Spark image

Wall of death

If the bike makes an angle q with the vertical we have: tanq= v2/rg

Aircraft banking

If the plane banks at an angle of q with the horizontal we have:

tanq= v2/rg
 

Cyclist cornering

If the cyclist leans over at an angle of q with the vertical we have:

R = mg F = mv2/r and tanq= F/R

The coat hangar

Take an ordinary wire coat hanger, bend the frame into a square and bend the hook until it faces the opposite corner of the square. File the end of the hook flat. Now balance a 1p coin on the hook and spin the coat hanger in a vertical circle with your finger in the top of the frame. The centripetal force of the hook on the coin will keep the coin balanced on it although it may be upside down!

Strength of rotating objects - an extension topic

This proof enables you to find the maximum tension of a wire before breaking in terms of its angular velocity.
Let the mass per unit length be r. The m = rL where L is the length of the wire.

Considering the forces acting on a short length of wire:

(T + dT) - T = -rw2dm giving dT = -rw2dr since dm = rdr

Integration with limits gives T = ½(mw2)(L -r2/L)
giving the maximum tension of ½ mw2L when r = 0. That is the wire will break at the point of attachment.

Maximum tension before breaking (T) = ½mw2L when r = 0


Example problem
A wire of mass 0.4 kg and length 2.0 m and cross sectional area 8x10-6 m is swung round in a horizontal circle. If the breaking stress is 8x109 Pa calculate the maximum frequency of rotation before the wire snaps.

Using the formula and the figures given above: f = 63.6 Hz

Useful data

Passenger jet – maximum legal banking angle = 27.5o
Daytona race track = 31o at 150 mph
Aston Martin test track = 11o for r = 516 m    v = 70 mph
 

A VERSION IN WORD IS AVAILABLE ON THE SCHOOLPHYSICS USB
 
 
 
 
© Keith Gibbs 2020