# Charged mass connected to spring, swung in circle in mag. field

1. May 18, 2013

### clubguppy

1. The problem statement, all variables and given/known data
A spring with an unstretched length of 20 cm and a force constant of 100 N/m is attached to a 2-kg mass with a charge of 3.0 C. The mass is swung in a circle in a zero gravity environment, so that the spring is perfectly horizontal and is parallel to the radius of the circle, as shown at right. A vertical 1.5-T magnetic field permeates the entire region.
[Broken]

If the mass is moving at 5 m/s, what is the maximum radius of its motion?

2. Relevant equations
Centripetal Force: $F= \frac{mv^{2}}{r}$
Hooke's Law: $F=kx$ where k is the spring constant and x is elongation (how long the string is stretched)
Magnetic Force: $F = qvBsin \theta$

3. The attempt at a solution
I tried qvBsin(90 degrees) = $qvB =F= \frac{mv^{2}}{r} + kr$
I assumed the force on the spring itself is the tenion (the constant * how long it stretched)

Last edited by a moderator: May 6, 2017
2. May 18, 2013

### mukundpa

What is x in F = kx ?

3. May 18, 2013

### clubguppy

I have updated the information in the question.

Last edited by a moderator: May 6, 2017
4. May 18, 2013

### mukundpa

is the elongation is equal to radius of the circular path?

5. May 18, 2013

### clubguppy

response

Yes, that is what I assumed. But, I can't get the radius in real number. What did I do wrong? Do you have suggestions for what I should do?

Should I change something about $qvB =F= \frac{mv^{2}}{r} + kr$ or do something different?

Last edited: May 18, 2013