Pendulum swing with an angle

Dorian Gray

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Jan 20, 2012
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143
Greetings math adorers!

I was wondering if somebody could please check my work for the problem below.

A pendulum with a length 2m has a velocity of 3 m/s at its lowest point. What is the largest angle it creates relative to the horizontal as it swings. Hint: use energy conservation.


Here is my work
mgh=mv^2/2,,,,,,,,,,h=0.459 m,,,,,,,,,cos(angle) = h/r=0.459/2,,,,,,,,,,,angle=76.7 degree


Please let me know if it is correct. If it is wrong, please give suggestions on how I should correct.

Thanks!
View attachment 2363
 

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Greetings math adorers!

I was wondering if somebody could please check my work for the problem below.

A pendulum with a length 2m has a velocity of 3 m/s at its lowest point. What is the largest angle it creates relative to the horizontal as it swings. Hint: use energy conservation.


Here is my work
mgh=mv^2/2,,,,,,,,,,h=0.459 m,,,,,,,,,cos(angle) = h/r=0.459/2,,,,,,,,,,,angle=76.7 degree


Please let me know if it is correct. If it is wrong, please give suggestions on how I should correct.

Thanks!
View attachment 2363

You have correctly used energy conservation to determine h, the height the pendulum rises above its lowest point. (Note: h is not the distance from the pendulum mass up to the pendulum support level.)

A question for you: Are you sure the angle you want to find is the one shown in your sketch? Could " largest angle it creates relative to the horizontal" be something else, or is there a diagram in your book that makes this clear?

Regardless, you need to draw a more complete sketch and show the triangle(s) you are solving for. Label all dimensions and angles. In particular, please show the right triangle in which .459 is the adjacent side and 2 is the hypotenuse (if you still think that triangle is appropriate). Drawing a detailed sketch will help you immensely.
 
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