# Blocks on a rotating disc connected by a spring

• Flibberti
In summary: The equation can be solved for x by using integration.Welcome to PF!If the friction force between the blocks and the disk is 0, the blocks will not rotate and the spring will remain at length l. If the friction force is not 0, the blocks will eventually reach the speed of the disk and the final extension of the spring will be maximum. You should be able to calculate that extension.If the friction force between the blocks and the disk is not 0, the blocks will eventually reach the speed of the disk and the final extension of the spring will be maximum.
Flibberti
To understand centripetal force due to friction better, I came up with this problem. I'm not entirely sure of my solution, though, so I'd be glad if someone else took it up too and suggested a way to work it out:

Two identical blocks, each of mass m, connected by a spring of spring constant k are placed on a disc of radius R rotating with an angular velocity ω. The natural length of the spring is l (<2R), and the spring is placed with its midpoint at the centre of the disc. The maximum possible frictional force on each block is inadequate to make the blocks move with uniform angular velocity ω at their positions. Describe the motion of the blocks- what will the final extension of the spring be? (The coefficient of friction between the blocks and the surface is n.)

Last edited:
Flibberti said:
To understand centripetal force due to friction better, I came up with this problem. I'm not entirely sure of my solution, though, so I'd be glad if someone else took it up too and suggested a way to work it out:

Two identical blocks, each of mass m, connected by a spring of spring constant k are placed on a disc of radius R rotating with an angular velocity ω. The natural length of the spring is l (<2R), and the spring is placed with its midpoint at the centre of the disc. The maximum possible frictional force on each block is inadequate to make the blocks move with uniform angular velocity ω at their positions. Describe the motion of the blocks- what will the final extension of the spring be? (The coefficient of friction between the blocks and the surface is n.)
Welcome to PF!

If the friction force between the blocks and the disk is 0, the blocks to not rotate and the spring will remain at length l. If the friction force is not 0, the blocks will eventually reach the speed of the the disk and the final extension of the spring will be maximum. You should be able to calculate that extension.

AM

I think I have an equation;
Frictional force between the block and the disc--the spring force=the centripetal force on the block.Let l be the original length of the spring
The displacement can easily calculated by the equation
kx-μmg=m((l/2)+x)(ω^2)
Here x is the displacement, k the spring constant, μ the coefficient of friction between the mass and the disc.
This equation is applied only to one block.
The total elongation of spring is 2x..

## 1. What is the purpose of studying blocks on a rotating disc connected by a spring?

The purpose of studying this system is to understand the dynamics and behavior of objects connected by a spring on a rotating disc. This system can help us understand concepts related to circular motion, harmonic motion, and energy conservation.

## 2. How does the rotation of the disc affect the motion of the blocks connected by a spring?

The rotation of the disc causes a centrifugal force that affects the motion of the blocks. This force is directed outward from the center of rotation and can change the tension in the spring, altering the motion of the blocks.

## 3. What factors affect the frequency of oscillation in this system?

The frequency of oscillation is affected by the mass of the blocks, the stiffness of the spring, and the radius of the rotating disc. As these factors change, the frequency of oscillation will also change.

## 4. Can this system be used in real-life applications?

Yes, this system can be used in real-life applications such as amusement park rides or mechanical systems that involve rotating parts connected by springs.

## 5. How does the initial position and velocity of the blocks affect the motion of the system?

The initial position and velocity of the blocks can affect the amplitude and phase of the oscillations in the system. The initial position also affects the equilibrium position of the blocks, which can change the overall motion of the system.

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