A mass hung from two attached springs

• shawli
In summary, the conversation discusses the concept of finding the total extension distance of a pair of light springs with different spring constants, holding an object of mass m at rest. The attempt at a solution involves treating the two springs as a single device and using the equation Fnet=0 to find the total extension distance. However, this approach is incorrect as the forces on each spring will be different. Instead, each spring should be treated as a separate system and the total distance can be found by adding the individual distances calculated using k1x = mg and k2x = mg. Clarification is needed to fully understand the system.

Homework Statement

A light spring with constant k1 is hung from an elevated support. From its lower end a second light spring is hung, which has spring constant k2. An object of mass m is hung at rest from the lower end of the second spring.

a) Find the total extension distance of the pair of the springs.

F= ma
Fs = kx

The Attempt at a Solution

I treated the two springs as a single device and made the following equation for the forces acting on the mass:

Fnet = 0
Fs1 + Fs2 - mg = 0
k1x + k2x = mg
(k1 + k2)x = mg
x = mg/(k1 + k2)

But this answer is incorrect. (Correct answer: x = mg(1/k1 + 1/k2).

Would someone be able to clarify what is happening in this system? I seem to be missing something...

Seems like you need to treat each spring as a separate system. They have different spring constants so will put out different forces.

k1x = mg gives x1=mg/k1 similarly x2 = mg/k2
add x1 and x2 gives you total distance the spring is stretched.

Just my \$0.02, this is my first year taking calculus based physics as well.

Hm I see. I was wrong to assume the forces on each spring would be the same...

Thank you! And I hope your physics course(s) are going well :)

What is a mass hung from two attached springs?

A mass hung from two attached springs is a physical system where a mass is suspended from two springs that are attached at the top. The mass can move up and down, causing the springs to stretch and compress.

How does the mass affect the behavior of the springs?

The mass affects the behavior of the springs by changing their equilibrium length. When the mass is added, the springs stretch and the equilibrium length becomes longer. When the mass is removed, the equilibrium length returns to its original state.

What factors affect the frequency of oscillation?

The frequency of oscillation is affected by the mass of the object, the stiffness of the springs, and the force of gravity. A heavier mass will have a lower frequency, while stiffer springs and a higher force of gravity will result in a higher frequency.

How do the two springs work together to support the mass?

The two springs work together to support the mass by evenly distributing the weight. As the mass moves up and down, one spring stretches while the other compresses. This allows for a more stable and balanced system.

What are some real-life applications of a mass hung from two attached springs?

This type of system is commonly used in physics experiments to study the behavior of springs and oscillations. It can also be found in various mechanical objects, such as car suspensions and door closers, that use springs for support and movement.