Pendulum find length when it rotates

In summary, the problem involves a pendulum with a string and a sphere, released from a position of 70 degrees from vertical. The string hits a peg located a distance d below the point of suspension and rotates about the peg. The goal is to find the smallest value of d in order for the sphere to swing in a full circle centered on the peg. Using conservation of energy, the equation mgh = 0.5mv^2 can be used to find the value of d. It is important to note that the length of the string is constant throughout the rotation, which may have been a misunderstanding in the problem.
  • #1

Homework Statement


A pendulum made of a string and a sphere is able to swing in a vertical plane. The pendulum is released from a position of 70 degree from vertical. The string hits a peg located a distance d below the point of suspension and rotates about the peg. Find the smallest value of d (highest peg position) in order for the sphere to swing in a full circle centered on the peg.

How do i start this?
I understand this is hard without a pic sorry guys.
 
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  • #2
I would suggest using conservation of energy. If the peg is located at the smallest value of d, the sphere should have just barely enough energy to make it up to the top of its full circle.
 
  • #3
yeah I thought about that but I could use it at the beginning and the point where the ball barely thouch the floor.
so the equation I use it
mgh=.5mv^2
but that is not going to give me the d. The thing is that the length of the string is 10 m to begin with but I want to find out what is the new length of the string when it rotates around the peg. if you see where I am getting at.
 
  • #4
Can the length of the string change? Because I don't think you mentioned that in the problem...
 
  • #5
well the length of the string is changing
so the string is really 10 m right and then there this stick or peg some where at distance d
which causes the rope to rotate. what is the distace d or the rope distance after it rotated both d are the same
 
  • #6
Sure, the string rotates (or rather, part of it rotates), but that doesn't mean the length of the string changes. I'm fairly confident that the length of the string is supposed to be constant; it seems that you may have been misinterpreting the problem.
 

What is a pendulum and how does it work?

A pendulum is a weight suspended from a fixed point that is able to swing back and forth due to the force of gravity. The motion of a pendulum is governed by the laws of physics, specifically the conservation of energy and the laws of motion.

How does the length of a pendulum affect its rotation?

The length of a pendulum is directly related to its rotation. The longer the length of the pendulum, the slower it will swing back and forth. This is because the longer pendulum has a longer period, or amount of time it takes to complete one full swing. Similarly, a shorter pendulum will have a faster rotation.

What factors affect the length of a pendulum?

The length of a pendulum is affected by several factors, including the force of gravity, the mass of the pendulum, and the angle at which it is released. These factors all contribute to the period or rotation of the pendulum.

How do you find the length of a pendulum when it is rotating?

To find the length of a pendulum when it is rotating, you will need to measure the period of the pendulum's swing. This can be done by counting the number of swings in a given amount of time. Once you have the period, you can use the equation: T = 2π√(L/g), where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity (9.8 m/s²).

Why is it important to find the length of a pendulum when it is rotating?

Knowing the length of a pendulum when it is rotating is important because it allows us to understand and predict the motion of the pendulum. This information can also be applied to other areas of science, such as timekeeping and vibration analysis, where pendulums are commonly used.

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