Motion in a vertical circle mg Examine the tension in the string when the ball is at the top. r To find the minimum speed of the ball put T = 0 T=0 means no pull needed!

W = 80 N b) Fc = W at slowest speed ie no tension felt c) v = 2 ms-1

At the Bottom: Ball & String - Tension force Examine the tension in the string when the ball is at the bottom. r T mg

Motion in a vertical circle The tension at any point in the circle T q r q mg top bottom

Motion in a vertical circle (biker / plane ~ loop de loop?) mg At the top: r N mg At the bottom: To find the minimum biking speed so that the biker feels weightlessness, put N = 0 Biker feels heavier at the bottom

Is it harder for the man to hold his partner when the partner is hanging straight down and is stationary or when the partner is swinging through the straight down position? It is harder for the man to hold his partner when the partner is swinging through. When stationary, the man only needs to hold the force of the partner against gravity e.g. 50kg x 9.8m/s2 = 490 N When the partner swing, the man needs to hold with the force from gravity, PLUS the centripetal force of the partner because they are accelerating (changing v)

Problems: A 150 g ball is at the end of a 1.10 m long string. It is swung in a vertical circle. What minimum speed must the ball have to clear the top of the swing? What tension in the string is required for the ball to move at twice the minimum speed at the bottom of its swing? Ans: 3.28 m/s; 7.35 N

Vertical Circular Motion review: An object under going vertical circle motion must satisfy the constraints of: centripetal force to remain in a circle, conservation of energy as Ep is converted to Ek when the mass moves up & downward. For VCM: Force(s) needed to provide Fc (eg tension, normal / support forces) which is still directed to center and constantly changing The object speed is not necessarily constant

For VCM to occur: require a combination of Forces (ΣF) eg weight, tension, lift, support forces are required to provide sufficient ΣF to keep the object moving in a circle! unlike horizontal circles, the Forces acting on vertical circles will vary as they go around. For uniform speed VCM ie (VUCM) to occur: the Fc is kept constant – This means the Forces acting must vary in a particular way… Possibly only if Forces acting are tension based !?!

http://www. learnerstv. com/animation/animation. php http://www.learnerstv.com/animation/animation.php?ani=40&cat=Physics Vertical Circular.swf

#1 Assume non constant speed Determine Fixed radius 10m, g = 10ms-2 Prove v = 10 ms-1 #1 Assume non constant speed

#2 Determine Fixed radius 10m, g = 10ms-2 Prove v = 21.6 ms-1 Assume non constant speed

#3 Determine Fixed radius 10m, g = 10ms-2 Prove v = 29.4 ms-1 Assume non constant speed

#4S Assume T and W are at 90o… Determine Fixed radius 10m, g = 10ms-2 Prove v = 21.6 ms-1 #4S Assume T and W are at 90o… Assume non constant speed

#5S T and W are not at 90o… θ =45o Determine Fixed radius 10m, g = 10ms-2 Prove v ~ 19 ms-1 #5S T and W are not at 90o… θ =45o θ Assume non constant speed

#6S θ =45o Determine Fixed radius 10m, g = 10ms-2 Prove v ~ 24.5 ms-1 Assume non constant speed

#7S Determine Fixed radius 10m, g = 10ms-2 Find θ = ? θ θ Assume non constant speed θ θ

#8S Solve in terms of energy Top ??? Assume non constant speed Bottom

Solve in terms of energy Top Solve in terms of energy θ Assume non constant speed θ= 45o ???

Ex: Bicycle loop If the radius of the loop is 2.7 m, what minimum speed must he have at the top?

Look at http://www.physicsclassroom.com/class/energy/Lesson-2/Bar-Chart-Illustrations