F_{cp} = N | m = kg | v = m/s | r = m |
a = m/s^{2} | 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. F_{N }is the normal force which is the perpendicular force that |
pushes the two surfaces together, F_{W }needs no introduction, and F_{cp} is the centripetal force. All the forces are expressed |
in newtons and F_{cp} is perpendicular to both F_{W} and F_{N}. 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 F_{f} is horizontal so you can let the field default to H. When doing a |
problem similar to Problem 2, the F_{f} 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 |