How Is Work Calculated When a Block Compresses a Vertical Spring?

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Homework Help Overview

The problem involves a block dropped onto a vertical spring, focusing on the work done by the block's weight and the spring during compression. The context includes concepts from mechanics, particularly energy conservation and spring dynamics.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the calculation of work done by the spring and the block's weight, with some attempting to apply the spring potential energy formula. Questions arise regarding the correctness of units and the definition of potential energy reference points.

Discussion Status

Some participants are exploring the relationship between gravitational potential energy and the work done by the spring. There is an acknowledgment of the need to consider the height from which the block is dropped, indicating a productive direction in the discussion.

Contextual Notes

Participants note the importance of understanding the initial height of the block before it contacts the spring, which may influence the calculations and assumptions being made.

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Homework Statement


A 315.0 g block is dropped onto a vertical spring with a spring constant k = 262.0 N/m. The block becomes attached to the spring, and the spring compresses 0.12 m before momentarily stopping. While the spring is being compressed, what work is done by the block's weight?

What work is done by the spring?

What was the speed of the block just before it hit the spring?


Homework Equations


Us = 1/2kx^2


The Attempt at a Solution


Us = 1/2 * 262 *.12^2
 
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Should be right, what is your question?
 
That is the work done by the spring right? Because it's saying it's wrong. I am getting an answer of 1.886N*m.
 
I don't understand why that equation is not working.
 
Are you sure that the units are all what you posted? Does it want you to define your zero potential in a certain way, has it located the origin for you, i.e. might it care about signs?

Yes,

F_s = -kx, so W_s = U_s = integral(-dU) = integral(-kx) = .5*kx^2
 
oh ok I got it..so for part do you just multiply that by the weight of the block?
 
You mean how do you find the speed of the block? It screams conservation of energy.
 
Ug = mgy

So is it just the formula for gravitational energy?
 
does anyone know the answer to this problem? I have the same issue... One thing to remember they block is being dropped from a height above the spring and then it compresses the spring so I need to find a way to find that height before it comes in contact with the spring
 

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