How Much Work is Done Moving an Object Against a Spring Force?

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Homework Help Overview

The discussion revolves around calculating the work done in moving an object against a spring force. The object has a specified mass and is connected to a spring with a known spring constant and equilibrium position. The initial and final positions of the object are also provided, raising questions about the work done during the movement.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss relevant equations, including conservation of energy and work-energy relations. There is confusion about the distances involved and how they relate to the forces exerted by the spring. Some participants question the role of mass in the work calculation and the implications of starting from a position not at equilibrium.

Discussion Status

The discussion is active, with participants offering guidance on relevant equations and clarifying the problem's parameters. There is no explicit consensus on the final answer, and multiple interpretations of the problem are being explored.

Contextual Notes

Participants are navigating the complexities of the problem, including the significance of the initial and final positions relative to the spring's equilibrium position. There is uncertainty regarding the impact of mass on the work done, as well as the interpretation of potential energy changes.

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An object with inertia m = 1.5 kg is connected to a spring with spring constant k = 250 N/m and equilibrium position at x0 = 5 cm (for x > x0, the force is directed toward the origin). The object is initially at rest at position x = 10 cm. You grab the object and move it slowly to position x = 20 cm. After you finish moving it, you continue to hold the object at rest at its new position. How much work did you do on the object? I know the main equations but i just done know what to do. Please Help!
 
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Welcome to PF;
You know the main equations, so a good first step is to write them down.

You need to know - conservation of energy, work-energy relation, potential energy stored in a spring.
 
could you help me get started. With what equation? and I'm kinda confused on the 3 distances given.
 
If it requires force kx to move a mass M as distance x, then the work necessary will be (1/2)kx^2. Is that the formula you needed?
 
Lets see - the three distances are:
x0, the equilibrium position.
x1, the initial position
x2, the final position

what's the problem?

If the mass were at x0, how much force would the spring exert on it?

The mass was at rest at x1 > x0, how much force does did spring exert on it? What was the total force on it? What do you deduce from that?

You moved the mass from x1 to x2 > x1 ...
 
Did you guys get 1.25 J as the answer. And if so, why did it give me the mass of. And how does that not affect work done?

My thought process: work is the change in energy which in this case is the change in potential (atleast I think it is). So I used the equation 1/2 kx squared.
 
Notice that the mass starts off at rest at a position that is not the equilibrium position?
What would you deduce from that information?
 

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