Two springs X and Y have spring constants k and 2k respectively.Spring X is stretched by a force F and spring Y is stretched by a force 2F. Each spring obeysHooke’s law during the extension.The work done in stretching spring X is WX and the work done in stretching spring Y is WY.What is the relationship between WX and WY?[1] 1A WY =WX2B WY = WXC WY = 2WXD WY = 4WX

Question

Two springs X and Y have spring constants k and 2k respectively.Spring X is stretched by a force F and spring Y is stretched by a force 2F. Each spring obeysHooke’s law during the extension.The work done in stretching spring X is WX and the work done in stretching spring Y is WY.What is the relationship between WX and WY?[1] 1A WY =WX2B WY = WXC WY = 2WXD WY = 4WX

Answer 1

The Answer is C

Answer 2

The work done in stretching a spring can be calculated using the formula W = (1/2)kx^2, where W is the work done, k is the spring constant, and x is the displacement of the spring.

In the given scenario, spring X is stretched by a force F, and spring Y is stretched by a force 2F. Since the force applied to spring Y is twice that of spring X, the displacement of spring Y would also be twice that of spring X. Let's assume the displacement of spring X is represented by x.

Therefore, the displacement of spring Y would be 2x. Now we can calculate the work done in stretching each spring.

Work done in stretching spring X (WX) = (1/2)kx^2
Work done in stretching spring Y (WY) = (1/2)(2k)(2x)^2 = 4(1/2)kx^2 = 2kx^2

Comparing the values of WX and WY, we can see that

WY = 2kx^2 = 2(WX)

Therefore, the relationship between WX and WY is:

C) WY = 2WX

Answer 3

To find the relationship between WX and WY, we can use the work-energy principle. According to this principle, the work done on an object is equal to the change in its potential energy. For a spring, the potential energy stored in it is given by the formula U = (1/2)kx^2, where U is the potential energy, k is the spring constant, and x is the displacement from the equilibrium position.

Now, let's analyze the situation:

For spring X: The work done WX is equal to the change in potential energy UX. Since the spring X is stretched by a force F, the displacement is x1, and the potential energy UX is given by UX = (1/2)kx1^2.

For spring Y: The work done WY is equal to the change in potential energy UY. Since the spring Y is stretched by a force 2F, the displacement is x2, and the potential energy UY is given by UY = (1/2)(2k)x2^2.

To compare WX and WY, we need to compare UX and UY:

UX = (1/2)kx1^2
UY = (1/2)(2k)x2^2

Now, let's substitute the values of x1 and x2:

We can assume that the forces applied are such that x1 and x2 are proportional. Therefore, we can write x2 = 2x1.

Substituting this value into UY:

UY = (1/2)(2k)(2x1)^2
= (1/2)(2k)(4x1^2)
= 4(kx1^2)
= 4UX

From the above calculation, we can conclude that UY = 4UX.

Since WX is equal to UX and WY is equal to UY, the relationship between WX and WY is:

WY = 4WX

Therefore, the correct answer is option D: WY = 4WX.