Question

A ball of mass 540 g hangs from a spring whose stiffness is 155 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?

Answer 1

I'm going to assume the diagram gives the tension in the string, because with what you stated you're missing a degree of freedom. Only two equations can be developed (Sum of forces = 0 in both the x and y direction). However, we're missing the tension's magnitude, spring forces magnitude, and spring forces direction.