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Lesson04.1 Vertical Circular Motion Lesson04.1 Vertical Circular Motion Lesson 4.1: Vertical Circular Key Points: Motion • Understand that vertical circular motion is not uniform. • Learn the forces that contribute to VCM. • Understand that for VCM, Fc= forces in – forces out. Sep 25­11:21 AM Vertical Circular Motion Motorcycle stunt drivers often perform a feat in which they drive their cycles around a vertical circular track, as in the figure at right. Usually, the speed varies in this stunt, decreasing as the cycle moves upward and increasing as the cycle comes downward. When the speed of travel on a circular path changes from moment to moment, the motion is said to be “non­uniform”. Sep 25­11:21 AM 1 Lesson04.1 Vertical Circular Motion Vertical Circular Motion As the speed changes in the motorcycle trick, the magnitude of the centripetal force also changes. There are two points on the circle where the centripetal force can be identified easily, as the figure at left indicates. Kooza video Simpsons Ball of death But remember, the centripetal force is not a new and separate force of nature, it is the sum of all the force components oriented along the radial direction and points toward the center of the circle. The drawing shows only the weight of the cycle plus the rider (mg) and the normal force pushing on the cycle (FN). Sep 25­11:21 AM Vertical Circular Motion As the cycle goes around, the magnitude of the normal force changes. At the bottom the normal force and the weight oppose each other, giving a centripetal force of magnitude Fc = FN – mg. At the top, in contrast, the normal force and the weight reinforce each other and provide a centripetal force whose magnitude is Fc = FN + mg. The general rule is that for any vertical circular motion the centripetal force (Fc) = Fin – Fout. Sep 25­11:21 AM 2 Lesson04.1 Vertical Circular Motion Vertical Circular Motion Riders who perform the loop the loop trick, know they must have a minimum speed at the top of the circle to remain on the track. Boomerang Griffon Coaster Hulk Coaster Sep 25­11:21 AM Example: • Calculate the minimum speed required for a roller coaster to remain on a vertical circular track of radius 9.0m. Sep 25­11:21 AM 3 Lesson04.1 Vertical Circular Motion Reasoning: • The minimum speed is determined considering the centripetal force at the top of the circle. The minimum speed required occurs when the normal force at the top of the circle is zero (meaning only the force of gravity mg is acting on the cycle and is equal to the centripetal force. Leaving us with: • mv2/r = mg or v = √rg Sep 25­11:21 AM Solution: • v = √(9.0m)(9.81m/s2) = 9.4m/s • Under these conditions, the rider experiences apparent weightlessness because the rider and the cycle are falling freely toward the center of the circle. Sep 25­11:21 AM 4 Lesson04.1 Vertical Circular Motion Review Activities • Do example problems 5.5 (p. 259), 5.6 (p.262), 5.7 (p.264) and 5.8 (p.267). • Read pages 258­268 and do all practice problems on those pages. • Do check and reflect questions on p. 268. Sep 25­11:21 AM Jan 19­1:36 PM 5 Lesson04.1 Vertical Circular Motion Jan 19­2:50 PM Jan 19­2:51 PM 6 Lesson04.1 Vertical Circular Motion Jan 19­2:53 PM Jan 19­2:54 PM 7 Lesson04.1 Vertical Circular Motion Jan 19­2:54 PM 1. You are riding your bike on a track that makes a vertical circular loop. The diameter of this loop is 10.0m, how fast would you have to travel in order to stay in the loop? (7.00m/s) 1 8 Lesson04.1 Vertical Circular Motion 2. You are rotating a bucket of water in a vertical circle. Assuming the radius of this circle is 0.95m, what is the minimum velocity of the bucket at the top of its swing if the water is not to spill? (3.1m/s) 2 3. A student has a weight of 655N. While riding a roller coaster this same student has an apparent weight of 1.95x103N at the bottom of the dip that has a radius of 18.0m/ What is the speed of the roller coaster? (18.8m/s) 3 9 Lesson04.1 Vertical Circular Motion 4. An amusement park ride spins in a vertical circle. If the diameter of this ride is 5.80m, what minimum speed must the ride have so that the 75.0kg passenger will remain against the wall when he is in the top position? (5.33m/s) 4 5. A string requires a 186N force to break. A 1.50kg mass is tied to this string and whirled in a vertical circle with a radius of 1.90m. What is the maximum speed that this mass can be whirled at without breaking the string? (14.7m/s) 5 10 Lesson04.1 Vertical Circular Motion 6. A wheel shaped space station whose radius is 48m produces artificial gravity by rotating. How fast must this station rotate so that the crew members have the same apparent weight in this station as they have on earth? (22m/s) 6 7. A 915kg car goes over a hill as shown in the diagram. If the radius of this curve is 43m, how fast must the car travel so that it exerts no force on the road at the crest? (21m/s) 7 11 Lesson04.1 Vertical Circular Motion 8. A 2.0 kg object is being whirled in a circle of radius of 3.0 m. If the object takes 20 seconds to make 10 revolutions, what is the speed of the object? 9.42m/s 8 9. A 5.0 kg object undergoing uniform circular motion takes 3.0 seconds to make one complete revolution around a circle of radius 4.0 m. a) What is the centripetal acceleration of the object? 17.5m/s2 b) What is the centripetal force acting on the object? 87.8N 9 12 Lesson04.1 Vertical Circular Motion 10. A 1050 kg roller coaster car (including a passenger) is moving in a vertical loop of radius 10 m at a speed of 35 m/s. a) What is the force of the track pushing up on the roller coaster car when the car is at the bottom of the loop? 1.4x105N b) What is the force of the track pushing up on the roller coaster car when the car is at the top of the loop? 1.2x105N c) What is the actual weight of a 50 kg passenger on the roller coaster? 4.9x102N d) What is the apparent weight of a 50 kg passenger on the roller coaster when the car is at the bottom of the loop? 6.6x103N e) What is the apparent weight of a 50 kg passenger on the roller coaster when the car is at the top of the loop? 5.6x103N 10 11. What is the minimum speed of a roller coaster car moving in a vertical loop of radius 10 m? 9.9m/s 11 13.
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