Solve the coefficient of friction in a problem involving circular motion

In summary, the car must have a coefficient of static friction of .40 in order to not skid when travelling at 95km/hr.
  • #1
adca14
11
0

Homework Statement


If a curve with a radius of 88m is perfectly banked for a car traveling 75km/hr, what must be the coefficient of static friction for a car not to skid when traveling at 95km/hr?


Homework Equations


i guess relevant equations would be tan θ = v^2/rg, but its says next to friction not needed?
f=ma or fr=mar
and Ffr = µs x Fn


The Attempt at a Solution



I made a free body diagram and since it said it was banked i set that in the y-axis there's no acceleration, so following the book (Giancoli), I got Fn=mg/cos θ. I solved for that and got 95^2/(88)(9.8) = .40 then inverse tan 10.46 or 84.5 for the angle

then in the x-axis i got Fn sin θ - Ffr = mar for the sum of the forces. I substituted Ffr for µs x Fn and Fn = mg cos θ. I
I then had Fn sin θ - µs mg cos θ = mar
I divided mass from both sides and divided both sides by m.
I then for ar substituted v^2/r
Then I isolated µs by dividing cos θ and subtracting Fn sin θ
So I then had µs = V^2/r x cos θ - Fn sin θ
I plugged everything in and I got 9015, I know this wrong just by looking at it, the back of the book says .22, I am completely clueless, so if anyone could help, I'd greatly appreciate it. Sorry if it is a little confusing.
 
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  • #2
The centripetal force of the car is caused by friction

The car is accelerating at [tex]a = \frac{v^2}{r}[/tex]

Equating the force of friction and the centripetal force, we have

[tex]F_f = \mu F_N = ma[/tex]

[tex]\mu * mg = \frac{mv^2}{r}[/tex]

[tex]\mu = \frac{v^2}{gr}[/tex]
 
  • #3
thank you, I forgot to convert 95km/hr to m/s too, anyways thanks again!
 

What is the coefficient of friction?

The coefficient of friction is a dimensionless number that represents the amount of friction between two surfaces in contact. It is typically denoted by the Greek letter µ (mu) and is used to calculate the force of friction in a given situation.

How do you solve for the coefficient of friction in a circular motion problem?

To solve for the coefficient of friction in a circular motion problem, you will need to know the radius of the circular path, the speed of the object, and the mass of the object. You can then use the formula µ = (mv^2)/r*g, where m is the mass, v is the speed, r is the radius, and g is the acceleration due to gravity.

What factors affect the coefficient of friction in a circular motion problem?

The coefficient of friction can be affected by a variety of factors, including the texture and material of the surfaces in contact, the weight and shape of the object, and the angle of the surface. It can also be affected by external factors such as temperature and humidity.

Why is it important to solve for the coefficient of friction in a circular motion problem?

Solving for the coefficient of friction in a circular motion problem allows us to better understand the forces at play and how they affect the motion of an object. It also helps us make predictions and calculations for future scenarios involving similar surfaces and objects.

How does the coefficient of friction affect circular motion?

The coefficient of friction plays a crucial role in circular motion by determining the amount of frictional force acting on an object as it moves along a curved path. This force can affect the object's speed, direction, and stability, making it an important factor to consider in any circular motion problem.

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