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CENTRIPETAL MOTION ON RIDES What is the tangential (linear) speed of the Whirly Gig? What do we need to know? What is the tangential (linear) speed of the Whirly Gig? What do we need to know? • Radius of the swing: • Time for 1 revolution at maximum speed: What is the tangential (linear) speed of the Whirly Gig? What do we need to know? • Radius of the swing: Let's say the radius from the center to the outer swing is 8 m. • Time for 1 revolution at maximum speed: Let's say the time for 1 revolution is 7.00 s. What is the tangential (linear) speed of the Whirly Gig? Equation: Equation: V = 2π R t V = 2π(8 m) 7.00s V = 7.18 m/s What is the Centripetal acceleration a rider feels on the Whirly Gig? What do we need to know? • Radius of the swing • Tangential velocity What is the Centripetal acceleration a rider feels on the Whirly Gig? What do we need to know? • Radius of the swing • R=8m • • Tangential velocity V = 7.18 m/s 8m What is the Centripetal acceleration a rider feels on the Whirly Gig? What do we need to know? • Radius of the swing • R=8m • Tangential velocity • V = 7.18 m/s • Equation • Ac = V2 = (7.18 m/s)2 R 8m • Ac = 6.44 m/s2 8m What is the Centripetal force a rider feels on the Whirly Gig? What do we need to know? • Centripetal Acceleration • Ac = 6.44 m/s2 • Mass of the rider • M = 65 kg What is the Centripetal force a rider feels on the Whirly Gig? What do we need to know? • Centripetal Acceleration • Ac = 6.44 m/s2 • Mass of the rider • M = 65 kg Fc = mac Fc = 65 kg (6.44 m/s2) Fc = 419 N What is the centripetal force of 65 kg rider on the swing? Fc = mac Fc = 65 kg (6.36 m/s2) θa Fc = 413 N θ m 0 0 m a = g*tanθ = (9.8 /s2)tan(90 57 ) = 6.36 /s2 FBD: FBD: FT mg FBD: FT mg FNet Net FT mg FBD: FT mg FNet Net FT mg Acc = 6.44 m/s22 M = 65 kg mv2 FNet = r F c = 419 N Centripetal Force... ...on a Roller Coaster Centripetal Force... ...on a Roller Coaster Before and after the loop, normal force and gravity are equal. Fnormal Fnormal Fgravity Fgravity Centripetal Force... ...on a Roller Coaster Fnet = ma = Fn Fg (ydirection) Fnet = ma = 0 N Fnormal Fnormal Fgravity Fgravity Centripetal Force... ...on a Roller Coaster Bottom of the loop: Fnormal Fgravity Centripetal Force... ...on a Roller Coaster Bottom of the loop: Fnormal Fgravity 2 mv Fnet = ma = r Centripetal Force... ...on a Roller Coaster Bottom of the loop: Fnormal Fgravity 2 mv Fnet = ma = r mv2 Fn Fg = r Centripetal Force... ...on a Roller Coaster Bottom of the loop: Fnormal Fgravity 2 mv Fnet = ma = r mv2 Fn Fg = r mv2 Fn = + F g r Centripetal Force... Fgravity Fnormal Top of the loop: ...on a Roller Coaster Centripetal Force... Fgravity Fnormal Top of the loop: ...on a Roller Coaster 2 mv Fnet = ma = r Centripetal Force... Fgravity Fnormal Top of the loop: ...on a Roller Coaster 2 mv Fnet = ma = r mv2 Fn + Fg = r Centripetal Force... Fgravity Fnormal Top of the loop: ...on a Roller Coaster 2 mv Fnet = ma = r mv2 Fn + Fg = r 2 mv Fn = F g r Centripetal Force... Fn Fg Fn Fg ...on a Roller Coaster
