# B Spring on a mass that is held back

#### helmi_xyz

Summary
Spring, mass, fixed body

Hi. I have a question regarding the above image and want to know whether I am right or not. In the image there is a body with mass m and in the middle of the body there is a spring. The body is pulled upwards and then it hits two fixed rods such that the body cannot move upwards any more. Now the spring is stretched to a certain amount delta_x. Now I know the spring force which is F_s = k * delta_x. The body itself has a reaction force F_m = - F_s pointing in the upward direction. On the other hand gravity still pulls the body downwards: F_g = m*g. All in all the reaction force at each rod is F_rr = (F_m - mg)/2 pointing in the downward direction.

My goal however is to measure the force that is necessary to stretch the spring to the amount delta_x. I can measure the reaction force F_w and it should always equal -F_s independent of the mass of the body. Am I right?

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#### vco

My goal however is to measure the force that is necessary to stretch the spring to the amount delta_x. I can measure the reaction force F_w and it should always equal -F_s independent of the mass of the body. Am I right?
Yes. The force $F_w$ at the supporting structure is always equal in magnitude compared to the spring force $F_s$ because these two forces are an action-reaction pair (Newton's third law).

By the way, your free body diagram is a bit misleading since you have both internal and external forces in your system. A properly drawn free body diagram should only include external forces. Divide your system into multiple smaller systems (=multiple free body diagrams) such that internal forces of interest become external forces in the smaller systems.

I have seen these improper free body diagrams in physics textbooks also, so this "mistake" is actually quite common.

"Spring on a mass that is held back"

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