How to find frequencies giving the coeffiecent friction and amplitude?

In summary, the conversation discusses a book placed on a horizontal wooden plane undergoing simple harmonic motion with an amplitude of 1.0 m and a coefficient of friction between the book and the plane of μ = 0.5. The frequency of the horizontal wooden platform when the book is about to slip is being determined. The equation A*cos(ω t) is mentioned but the individual is unsure of which equation to use. The concept of force acting on the book is also brought up.
  • #1
kelambumlm
5
0
A book is placed on a horizontal wooden plane that is undergoing simple harmonic
motion with an amplitude of 1.0 m. The coefficiet of friction btween the book and
the horizontal wooden plane is given by μ = 0.5. Determine the frequebcy of the
horizontal wooden platform when the book is about to slip from the horizontal
wooden plane.
 
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  • #2
kelambumlm said:
A book is placed on a horizontal wooden plane that is undergoing simple harmonic
motion with an amplitude of 1.0 m. The coefficiet of friction btween the book and
the horizontal wooden plane is given by μ = 0.5. Determine the frequebcy of the
horizontal wooden platform when the book is about to slip from the horizontal
wooden plane.
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  • #3
i have no idea what equation that i must to use.
1st freq = omega/2pi
vmax=omega*Amplitude

what about A*cos(ω t)
 
  • #4
What can you say about the force acting on the book when it is about to slip?
 

1. What is the coefficient of friction and how does it relate to frequency and amplitude?

The coefficient of friction is a measure of the resistance between two surfaces in contact. It is typically denoted by the symbol "μ" and can range from 0 to 1, with higher values indicating a greater resistance to motion. In the context of finding frequencies, the coefficient of friction is important because it affects the amplitude of a vibrating system. Higher coefficients of friction result in lower amplitudes, while lower coefficients of friction result in higher amplitudes.

2. How do I determine the coefficient of friction for a particular system?

The coefficient of friction can be determined experimentally by measuring the force required to move one surface over another. This force is divided by the normal force, or the force perpendicular to the surfaces, to calculate the coefficient of friction. It can also be estimated based on the materials and surface conditions of the system.

3. How do I find the frequency that will result in a desired coefficient of friction?

The relationship between frequency and coefficient of friction is not linear, so there is no one frequency that will result in a specific coefficient of friction. However, as frequency increases, the coefficient of friction generally decreases. To find the frequency that will result in a desired coefficient of friction, it is important to experimentally test different frequencies and measure the resulting coefficient of friction.

4. Can I use mathematical equations to calculate the frequency and coefficient of friction for a system?

Yes, there are equations that can be used to calculate the frequency and coefficient of friction for a system. These equations take into account factors such as the mass, stiffness, and damping of the system, as well as the surface properties. However, these equations may not always accurately predict the behavior of a real-world system and it is still important to experimentally test and verify the results.

5. What are some factors that can affect the coefficient of friction and amplitude of a vibrating system?

The coefficient of friction and amplitude of a vibrating system can be affected by various factors such as the surface roughness, material properties, temperature, and lubrication. Additionally, the mass, stiffness, and damping of the system can also play a role in determining the coefficient of friction and amplitude. It is important to consider all of these factors when trying to find the frequencies that will result in a desired coefficient of friction and amplitude for a particular system.

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