What would be the relaxed length of the spring?

[kdunkzz]

Homework Statement

A ball of mass 620 g hangs from a spring whose stiffness is 115 Newtons per meter. A string is attached to the ball and you are pulling the string to the right, so that the ball hangs motionless, as shown in the figure. In this situation the spring is stretched, and its length is 15 cm.

What would be the relaxed length of the spring, if it were detached from the ball and laid on a table?

Homework Equations

I wish I knew...

The Attempt at a Solution

I keep getting 10 cm, and I can't figure out what I'm doing wrong!
.620 x 9.8= 6.076/115N/m
=0.0528 roughly 5.28cm
15-5.28= 9.7 roughly 10 cm
I have tried both 10 cm and 9.7 cm and they are both wrong

 

[gneill]

Can you explain what you're trying to do in your calculations? I can't make sense of your first line of numbers. I can see mg on the left hand side (even with no units shown), then that is set equal to some number that seems to spring from nowhere (6.076, no units given) divided by the spring constant. I don't see any logic to this. The left side is clearly not equal to the right side and there can be no doubt since they are all numbers, no variables.

Perhaps you're thinking of dividing the gravitational force on the ball by the spring constant to try to find the Δx of the spring? If so that won't work because the gravitational force is not acting along the same direction as the spring; the spring is hanging on a slant, and gravity always works vertically. So you need to look at vector components.

Did you draw a free body diagram for the forces acting on the ball?

 

[olivermsun]

I suggest you start by drawing a force diagram for the ball. The spring is pulling on the ball, but not straight up, with an amount of force that you want to figure out. Gravity and you are also pulling on the ball in various other directions...

Edit: What gneill said!