Motion in a vertical circle

Motion in a vertical circle: Demo - cup and plate Concept 0: ac > 9.81 m/s/s so the string stays taut. Example - What is the minimum speed at the top for my bucket if r = 1.12 m? (So the cup does not fall off) a = v2/r 9.81 m/s/s = v2/(1.12 m) v ≈ 3.31 m/s

Concept 1B: You feel one more “g” at the bottom of the ride. Concept 1A: You feel one less “g” than the ride “pulls” at the top of the circle. Concept 1B: You feel one more “g” at the bottom of the ride. Feel one “g” less Feel one “g” more

Ferris Wheel at Oaks Park!!!

Rock-O-Plane

A) How many “g”s is the ride pulling? A rider moving in a 3.75 m radius vertical circle feels 1.2 “g”s at the top of the circle. A) How many “g”s is the ride pulling? B) How many “g”s do they feel at the bottom? C) What is their tangential velocity? A) - The ride is “pulling one more “g” than 1.2 or 2.2 “g”s B) At the bottom you would feel one more “g” than the ride is pulling or 2.2 + 1 = 3.2 “g”s C) ac = (2.2)(9.81 m/s/s) = 21.582 m/s/s ac = v2/r 21.582 m/s/s = v2/(3.75 m), v = 8.9962 ≈ 9.0 m/s Feel one 1.2 “g”s (one less than the ride) Feel one “g” more than the ride

Motion in a vertical circle Whiteboards: Motion in a vertical circle 1 | 2 | 3 | 4 TOC

What is the maximum radius you can twirl a bucket full of water going 2.3 m/s at the top? a = v2/r 9.81 m/s/s = (2.3 m/s)2/r r = 0.539245668 ≈ 0.54 m W 0.54 m

If a roller coaster pulls 2 If a roller coaster pulls 2.5 “g”s in a vertical circle, what do you feel at the top of the loop, and at the bottom? (2 answers) Top = 2.5 - 1 = 1.5 “g”s Bottom = 2.5 + 1 = 3.5 “g”s W 1.5 “g”s, and 3.5 “g”s

You feel 2. 1 “g”s at the bottom of a roller coaster loop You feel 2.1 “g”s at the bottom of a roller coaster loop. What is the ride “pulling” and what do you feel at the top? Ride pulls one less than what you feel or 1.1 “g”s At the top you would feel one less than that or .1 “g”s W 1.1 “g”s and .1 “g”s

What is your centripetal acceleration if at the top of a roller coaster loop you read .75 “g”s? The ride is pulling one more than .75 = 1.75 “g”s W 1.75 “g”s

What is your speed at the top of a roller coaster loop if you read What is your speed at the top of a roller coaster loop if you read .75 “g”s and the loop has a radius of 3.8 m? (1) The ride is pulling one more than .75: 1.75 “g”s a = (1.75)(9.81 m/s/s) = 17.1675 m/s/s a = v2/r 17.1675 m/s/s = v2/(3.8 m) v = 8.076911538 ≈ 8.1 m/s W 8.1 m/s

Example – O – Rama: A 5.00 kg object goes 9.00 m/s in a 3.75 m radius vertical circle. Find the force needed at the top, and at the bottom. 1. ac = v2/r = (9.0 m/s)2/(3.75) = 21.6 m/s/s 2. F = ma at top. Forces = weight, and tension, a is down (-) 3. F = ma at bottom, same forces, a is up (+) 4. Voodoo way: Feel one “g” less than the ride Feel one “g” more than the ride

An 9. 0 kg mass moves at a uniform speed of 4. 0 m/s in a 2 An 9.0 kg mass moves at a uniform speed of 4.0 m/s in a 2.0 m radius circle on the end of a rod. What force is needed at the top and at the bottom? ac = v2/r = (4.0 m/s)2/(2.0 m) = 8.0 m/s/s weight = mg = (9.0 kg)(9.8 N/kg) = 88.2 N Top <T - 88.2 N> = (9.0 kg)(-8.0 m/s/s) Bottom <T - 88.2 N> = (9.0 kg)(+8.0 m/s/s) or voodoo = at top 9.8 less than 8.0 = -1.8(9) = 16 N bottom one g more, 8+9.8 = 17.8(9) W Top = 16 N up Bottom = 160 N up

a) What is the centripetal acceleration of the mass? A 1.15 kg mass moves at a uniform speed in a 3.78 m radius circle on the end of a rod. At the top, the rod is exerting a downward force of 5.02 N on the mass. a) What is the centripetal acceleration of the mass? b) What is its speed? c) What force does the rod exert at the bottom? weight = mg = (1.15 kg)(9.81 N/kg) = 11.2815 N a) Top: <-5.02N - 11.2815 N> = (1.15 kg)a, a = -14.175 m/s/s b) ac = v2/r, 14.175 m/s/s = v2/(3.78 m), v = 7.3200 m/s c) Bottom: <T - 11.2815 N> = (1.15 kg)(+14.175 m/s/s), T = 27.583 N ≈ 27.6 N W 14.2 m/s/s, 7.32 m/s, 27.6 N