Circular motion of a small block

In summary, the question is asking for the frequency at which a small block will begin to slide off a horizontally rotating turntable given its distance from the center and coefficient of static friction. The solution involves finding the relationship between the speed of the block and the frequency of the turntable, and using this to solve for the required frequency. A force diagram is attached for reference.
  • #1
Priscilla
31
0

Homework Statement


A small block sits 0.15 m from the center of a horizontal turntable whose frequency of rotation can be smoothly increased. If the coefficient of static friction between the block and the turntable is 0.55, at what frequency will the block begin to slide off? (Draw a force diagram).

Homework Equations


f_s = U_s F_n
F = ma
a = v^2/R

The Attempt at a Solution


f_s = U_s F_n
-f_s = ma
a = -f_s/m = -(U_s mg)/m = -U_s g
a = v^2/R
-U_s g = v^2/R
v = Sq rt(-R u_s g)

I am not sure what the question is really asking. What's frequency? Is it velocity?
I attached a force diagram.
 

Attachments

  • Diagram.bmp
    167.5 KB · Views: 511
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  • #2
The rotation of the turntable is a periodic motion. It makes a turn in T time, T is the time period. Frequency is the reciprocal of the time period f=1/T: here it is the same as revolutions per second.

First you need to find out the relation between the speed of the block and the frequency of the turntable.

ehild
 
  • #3
o~
So,
v = rw = r(2[pi]/T) f=1/T
v=2[pi]rf

Right?
 
  • #4
Yes!

ehild
 
  • #5
Then f_s = F_c
And then I can solve for f!
 
  • #6
Well done!

ehild
 
  • #7
Thanks alot!
 

Related to Circular motion of a small block

1. What is circular motion?

Circular motion is the movement of an object along a circular path or orbit, where the distance from the center remains constant. This type of motion is characterized by a constant speed and a continuously changing direction.

2. How is circular motion different from linear motion?

Circular motion involves an object moving in a circular path, while linear motion involves an object moving along a straight line. In circular motion, there is a centripetal acceleration towards the center, while in linear motion there is a constant velocity in one direction.

3. What is centripetal force in circular motion?

Centripetal force is the force that keeps an object moving in a circular path. It acts towards the center of the circle and is necessary to maintain the object's circular motion. This force is provided by the tension in a string, the normal force from a surface, or the force of gravity in a planetary orbit.

4. How is centripetal force related to circular motion?

Centripetal force is directly proportional to the mass of the object, the square of its velocity, and the inverse of the radius of the circular path. This means that as any of these factors increase, the centripetal force required to maintain circular motion will also increase.

5. How does circular motion affect the velocity of an object?

In circular motion, the velocity of an object is constantly changing, even if the speed remains constant. This is because velocity is a vector quantity that takes into account both speed and direction. In circular motion, the direction of the object is constantly changing, resulting in a change in velocity.

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