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

In summary, the tension at the highest point of motion for a 2 kg pendulum bob released with a velocity of 1 m/s and a string length of 3m at an angle of 30 degrees is 16.97 N. However, using energy conservation may be a better approach in finding the highest point.
  • #1
chxmilan
2
0
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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  • #2
What angle does it make when it's at its highest point?
 
  • #3
Wouldn't the angle still be 30° at the highest point?
 
  • #4
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.
 
  • #5
I would suggest you to use energy instead.
 
  • #6
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.
 

1. What is a pendulum bob on a string?

A pendulum bob on a string is a simple pendulum consisting of a small mass, known as the bob, attached to a string or rod that is suspended from a fixed point. It is a common tool used in physics to demonstrate the principles of harmonic motion and gravity.

2. How does a pendulum bob on a string work?

A pendulum bob on a string works by converting potential energy into kinetic energy and back again as it swings back and forth. The bob's motion is governed by the laws of gravity, which cause it to accelerate towards the center point of the pendulum's swing, known as the equilibrium position.

3. What factors affect the motion of a pendulum bob on a string?

The motion of a pendulum bob on a string is affected by three main factors: the length of the string, the mass of the bob, and the amplitude of the swing. The longer the string, the slower the pendulum will swing. The heavier the bob, the faster it will swing. And the higher the amplitude, the longer it takes for the pendulum to complete one full swing.

4. What is the period of a pendulum bob on a string?

The period of a pendulum bob on a string is the time it takes for the pendulum to complete one full swing, from its starting position, through its equilibrium position, and back to its starting position. The period is affected by the length of the string and the acceleration due to gravity, and can be calculated using the formula T = 2π√(L/g), where T is the period, L is the length of the string, and g is the acceleration due to gravity.

5. How is a pendulum bob on a string used in scientific experiments?

A pendulum bob on a string is commonly used in scientific experiments to study the principles of harmonic motion and gravity. It can be used to measure the acceleration due to gravity, as well as to demonstrate concepts such as period, frequency, and amplitude. It is also used in the construction of timekeeping devices such as pendulum clocks.

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