Static Friction and Uniform Circular Motion

In summary, the cat on the merry go round has a radius of 4.0m and makes one complete rotation every 6.3 seconds. To keep the cat in place, the least coefficient of static friction needed is μ = ω^2 * r / g. The circumference of the circle traveled by the cat is 25.13m and its velocity is 3.99 m/s. The centripetal acceleration of the cat is 3.98 m/s^2. The force of static friction is equal to the centripetal force, which is provided by the normal reaction N. Therefore, the mass of the cat is not needed in this calculation.
  • #1
harpua09
4
0

Homework Statement



A cat sits on a merry go round at a radius of 4.0m from the center. The ride makes one complete rotation every 6.3 seconds. What is the least coefficient of static friction to keep the cat in place?

Homework Equations


Circumference = 2Pi*r
V=d/t
a=v^2/r


The Attempt at a Solution


I first figured out the circumference of the circle traveled by the cat to be:

2 x 4.0 x Pi= 25.13m

Velocity of the cat:

V = 25.13/6.3 = 3.99 m/s

Centripetal acceleration of the cat:

a = 3.99^2 / 4.0 = 3.98 m/s^2

I'm assuming that i have to use the formula for static friction in some way, but i am not sure how to apply it to what i have calculated so far. Any help would be greatly appreciated, thanks.
 
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  • #2
harpua09 said:

The Attempt at a Solution


I first figured out the circumference of the circle traveled by the cat to be:

2 x 4.0 x Pi= 25.13m

Velocity of the cat:

V = 25.13/6.3 = 3.99 m/s

Centripetal acceleration of the cat:

a = 3.99^2 / 4.0 = 3.98 m/s^2

Your answer here is correct, but you could have alternatively just found ω since they said "1 revolution in 6.3s" and then use a=ω2r


harpua09 said:
I'm assuming that i have to use the formula for static friction in some way, but i am not sure how to apply it to what i have calculated so far. Any help would be greatly appreciated, thanks.

Well the force of static friction is providing the centripetal force needed to keep the cat in circular motion. If the mass of the cat is 'm', then its weight is 'mg' and the normal reaction is 'N'. The frictional force is therefore F= μN.

Just equate the two and solve.
 
  • #3
I'm not sure what you are referring to with "ω". I am also not sure hot to find N, if i do not know the mass of the cat.
 
  • #4
Interesting. Seems like mass is indeed needed.
 
  • #5
harpua09 said:
I'm not sure what you are referring to with "ω". I am also not sure hot to find N, if i do not know the mass of the cat.

ω=angular velocity, you did not need to use it, but it would have just been easier instead of finding the velocity and then using v2/r

fawk3s said:
Interesting. Seems like mass is indeed needed.

Not really. Remember, the cat is not moving upwards so the normal reaction N is just the weight 'mg'. N=mg.

and if Fcentripetal=Ffriction mass is not needed :wink:
 
  • #6
Figured it out, thanks!
 
  • #7
rock.freak667 said:
Not really. Remember, the cat is not moving upwards so the normal reaction N is just the weight 'mg'. N=mg.

and if Fcentripetal=Ffriction mass is not needed :wink:

Oh, my bad. Sorry. I seem to be missing a lot lately. For some fudgy reason my head thought of the centripetal acceleration as the force (without multiplying with mass).

/facepalm
 

Related to Static Friction and Uniform Circular Motion

1. What is static friction?

Static friction is the force that resists the relative motion between two surfaces that are in contact and at rest.

2. How is static friction different from kinetic friction?

Static friction only occurs when two surfaces are not moving relative to each other, while kinetic friction occurs when two surfaces are moving relative to each other.

3. What is the maximum value of static friction?

The maximum value of static friction is the product of the coefficient of static friction and the normal force between the two surfaces.

4. Can static friction cause circular motion?

Yes, static friction can cause circular motion when an object is moving in a circular path at a constant speed. The friction force acts as the centripetal force that keeps the object in its circular path.

5. How does the coefficient of static friction affect uniform circular motion?

The coefficient of static friction determines the maximum speed at which an object can move in a circular path without slipping. If the speed of the object exceeds this maximum value, the object will start to slip and kinetic friction will take over.

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