Static Friction Coefficient

In summary, the static friction coefficient is a measure of the force required to overcome resistance between two surfaces that are not moving. It is different from kinetic friction coefficient and is affected by factors such as materials, roughness, and force. It can be measured using a friction coefficient tester and is important in everyday life and engineering.
  • #1
DoctorB2B
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Homework Statement


What is the minimum coefficient of static friction necessary to allow a penny to rotate without sliding off a 33.5rpm record (diameter of these old-fashioned records is 0.3), when the penny is placed at the edge of the record. Ignore the size of the penny.

The Attempt at a Solution


I know the equation to determine the static friction coefficient. However, I am clueless as to how to proceed from here.
 
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  • #2
Which force slides off the penny from the record? What is its magnitude?
What is the direction and magnitude of the frictional force?
 
  • #3


I would approach this problem by first understanding the concept of static friction and its relationship to the coefficient of friction. The coefficient of static friction is a measure of the force required to initiate movement between two surfaces in contact with each other. In this case, the two surfaces would be the record and the penny.

To find the minimum coefficient of static friction necessary for the penny to rotate without sliding off the record, we can use the following equation:

μs = F/N

Where μs is the coefficient of static friction, F is the force required to initiate movement, and N is the normal force between the two surfaces. In this case, the normal force would be the weight of the penny acting downward on the record.

To find the force required to initiate movement, we can use the equation:

F = ma

Where F is the force, m is the mass of the penny, and a is the acceleration of the penny. In this case, the acceleration of the penny would be the centripetal acceleration required for it to rotate at 33.5 revolutions per minute (rpm). We can find this acceleration using the equation:

a = ω^2r

Where ω is the angular velocity, which is equal to 33.5 revolutions per minute (rpm) converted to radians per second (rad/s), and r is the radius of the record, which is equal to half of its diameter, or 0.15 meters.

Now, we can plug in the values into the equation for the force required to initiate movement:

F = ma = m(ω^2r)

Next, we can substitute this value for F into the equation for the coefficient of static friction:

μs = F/N = m(ω^2r)/mg

Where g is the acceleration due to gravity, which is approximately 9.8 m/s^2.

Finally, we can plug in the mass of the penny (which we are ignoring the size of), the converted angular velocity, and the radius of the record into the equation to solve for the coefficient of static friction:

μs = (0.01 kg)(2π(33.5 rpm/60 s)^2(0.15 m))/(0.01 kg)(9.8 m/s^2) = 0.16

Therefore, the minimum coefficient of static friction necessary for the penny to rotate without sliding off the record is approximately 0.16. This means that the
 

1. What is static friction coefficient?

The static friction coefficient is a measure of the amount of force required to overcome the resistance between two surfaces that are not moving relative to each other. It is a dimensionless quantity that is represented by the symbol μs.

2. How is static friction coefficient different from kinetic friction coefficient?

Static friction coefficient refers to the resistance between two surfaces that are not moving, while kinetic friction coefficient refers to the resistance between two surfaces that are moving relative to each other. The value of static friction coefficient is generally higher than that of kinetic friction coefficient.

3. What factors affect the value of static friction coefficient?

The value of static friction coefficient depends on the materials of the two surfaces in contact, the roughness of the surfaces, and the amount of force applied to the surfaces. It also varies with temperature and can be affected by the presence of any lubricants or contaminants between the surfaces.

4. How is static friction coefficient measured?

Static friction coefficient can be measured by using a device called a friction coefficient tester, which applies a known force to two surfaces and measures the force required to overcome the static friction. It can also be calculated by dividing the maximum force of static friction by the normal force between the two surfaces.

5. Why is static friction coefficient important in everyday life?

Static friction coefficient is important in everyday life because it affects our ability to move objects and perform tasks. For example, a high static friction coefficient between our shoes and the ground allows us to walk without slipping, while a low static friction coefficient between a tool and a surface allows us to slide the tool easily. It is also important in engineering and design, as it helps determine the stability and performance of structures and machines.

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