# Mechanics Problems, involving spring system and gravitation

• Thundagere
In summary: The Attempt at a SolutionI honestly have no idea how to solve this one. With this equation, I can calculate the velocity of an elliptical orbit, but the way they worded the problem, so that it's between two points—well, that honestly has me stumped. I thought about taking the minimum and maximum values and finding a range, but the thing is, I don't know for certain what the semi major axis is.All help on either of these is very much appreciated!
Thundagere

## Homework Statement

A spring system is set up as follows: a platform with a weight of 10 N is on top of two springs, each with spring constant 75 N/m. On top of the platform is a third spring with spring constant 75 N/m. If a ball with a weight of 5.0 N is then fastened to the top of the third spring and then slowly lowered, by how much does the height of the spring system change?

http://img856.imageshack.us/img856/4352/screenshot20130127at101.png

## Homework Equations

Ktotal parallel = K1 + K2 + ... Kn
F = -kx

## The Attempt at a Solution

Initially, I tried adding up all the springs in the system for an equivalent spring of 210 N/m, and then solving. That didn't work and the answer was incorrect. I feel like the 5 N ball will make the first spring push back some, and the 2nd and 3rd springs push back with a different amount of force. The trouble is, I'm lacking the conceptual understanding of how to go about calculating those values.

## Homework Statement

Consider the two orbits around the sun shown below. Orbit P is circular with radius R, orbit Q is elliptical such that the farthest point b is between 2R and 3R, and the nearest point a is between R/3 and R/2. Consider the magnitudes of the velocity of the circular orbit vc, the velocity of the comet in the elliptical orbit at the farthest point vb, and the velocity of the comet in the elliptical orbit at the nearest point va. Which of the following rankings
is correct?
(A) vb > vc > 2va
(B) 2vc > vb > va
(C) 10vb > va > vc
(D) vc > va > 4vb
(E) 2va >vb√2 > vc

http://img835.imageshack.us/img835/4352/screenshot20130127at101.png

## Homework Equations

vellipse = √GM ((2/R)-(1/a))

## The Attempt at a Solution

I honestly have no idea how to solve this one. With this equation, I can calculate the velocity of an elliptical orbit, but the way they worded the problem, so that it's between two points—well, that honestly has me stumped. I thought about taking the minimum and maximum values and finding a range, but the thing is, I don't know for certain what the semi major axis is.
All help on either of these is very much appreciated!

Last edited by a moderator:
Thundagere said:
Initially, I tried adding up all the springs in the system for an equivalent spring of 210 N/m, and then solving. That didn't work and the answer was incorrect.
The behaviour of springs in series can be a bit surprising.
If you had two springs in series, each 75 N/m, that would be just the same as one spring with a constant of 75 N/m - just longer. If they undergo a total extension of x, each extends x/2, generating a force 75x/2, and adding up to 75x.

Btw, it's better to use separate threads for unrelated posts.

Last edited:
But aren't all these in parallel? Which two springs are in series?

Thundagere said:
But aren't all these in parallel? Which two springs are in series?
The two at the bottom are in parallel with each other, but as a pair they are in series with the one above.

Why isn't it

(1/kequivalent)=(1/75) + (1/75)
kequivalent=75/2

Isn't that the equation for springs in series?
Also, why are those in series? I was under the impression that two springs on either side of an object would be considered in parallel...could you explain when a spring is in parallel vs series for me?

Thundagere said:
Also, why are those in series? I was under the impression that two springs on either side of an object would be considered in parallel...could you explain when a spring is in parallel vs series for me?
If you had a mass attached to two springs, one each side, and the other ends were fixed, then that would behave as parallel. But as far as the mass on top is concerned here, they're in series. Whether they're in series or in parallel wrt the platform is a bit hard to say because neither end of the top spring is fixed. So safest is to forget about trying to classify the system this way and just work from first principles.
Create unknowns for the spring extensions and derive the force balance equations.

## 1. What is a spring system and how does it work?

A spring system is a mechanical system that consists of a spring, a mass, and a fixed support. The spring is a flexible object that can be stretched or compressed, and it exerts a force on the mass when it is deformed. This force is known as the spring force and is proportional to the displacement of the mass from its equilibrium position. When the spring force is balanced by the force of gravity, the system is said to be in equilibrium.

## 2. How do you calculate the period of oscillation in a spring system?

The period of oscillation in a spring system can be calculated using the equation T = 2π√(m/k), where T is the period in seconds, m is the mass in kilograms, and k is the spring constant in Newtons per meter (N/m). The period is the time it takes for the mass to complete one full oscillation, or back-and-forth motion, in the spring system.

## 3. What is the relationship between the spring constant and the stiffness of a spring?

The spring constant is a measure of the stiffness of a spring. It represents the amount of force required to stretch or compress a spring by a certain amount. A higher spring constant means a stiffer spring, which requires more force to deform it. The spring constant is typically measured in units of N/m.

## 4. How does gravity affect a spring system?

Gravity plays a crucial role in a spring system, as it provides the force that pulls the mass towards the earth's center. This force, known as the force of gravity, is what keeps the mass in place and allows the spring to stretch or compress. In turn, the spring exerts a force on the mass that is equal in magnitude but opposite in direction to the force of gravity, resulting in a state of equilibrium.

## 5. Can a spring system be used to measure the force of gravity?

Yes, a spring system can be used to measure the force of gravity. By measuring the displacement of the mass and knowing the spring constant, the force of gravity can be calculated using the equation F = -kx, where F is the force of gravity in Newtons, k is the spring constant in N/m, and x is the displacement of the mass from its equilibrium position in meters. This is known as Hooke's law and can be used to determine the strength of the gravitational field at a given location.

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