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Uniform Circular Motion

Uniform Circular Motion. Centripetal forces keep these children moving in a circular path. v. Constant velocity tangent to path. Constant force toward center. Uniform Circular Motion.

fredericka-nolan
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Uniform Circular Motion

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  1. Uniform Circular Motion Centripetal forces keep these children moving in a circular path.

  2. v Constant velocity tangent to path. Constant force toward center. Uniform Circular Motion Uniform circular motion is motion along a circular path in which there is no change in speed, only a change in direction. Fc Question: Is there an outwardforce on the ball?

  3. v Uniform Circular Motion (Cont.) The question of an outward force can be resolved by asking what happens when the string breaks! Ball moves tangent to path, NOT outward as might be expected. When central force is removed, ball continues in straight line. Centripetal force is needed to change direction.

  4. Fc Examples of Centripetal Force You are sitting on the seat next to the outside door. What is the direction of the resultant force on you as you turn? Is it away from center or toward center of the turn? • Car going around a curve. Force ON you is toward the center.

  5. Reaction The centripetal force is exerted BY the door ON you. (Centrally) Fc F’ Car Example Continued There is an outward force, but it does not act ON you. It is the reaction force exerted BY you ON the door. It affects only the door.

  6. R Disappearing platform at fair. Fc Another Example What exerts the centripetal force in this example and on what does it act? The centripetal force is exerted BY the wall ON the man. A reaction force is exerted by the man on the wall, but that does not determine the motion of the man.

  7. Spin Cycle on a Washer How is the water removed from clothes during the spin cycle of a washer? Think carefully before answering . . . Does the centripetal force throw water off the clothes? NO. Actually, it is the LACK of a force that allows the water to leave the clothes through holes in the circular wall of the rotating washer.

  8. v m R Example 1:A 3-kg rock swings in a circle of radius 5 m. If its constant speed is 8 m/s, what is the centripetal acceleration? m = 3 kg R = 5 m; v = 8 m/s F = (3 kg)(12.8 m/s2) Fc = 38.4 N

  9. v = 15 m/s Fc R 450 N 30 m m=? Speed skater Example 2:A skater moves with 15 m/s in a circle of radius 30 m. The ice exerts a central force of 450 N. What is the mass of the skater? Draw and label sketch m = 60.0 kg

  10. Draw and label sketch Newton’s 2nd law for circular motion: m = 80 kg; v = 4 m/s2 Fc = 600 N r = ? Example 3.The wall exerts a 600 N force on an 80-kg person moving at 4 m/s on a circular platform. What is the radius of the circular path? r = 2.13 m

  11. v R Car Negotiating a Flat Turn Fc What is the direction of the force ON the car? Ans.Toward Center This central force is exerted BY the road ON the car.

  12. v Fc R Car Negotiating a Flat Turn Is there also an outward force acting ON the car? Ans.No, but the car does exert a outward reaction force ON the road.

  13. n Fc R fs m R v mg Car Negotiating a Flat Turn The centripetal force Fc is that of static friction fs: Fc = fs The central force FC and the friction force fsare not two different forces that are equal. There is just one force on the car. The nature of this central force is static friction.

  14. n Fc Fc = fs R fs m R v mv2 R Fc = mg Finding the maximum speed for negotiating a turn without slipping. The car is on the verge of slipping when FC is equal to the maximum force of static friction fs. fs = msmg Fc = fs

  15. n fs R Fc R m mg v mv2 R = msmg v = msgR Maximum speed without slipping (Cont.) Fc = fs Velocity v is maximum speed for no slipping.

  16. m Fc R mv2 R Fc = ms = 0.7 v v = msgR Example 4:A car negotiates a turn of radius 70 m when the coefficient of static friction is 0.7. What is the maximum speed to avoid slipping? fs = msmg From which: g = 9.8 m/s2; R = 70 m v = 21.9 m/s

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