of the swing, all of the potential energy will be converted into kinetic energy.
KE = 1/2 m v ^2
K E = 1.748= 1/2 *2*v^2
1.748 = 1/2* 2*v^2
v= 1.322 m/s the velocity of the pendulum through the bottom of its swing
.

Answer by ikleyn(52813)   (Show Source):
You can put this solution on YOUR website!
.

In the post by @mananth the logic, the numbers and calculations are correct.

The only deficiency is that the plot is inconsistent and irrelevant.

Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!

Tutor @mananth has an incorrect diagram. Or at the very least, it's misleading.
The pendulum should sweep out part of a circle, but the fixed point of the pendulum (the point where it's hanging from) should be the center of the circle. It should not be a point on the circle itself.

This is what the diagram should look like