Horizontal Circular Motion

 

  Fcp =   N   m =  kg v =  m/s     r =  m
    a =   m/s2   T =  s      ω =  rev/s μ =  
It is not often that one finds the need to twirl a mass at the end of a string above their head in a horizontal plane. For that
reason, this animation will examine a couple of "real-life" applications. Everything discussed in the
Introduction Of Circular Motion still applies but the factors of friction and weight must be considered.
 
The force diagram in the animation consists of three forces. FN is the normal force which is the perpendicular force that
pushes the two surfaces together, FW needs no introduction, and Fcp is the centripetal force. All the forces are expressed
in newtons and Fcp is perpendicular to both FW and FN. The force diagram is best visualized as an astute observer such
as the one in the animation who is not the least bit animated.
 
Important notes to keep in mind when using the simulator:
 
If there is no friction in the problem, the input, μ, must be left blank. The last input which is unlabeled serves two
purposes:
 
     (i) The options for this input are H (horizontal) and V (vertical). The H and the V refer to the direction of the
          frictional force. For example in Problem 1, the Ff is horizontal so you can let the field default to H. When doing a
          problem similar to Problem 2, the Ff is vertical, so you must enter a V.
 
     (ii) When doing a problem similar to Problem 3 pertaining to banked curves, you must enter a -1 for the μ and the
          last unlabeled field will be used to display the angle.
 
    (iii) When determining μ for a flat road, you must enter a 0 for μ and that field will display the computed μ.
 
The simulator accepts simple factors for entries. For example, if a problem gives the weight of an object (685 N) rather
than its mass, simply enter 685/9.80 for its mass.
 
Unlike some of the other animations, you must enter your inputs before pressing Play.
 
1) A 2.0 kg box is placed at the edge of a merry-go-round of radius of 6.0 m. The coefficient of friction between the box
    and the merry-go-round is 0.30.
    (a) Draw a free-body diagram of the box.
    (b) Determine the speed at which the box slides off the edge.
    (c) How would your answer to (b) change if the mass of the box was doubled? Support your answer.
 
2) The Rotor-Ride, a ride found at many amusement parks consist of a hollow cylindrical room approximately 2.5 m in
     radius. After the room rotates to a certain speed, the floor drops away. A rider is left stationary because they are
     supported by the static friction. Assume the rider has a mass of 75 kg and the coefficient of friction is 0.35.
     Calculate the:
     (a) speed required to prevent the rider from slipping down the wall
     (b) frequency of rotation corresponding to this speed
 
3) A car with a mass of 850. kg traveling at 18 m/s approaches a curve with a radius of 75.0 m.
    (a) Determine the banking angle such that no friction is required between the car's tires and the banked curve.
    (b) Does this angle apply for all cars? Justify your answer.
    (c) Does the banking angle increase or decrease with an increase of speed? Justify your answer.
    (d) Does the banking angle increase or decrease with a decrease of radius? Justify your answer.
 
4) A 1.54 kg mass is attached to a 0.60 m rope and is swung in a horizontal circle. The string makes an angle of 12.0°
    with the vertical and the speed remains constant. Determine the:
    (a) tension in the string
    (b) speed of the mass

 

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