What Determines the Coefficient of Static Friction in Oscillating Blocks?

In summary, the two blocks in the figure have a period of oscillation of 1.5 s on a frictionless surface. When the amplitude is increased to 36 cm, the upper block just begins to slip. The question is asking for the coefficient of static friction between the two blocks. The solution involves considering the forces involved, such as friction, normal force, and the coefficient of friction, while taking into account the period and amplitude of oscillation. The maximum acceleration that the upper block can have without slipping can be found by using the coefficient of static friction.
  • #1
Havok104
1
0

Homework Statement


The two blocks in the figure oscillate on a frictionless surface with a period of 1.5 s. The upper block just begins to slip when the amplitude is increased to 36 cm.

What is the coefficient of static friction between the two blocks?

Homework Equations





The Attempt at a Solution



I've tried to think of the forces involved (ie. friction -normal force * coefficient of friction etc)
But I'm having trouble incorporating the period and the amplitude into equations with forces in them.

Any help is greatly appreciated!
 
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  • #2
Welcome to PF!

Hi Havok104! Welcome to PF! :smile:

Hint: call the coefficient of static friction µ.

What is the maximum acceleration that the upper block can have without slipping? :wink:
 
  • #3


I would approach this problem by first identifying the key variables and parameters involved. The period of oscillation and the amplitude of oscillation are given, and the question asks for the coefficient of static friction between the two blocks.

To solve this problem, we can start by considering the forces acting on the upper block. The only horizontal force acting on the upper block is the static friction force from the lower block. This friction force must be equal to the centripetal force needed to keep the upper block in circular motion. Therefore, we can use the equation Fc = mv^2/r, where Fc is the centripetal force, m is the mass of the upper block, v is its velocity, and r is the radius of the circular motion (in this case, the amplitude of oscillation).

We also know that the period of oscillation is related to the velocity and amplitude by the equation T = 2πr/v. Rearranging this equation, we get v = 2πr/T.

Now we can substitute this expression for velocity into the centripetal force equation to get Fc = m(2πr/T)^2/r. Simplifying, we get Fc = 4π^2mr/T^2.

Next, we can consider the forces acting on the lower block. It is in contact with the surface, so there must be a normal force acting on it. This normal force must be equal in magnitude to the weight of the upper block, since the two blocks are in equilibrium. Therefore, we can write Fc = mg, where g is the acceleration due to gravity.

Finally, we can equate the two expressions for Fc and solve for the coefficient of static friction, μs. This gives us μs = 4π^2m/T^2g. Plugging in the given values of the period and the mass of the upper block, we can calculate the coefficient of static friction between the two blocks.
 

FAQ: What Determines the Coefficient of Static Friction in Oscillating Blocks?

What causes oscillations on a horizontal surface?

Oscillations on a horizontal surface are caused by a restoring force acting on an object. This restoring force can be due to gravity, springs, or other forces that pull the object back to its equilibrium position.

How is the frequency of oscillations on a horizontal surface determined?

The frequency of oscillations on a horizontal surface is determined by the mass of the object, the strength of the restoring force, and the stiffness of the surface. It can be calculated using the equation: f = 1/(2π) √(k/m), where k is the spring constant and m is the mass of the object.

What factors affect the amplitude of oscillations on a horizontal surface?

The amplitude of oscillations on a horizontal surface can be affected by the initial displacement of the object, the strength of the restoring force, and any damping forces present. Higher initial displacement and stronger restoring forces result in larger amplitudes, while damping forces decrease the amplitude over time.

How does the angle of the surface affect oscillations on a horizontal surface?

The angle of the surface can affect oscillations on a horizontal surface by changing the direction and strength of the restoring force. For example, on an inclined surface, the force of gravity acts in a different direction, causing the object to oscillate in a curved path instead of a straight line.

What is the relationship between the period of oscillations and the amplitude on a horizontal surface?

The period (T) of oscillations on a horizontal surface is independent of the amplitude. This means that changing the amplitude does not affect the time it takes for the object to complete one full oscillation. The period is only affected by the mass, restoring force, and stiffness of the surface.

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