# Spring on a mass that is held back

• helmi_xyz
In summary, the conversation discusses a body with mass m attached to a spring and pulled upwards until it hits two fixed rods. The reaction force at each rod is calculated to be F_rr = (F_m - mg)/2 pointing downwards. The goal is to measure the force necessary to stretch the spring to a certain amount, and it is determined that the reaction force at the supporting structure, F_w, should always equal -F_s independent of the mass of the body. It is also mentioned that the free body diagram used in the conversation may be misleading and suggests dividing the system into smaller systems for a more accurate representation.
helmi_xyz

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?

helmi_xyz said:
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.

## 1. How does the spring force change when a mass is held back?

When a mass is held back, the spring force remains constant until the mass is released. This is because the spring is still stretched or compressed to the same length, and therefore exerts the same force on the mass.

## 2. What happens to the spring's potential energy when a mass is held back?

When a mass is held back, the spring's potential energy increases. This is because the spring is being stretched or compressed further than its equilibrium position, and therefore has more stored energy.

## 3. How does the period of oscillation change when a mass is held back?

The period of oscillation, or the time it takes for one complete back-and-forth motion, remains constant when a mass is held back. This is because the period is determined by the mass and spring constant, which do not change when the mass is held back.

## 4. Does the amplitude of oscillation change when a mass is held back?

The amplitude of oscillation, or the maximum displacement from equilibrium, does not change when a mass is held back. However, the amplitude may appear smaller if the mass is not released from the same starting point as when it was not held back.

## 5. How does the frequency of oscillation change when a mass is held back?

The frequency of oscillation, or the number of oscillations per unit time, remains constant when a mass is held back. This is because the frequency is determined by the mass and spring constant, which do not change when the mass is held back.

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