Lesson04.1 Vertical Circular Motion - Holy Trinity Academy
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Lesson04.1 Vertical Circular Motion 1 Sep 2511:21 AM Lesson 4.1: Vertical Circular Motion Key Points: • Understand that vertical circular motion is not uniform. • Learn the forces that contribute to VCM. • Understand that for VCM, F c = 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”.
Transcript of Lesson04.1 Vertical Circular Motion - Holy Trinity Academy
Lesson04.1 Vertical Circular Motion
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Sep 2511:21 AM
Lesson 4.1: Vertical Circular MotionKey Points:
• 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”.
Lesson04.1 Vertical Circular Motion
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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.
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).
Kooza video Simpsons Ball of death
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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.
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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.
Griffon CoasterHulk Coaster
Boomerang
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Example: • Calculate the minimum speed required for a roller coaster to
remain on a vertical circular track of radius 9.0m.
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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
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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.
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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.
Jan 191:36 PM
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Jan 192:50 PM
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Jan 192:53 PM
Jan 192:54 PM
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Jan 192:54 PM
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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)
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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)
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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)
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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)
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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)
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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)
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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)
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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
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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/s2b) What is the centripetal force acting on the object? 87.8N
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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? 1.4x105Nb) What is the force of the track pushing up on the roller coaster car when the car is at the top of the loop? 1.2x105Nc) What is the actual weight of a 50 kg passenger on the roller coaster? 4.9x102Nd) What is the apparent weight of a 50 kg passenger on the roller coaster when the car is at the bottom of the loop? 6.6x103Ne) 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
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11. What is the minimum speed of a roller coaster car moving in a vertical loop of radius 10 m? 9.9m/s
