Two masses attached by a spring

In summary: Now you can apply Fnet = ma to the 2 kg mass to get the acceleration of the 2 kg mass.And since the 2 kg mass is tied to the 8 kg mass by the spring, the 2 kg mass will have the same acceleration as the 8 kg mass.So you can use Fnet = ma on the 8 kg mass also. The net force on the 8 kg mass is 4.0 N to the right and the spring force to the left.Solve for the acceleration in terms of the spring force.Okay! So I get that the acceleration for the 2kg mass is simply the spring force divided by the mass of the block (2kg) and
  • #1
fuddyduddy
13
0
This problem was on my test today and I am not sure if my solution is correct.

Homework Statement


A box of mass 2 kg and another of mass 8 kg are attached by a spring with a spring constant of 80 N/m. A 4.0 N force is applied to the 8 kg box. Both of the boxes move with a constant acceleration on a horizontal frictionless surface. Find the acceleration.


Homework Equations


Fs = -kx
Fnet = ma

The Attempt at a Solution


Here is where I'm not sure if I am right or if my classmate is right. He did this:

total mass of system = 10 kg, total applied force = 4.0 N
4 = (10 kg)(a)
a = 0.4

What I did was find the Fnet of the 8 kg box and the 2 kg box respectively and set the accelerations as equal. I think this is where I kind of went off the rails - I pictured it as the spring pulling in on both of the boxes, meaning the Fnet of the 8 kg box is 4 - Fs and the Fnet for the 2 kg is 4 + Fs.

Box A (2 kg)
Fnet = ma
a = Fnet/m
a = (4 + Fs)/2

Box B (8 kg)
a = Fnet/m
a = (4 - Fs)/8

Then set them equal: (4 + Fs)/2 = (4 - Fs)/8

Cross multiply to get: 32 + 8Fs = 8 - 2Fs
10Fs = -24
Fs = -2.4 N

When I plug in these numbers into the free body diagrams it all seems to work out, but that might be circular logic - I get an acceleration of 0.8 m/s^2

Please help! :(
 
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  • #2
Hello fuddyduddy. Welcome to PF!

fuddyduddy said:
Box A (2 kg)
Fnet = ma
a = Fnet/m
a = (4 + Fs)/2

Does the 4 N force act on the 2 kg mass or does it act only on the 8 kg mass?
 
  • #3
It acts on the 8 kg mass, the picture was as such:

[2 kg]--(spring)--[8 kg]--> 4.0 N

And thank you for the welcome! :)
 
  • #4
OK. When thinking about the forces acting on on the 2 kg mass, the force of gravity is an "action-at-a-distance" force (from the earth). All other forces on the 2 kg mass are "contact" forces coming from other objects in contact with the 2 kg mass.

So, if someone pulls on the 8 kg mass to create the 4.0 N force on the 8 kg mass, that pulling force is a contact force on the 8 kg mass, not a force on the 2 kg mass.

So, what should you write for the net horizontal force on the 2 kg mass?
 
  • #5
Okay, I see now! So the net force acting on the 2 kg block is simply the spring force directed to the right. Thank you!
 
  • #6
Yes. Good.
 

FAQ: Two masses attached by a spring

What is a "Two masses attached by a spring" system?

A "Two masses attached by a spring" system is a physical system consisting of two masses connected by a spring. The two masses are able to move freely along a horizontal or vertical axis, while the spring provides a restorative force that pulls the masses towards each other when they are displaced from their equilibrium position.

How does the spring affect the motion of the two masses?

The spring in a "Two masses attached by a spring" system acts as a restoring force, meaning that it pulls the masses towards each other when they are displaced from their equilibrium position. This affects the motion of the masses by creating oscillations, where the masses move back and forth around their equilibrium position. The properties of the spring, such as its stiffness or elasticity, can also affect the amplitude and frequency of these oscillations.

What is the equilibrium position in this system?

The equilibrium position in a "Two masses attached by a spring" system is the point where the spring is neither stretched nor compressed and the two masses are at rest. At this point, the forces acting on the masses are balanced and there is no acceleration. This can be thought of as the "natural" position of the system, where it will return to when there is no external force acting on it.

How does the mass of the two masses affect the system?

The mass of the two masses affects the "Two masses attached by a spring" system in several ways. First, the heavier the masses, the more inertia they have and the more difficult it is to change their motion. This can affect the amplitude and frequency of the oscillations. Additionally, the mass of the masses can affect the period of the oscillations, with heavier masses resulting in longer periods. Finally, the mass of the masses can also affect the amount of potential and kinetic energy in the system.

Can this system exhibit simple harmonic motion?

Yes, a "Two masses attached by a spring" system can exhibit simple harmonic motion under certain conditions. Simple harmonic motion is a type of periodic motion where the acceleration of the object is directly proportional to its displacement from its equilibrium position and is always directed towards the equilibrium position. For this system to exhibit simple harmonic motion, the spring must be ideal (massless and perfectly elastic) and the oscillations must be small.

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