Work and Energy Problem, Help please?

In summary: You want to calculate the distance from the point (x,y) to the point (L,0).In summary, the potential energy of a two-spring system after the point of connection has been moved to position (x,y) can be expressed as Us = 1/2k((x-L)+(y-0))^2 using the distance formula. This takes into account the negligible un-stretched length of each spring and the force required to move the junction point from (±L,0) to (x,y) in the first quadrant.
  • #1
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Homework Statement


The ends of two identical springs are connected. Their un-stretched lengths Lo are negligibly small and
each has spring constant k. After being connected, both springs are stretched an amount L and their free
ends are anchored at y = 0 and x = ±L as shown . The point where the springs are connected to each
other is now pulled to the position (x,y). Assume that (x,y) lies in the first quadrant


A. What is the potential energy of the two-spring
system after the point of connection has been
moved to position (x,y). Keep in mind that the unstretched length of each spring Lo is much less
than L and can be ignored (i.e., Lo << L).
Express the potential U in terms of k, x, y, and L



Homework Equations



Us=1/2k(deltax)^2

The Attempt at a Solution



So this is what I did. L_o is negligible as stated in the problem. So +or- L is my original length(Xi).
In order for the junction pt 1 of the spring to go from (+or-L,0) to somewhere in the first quadrant of (x,y), a force has to be applied that moves the spring from (+-L,0) to (positive x, positive y).

So, taking both x and y into account for this equation I got:
Us=1/2k((Xf-(+or-L))+(Yf-Yi))^2-------------and Yi=0 so we can disregard that from the equation. Does this seem correct? I feel a bit lost on this problem.
 
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  • #2
jcfor3ver said:

The Attempt at a Solution



So this is what I did. L_o is negligible as stated in the problem. So +or- L is my original length(Xi).
In order for the junction pt 1 of the spring to go from (+or-L,0) to somewhere in the first quadrant of (x,y), a force has to be applied that moves the spring from (+-L,0) to (positive x, positive y).

So, taking both x and y into account for this equation I got:
Us=1/2k((Xf-(+or-L))+(Yf-Yi))^2-------------and Yi=0 so we can disregard that from the equation. Does this seem correct? I feel a bit lost on this problem.
You're sort of on the right track. Are you trying to figure out the length of each spring?

The Distance Formula from geometry is
D2 = (x1 - x2)2 + (y1 - y2)2
(It looks like you were not remembering it correctly.)
 

1. What is the definition of work and energy?

Work is defined as the force applied to an object multiplied by the distance the object moves in the direction of the force. Energy is the ability to do work.

2. How are work and energy related?

Work and energy are directly related as work is a measure of the change in energy of an object. When work is done on an object, its energy changes. Similarly, when an object does work, it loses or gains energy.

3. What are the different types of energy?

There are several types of energy, including kinetic energy (energy of motion), potential energy (energy of position), thermal energy (heat), chemical energy, and nuclear energy.

4. How can I solve work and energy problems?

In order to solve work and energy problems, you will need to apply the relevant equations, including the work-energy theorem (W=ΔKE), conservation of energy (KEi + PEi = KEf + PEf), and the formulas for calculating kinetic and potential energy (KE = ½mv², PE = mgh).

5. What are some real-world applications of work and energy?

Work and energy are involved in many everyday activities, such as walking, lifting objects, and driving a car. They are also crucial in various fields of science, including physics, engineering, and chemistry, and are used in the development of renewable energy sources.

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