Finding x: Block Sliding on Spring SHM

In summary, a block of mass m attached to a horizontal spring with constant k has another block of mass m resting on top of it, with a coefficient of static friction mu between the two blocks. When the spring is initially at equilibrium length and given a push, the top block moves in SHM. At a certain distance from equilibrium, the top block starts to slide off the bottom one. The point at which this occurs is when umg=ma. To find the x in terms of the given quantities and g, the spring force must equal the frictional force. This also tells us the maximum acceleration the top block can withstand before sliding. The acceleration of the system can be found as a function of distance from equilibrium using the force on
  • #1
physicsss
319
0
A block of mass m is attached to a horizontal spring with constant k. resting on top of this block is another block of mass m. a coefficient of static friction mu exists between the two blocks. now suppose the spring is initially at equilibrium length, and someone gives it a push. the block moves in SHM in response. At a certain distance from equilibrium, the top block starts wo slide off the bottom one, find the x in terms of the given quantities and g.

So with the the moment when the top block slides off the block is when umg=ma? and where do I go from here?
 
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  • #2
[tex]
\mu mg = kx
[/tex]

The spring force = the frictional force.
 
  • #3
physicsss said:
So with the the moment when the top block slides off the block is when umg=ma?
Right. So this tells you the maximum acceleration that the top block can withstand before it starts sliding. So find the acceleration of the system as a function of distance from the equilibrium postion. (You know the force on the system from the spring, and you know the mass of the system.)
 
  • #4
Hey futb0l,

Are you sure about that? I could be wrong but for the top block [tex]ma <_= \mu m g [/tex] (couldn't figure out less than or equal sign) . So when it isn't slipping [tex] kx = 2ma [/tex]
 

FAQ: Finding x: Block Sliding on Spring SHM

What is "Finding x: Block Sliding on Spring SHM"?

"Finding x: Block Sliding on Spring SHM" is a scientific experiment that involves studying the motion of a block sliding on a spring that is undergoing simple harmonic motion (SHM). This experiment aims to determine the displacement of the block, represented by the variable x, over time as the spring oscillates.

Why is this experiment important?

This experiment is important because it allows us to study the principles of SHM and its application in real-world scenarios. It also helps us understand the relationship between displacement, time, and other variables involved in SHM, which has many practical applications in fields such as engineering and physics.

How is the displacement of the block determined in this experiment?

The displacement of the block is determined by measuring the position of the block at different time intervals as it slides on the spring. This data is then used to plot a graph of displacement vs. time, from which the displacement of the block can be calculated at any given time.

What factors can affect the displacement of the block in this experiment?

The displacement of the block can be affected by several factors, including the amplitude and frequency of the spring's oscillations, the mass of the block, and any external forces acting on the block. The stiffness of the spring and the surface on which the block is sliding can also play a role in determining the displacement.

How is this experiment set up and conducted?

To conduct this experiment, a spring is attached to a horizontal surface, and a block is placed on top of the spring. The displacement of the block is measured using a ruler or other measuring device at different time intervals as the spring undergoes SHM. The data is then recorded and used to analyze the relationship between displacement and time.

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