Physics 20 Lesson 20 Uniform Circular Motion Vertical Plane

Transcription

1 Physis 0 Lesson 0 Uniform Cirular Motion Vertial Plane I. Vertial uniform irular motion Refer to Pearson pages 60 to 64 for a disussion about irular motion. So far we hae onsidered uniform irular motion problems whih hae inoled only one applied fore and the plane of motion has been horizontal. What if we start to rotate something in a ertial plane? If the objet is rotating in the ertial plane, rather than horizontally, there are now two fores ating: the fore of graity (weight) and a tension or normal fore, depending on the situation. Objets moing in a ertial irle (ertial plane) reate unique problems beause the weight plays different roles at different points in the irle. If we define diretion as (+) for fores ating toward the enter of the irle and ( ) for fores ating away from the enter of the irle, onsider the two situations below op of the irle: F At the top of the irle, the weight is ating toward the enter of the irle. he tension fore is relatiely small. hus: F Bottom of the irle: F F = F g + F At the bottom of the irle, the weight is ating away from the entre of the irle. he tension fore required is greater. hus: F = F + F F Uniform irular motion requires a onstant entripetal fore. hus, if the motion is to remain uniform, the tension fore must hange from the top of the irle to the bottom of the irle. his is due to the fat that the diretion of the graitational fore (weight) remains downward throughout the motion. Dr. Ron Liht 0-1

2 Example 1 A 1.8 kg objet is swung from the end of a 0.50 m string in a ertial irle. If the time of reolution is 1. s, what is the tension in the string A. at the top of the irle? B. at the bottom of the irle? For uniform irular motion the entripetal fore is onstant, although its diretion hanges. We an alulate F from the information in the problem. 4 mr F 4 (1.8kg)(0.50m) F (1.s) F 4.67N We an also alulate = mg = 1.8 kg(9.81 m/s ) = N A. at the top B. at the bottom g F 4.67N 17.66N F = 7.01 N F F F F g F 4.67N 17.66N F = 4.33 N Dr. Ron Liht 0 -

3 Example An objet is swung in a ertial irle with a radius of 0.85 m. What is the minimum speed of the objet so that it remains in irular motion? he position where the minimum speed an be alulated is at the top of the irle. If the speed is less than the minimum, the objet will fall out of irular motion at the top. hus, at the minimum speed, graity will be the only fore required to maintain the irular motion. F 0 F m r F g mg gr 9.81 (0.85m) m s =.89 m/s (mass anels) II. Pratie problems 1. Mr. Liht is rotating a pail of water with a mass of.00 kg in a ertial irle. Mr. Liht s arm is 70 m long. A. If the pail has a speed of 3.00 m/s, what is the tension in Mr. Liht s arm: i. At the top of the swing? (6.09 N) ii. At the bottom of the swing? (45.3 N) Dr. Ron Liht 0-3

4 . What is the minimum speed required so that a roller oaster ar will safely go around a ertial loop whih has a radius of 5.0 m? (7.0 m/s) III. Hand-in assignment 1. For eah situation below, draw aurate free-body diagrams showing all fores ating on the rok. A. Swinging on a rope, at lowest position. No frition. B. ied to a post and moing in a irle at onstant speed on a fritionless horizontal surfae. Coming straight out of the paper. C. ied to point A by a string. Moing in a horizontal irle at onstant speed. Not resting on a solid surfae. No frition. Coming straight out of the paper. D. Swinging on a rope. No frition. E. Swinging on a rope, at the top of a ertial irle. F. Riding on a horizontal disk that is rotating at onstant speed about its ertial axis. Frition preents rok from sliding. Rok is moing straight out of the paper. Dr. Ron Liht 0-4

5 . You are riding your bike on a trak that forms a ertial irular loop. If the diameter of the loop is 7.0 m, how fast would you hae to be traelling when you reahed the top of the loop so that you would not fall? (5.86 m/s) 3. You are rotating a buket of water in a ertial irle. Assuming that the radius of the rotation of the water is 0.95 m, what is the minimum eloity of the buket at the top of its swing if the water is not to spill? (3.05 m/s) 4. A student has a weight of 655 N. While riding on a roller-oaster this same student has an apparent weight of 1.96 x 10 3 N at the bottom of the dip that has a radius of 18.0 m. What is the speed of the roller-oaster? (18.76 m/s) 5. A string requires a 186 N fore in order to break. A 1.50 kg mass is tied to this string and whirled in a ertial irle with a radius of 1.90 m. What is the maximum speed that this mass an be whirled without breaking the string? (14.73 m/s) 6. A. kg objet is whirled in a ertial irle whose radius is 1.0 m. If the time of one reolution is 0.97 s, what is the tension in the string (assume uniform speed) (a) when it is at the top? (70.7 N) (b) when it is at the bottom? (113.9 N) Dr. Ron Liht 0-5