Position of Block when Spring Stops

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The discussion revolves around the mechanics of a block attached to a spring on a frictionless surface, subjected to a constant applied force. When the block stops, the spring force equals the applied force, leading to a net force of zero. Using Hooke's law, the position of the block at stopping is calculated to be 0.08 m, with the work done by the applied force being negative. There is confusion regarding whether the block stops while the force is still acting, which is clarified by understanding that the forces balance at the stopping point. The calculations for work done by both the applied force and the spring force are also discussed, emphasizing the importance of sign conventions in the results.
mochabcha
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position of a spring!

Okay, Here's the problem
The block in Figure 7-11a (Figure not important) lies on a horizontal frictionless surface and is attached to the free end of the spring, with a spring constant of 35 N/m. Initially, the spring is at its relaxed length and the block is stationary at position x = 0. Then an applied force with a constant magnitude of 2.8 N pulls the block in the positive direction of the x axis, stretching the spring until the block stops. Assume that the stopping point is reached. (a) What is the position of the block? (b) What is the work that has been done on the block by the applied force? (c) What is the work that has been done on the block by the spring force?

(a) I drew a free body diagram and it seems like when the block stops the spring force catches up to the applied force counteracting it and stopping the motion of the block. So, Hooke's law states that F(spring) = -kx; since F(spring) = F(applied) --> F(applied) = -kx.
I crunched those numbers and got -.08 which made sense because the applied force is going to be positive [f(s) is negative in Hooke's law and x being a negative number will cancel the negatives].
BUT THAT'S WRONG what's the problem!
 
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Does the block stop WHILE the force is still acting? If this is so then there is a point at which the net force on the block is zero. That means the friction (which will be opposite to instantaneous velocity), the spring force and the applied force will give rise to a net zero force at what you call the "stopping point". Rest of the problem seems pretty standard to me.
 
The force is negative, so it's -2.8N and you should get 0.08 m. Then you can find the work which is negative too.
 
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