Centripetal Force Applications

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Presentation transcript:

Centripetal Force Applications Circus cycle show

The Maximum Speed to Travel in a Horizontal Circular Path f=Fc f=uN f=μW μmg= mv2/r μg=v2/r f Maximum speed to round a horizontal circular path. f f W r f N Minimum μ to round circular path. W=N on a flat, level surface.

An object traveling in a vertical circle:

The Force on a Mass Traveling in a Vertical Circular Path Fnet=Fc Forces towards the center of the circular path are positive and forces away from the center from the circular path are negative. At the path bottom: F-W=mac F=W+mac At path top: F+W=mac F=-W+mac The forces at the top of the circular vertical path. There is a smaller force applied at the top of the path than the bottom because gravity aids in the centripetal force on the top of the path. The force has to overcome gravity on the bottom of the path. F W Minimum speed needed to round a vertical circle: F=0 if there is not enough speed to round the vertical circle 0=W-mac mac=mg ac=g*v2/r=g F *The centripetal acceleration must at least be equal to g (9.8 m/s2). The forces on the bottom of a vertical circular path. or W Minimum speed needed to round a vertical circular path

Vertical Suspension while Traveling a Horizontal Circle forces ΣFx = Fc N = Fc f ΣFy = 0 f-w=0  W=f mg=μN  mg=μ(Fc) mg=μ(mv2/r)g=μv2/r N Fc Horizontal forces Minimum speed need for an object to remain vertically suspended while traveling around in a horizontal circlur path. W r

An object spinning horizontally at the end of a string that makes an angle: ΣFx=Fc Tx=Fc Tx=mac Tcosθ=mac T ΣFy=0 Ty-W=0Ty=W Tsinθ=W Tsinθ=mg Ty θ Tx r Since T is a variable in both equations, then the two equations can be combined into one, giving  W

Equation Summary F = W+mac F = -W+mac The maximum speed an object can travel in a circular horizontal path without sliding. . The minimum coefficient of friction needed for an object to travel in a horizontal circular path without sliding. The force exerted on an object traveling in a vertical circular path at the bottom F = W+mac F = -W+mac The force exerted on an object traveling in a vertical circular path at the top. The minimum speed needed to travel in a vertical circular path. The minimum speed needed to remain vertically suspended while traveling in a horizontal circular path. A relationship between the angle, acceleration due to gravity, and centripetal acceleration for a mass at the end of a string, rope, or chain that is whirled in a horizontal circular path.