What is the correct formula for finding tension in a pendulum bob on a string?

AI Thread Summary
To find the tension in a pendulum bob at its highest point, the correct approach involves considering both gravitational forces and the initial velocity. The initial calculation using Newton's second law yielded 16.97 N, but the correct answer is 16.6 N, indicating a miscalculation. The angle of 30 degrees applies only at the release point, not at the highest point due to the push given to the bob. Using energy conservation principles is recommended to accurately determine the highest point and the corresponding tension. This method accounts for the dynamics of the pendulum's motion more effectively.
chxmilan
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A 2 kg pendulum bob on a string that is 3m long is released with a velocity of 1 m/s when the support string makes an angle of 30 degrees with the vertical. What is the tension at the highest point of its motion?

The Attempt at a Solution


Ok so using Newton's second Law, the equation should be Force of tension =mg cos θ. Adding the numbers in =2 kg (9.80 m/s)cos 30°=16.97 N. However its telling me its wrong and the answer should be 16.6 N. I'm confused as to where I've gone wrong. I realize that I skipped over length of the string but I was told that because we're dealing the the vertical component, its not needed.
 
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What angle does it make when it's at its highest point?
 
Wouldn't the angle still be 30° at the highest point?
 
chxmilan said:
Wouldn't the angle still be 30° at the highest point?
It would be if it were released from rest at that point, but it was given a push.
 
I would suggest you to use energy instead.
 
agostino981 said:
I would suggest you to use energy instead.
One would use energy conservation to find the highest point, if that's what you mean.
 
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