Why is the ratio of displacements in springs different than expected?

  • Thread starter erisedk
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In summary, a block B attached to two springs with different spring constants is displaced and released, causing it to move a maximum distance y towards one wall. The ratio of this distance to the initial displacement x is 1/2, as determined by energy conservation.
  • #1
erisedk
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Homework Statement


A block (B) is attached to two unstretched springs S1 and S2 with spring constants k and 4k, respectively (see figure I). The other ends are attached to identical supports M1 and M2 not attached to the walls. The springs and supports have negligible mass. There is no friction anywhere. The block B is displaced towards wall 1 by a small distance x (figure II) and released. The block returns and moves a maximum distance y towards wall 2. Displacements x and y are measured with respect to the equilibrium position of the block B. The ratio y/x is

1423749846508Capture.PNG

Homework Equations

The Attempt at a Solution



I don't really know how to do this, but here's what I know:
From energy conservation, 1/2 k x2 + 1/2 (4k) x2 = 1/2 k y2 + 1/2 (4k) y2
So, I get y=x.
Which isn't the answer. The answer is (C).
I don't understand why.
 
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  • #2
What's (C) mean?
 
  • #3
Oh sorry, I meant the answer is 1/2
 
  • #4
Hint : Energy conservation is the correct method to use here. Application, though, is wrong.

When you move B x to the right, consider M2 and B to be one system(Why?).
Similarly, when B moves y to the left, consider M1 and B to be one system(Why?).

The reasoning for this can be obtained from diagram II.

Hope this helps,
Qwertywerty.
 

1. What is a displacement in a spring?

A displacement in a spring refers to the change in position of the spring from its equilibrium position. It is typically measured in meters and can be positive or negative depending on the direction of the displacement.

2. How is the displacement of a spring calculated?

The displacement of a spring can be calculated using Hooke's Law, which states that the displacement is directly proportional to the force applied to the spring and inversely proportional to the spring's stiffness (or spring constant). The formula for displacement is x = F/k, where x is the displacement, F is the applied force, and k is the spring constant.

3. What factors affect the displacement of a spring?

The displacement of a spring is affected by several factors, including the force applied to the spring, the spring's stiffness (or spring constant), the mass of the object attached to the spring, and any external forces acting on the spring.

4. How does displacement affect the behavior of a spring?

The displacement of a spring determines how much potential energy is stored in the spring. The greater the displacement, the more potential energy the spring has. This potential energy is then converted into kinetic energy as the spring returns to its equilibrium position, causing the spring to oscillate.

5. How can the displacement of a spring be used in practical applications?

The displacement of a spring has many practical applications, including in shock absorbers, car suspensions, and weighing scales. It is also used in many scientific experiments to measure the force or weight of an object. Additionally, knowing the displacement of a spring can help determine its stiffness and potential energy, which can be useful in designing and building structures that require springs.

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