# Finding the Length and Velocity of a Spring in Circular Motion

• Ruskointhehizzy
In summary, the ball moves at .73m/s when it is attached to the spring and the spring has a spring constant of 35.0 N/m.
Ruskointhehizzy

## Homework Statement

A ball of mass 0.250 kg is attached to a spring with spring constant 35.0 N/m and relaxed length 0.200 m. The other end of the spring is attached to a vertical pole. The ball is set into circular motion in the horizontal plane with the spring making an angle 25degrees with the pole.
a) find the length of the spring during this motion.
b) find the velocity of the ball during this motion.

## The Attempt at a Solution

I have set it up to find v, but am stuck on how to find x. Thank you very much.

#### Attachments

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ephphatha16
##T_s = kx## should be the missing equation. Simply the equation of the spring extension.

Some comments what you calculate where would make it easier to follow.

ephphatha16 and Ruskointhehizzy
mfb said:
##T_s = kx## should be the missing equation. Simply the equation of the spring extension.

Some comments what you calculate where would make it easier to follow.
Okay I thought so but wasn't sure. I will be sure to include comments from here on forth. Thank you very much! I love this site you guys are the best

mfb
I’d just like to point out, “L+x” is not a final answer to part a). The ‘extension’ x is a variable introduced by you, not given in the problem.

If you use T_s = kx in your vertical equation (on the left) then you can express x in terms of known variables, and then you could calculate the length explicitly.

ephphatha16
Nathanael said:
I’d just like to point out, “L+x” is not a final answer to part a). The ‘extension’ x is a variable introduced by you, not given in the problem. .
I set Tx to kx and found x using known terms and it gave me .077 which is correct.
using the tension I found and the new length I was able to calculate the velocity at .73m/s which is also correct. Thanks for pointing that out.

thanks for the help everyone! I really enjoyed this problem.

## 1. What is a spring problem?

A spring problem is a physics concept that involves the calculation of the force exerted by a spring when it is stretched or compressed. It is commonly used in engineering and design to determine the behavior and stability of objects.

## 2. How do I solve a spring problem?

Solving a spring problem involves using Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position. This can be represented by the equation F = -kx, where F is the force, k is the spring constant, and x is the displacement.

## 3. What is the spring constant?

The spring constant is a measure of the stiffness of a spring. It is represented by the letter k and is measured in units of force per distance, such as N/m or lb/in. The higher the spring constant, the stiffer the spring.

## 4. What are some common applications of spring problems?

Spring problems are commonly used in various fields such as mechanical engineering, civil engineering, and architecture. They are used in designing suspension systems, shock absorbers, and bridges, among other things.

## 5. What should I do if I am having trouble with a spring problem?

If you are having trouble with a spring problem, it is best to review the basic principles of Hooke's Law and ensure that you understand the concepts involved. You can also seek help from a tutor or consult with a colleague who has experience with spring problems.

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