Glass Center

Glass Center




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Glass Center

At what angle to the table would the base be when it tips over?

1. A wine glass has a circular base 70mm in diameter. When empty the centre of mass of the glass is 130mm above the table. At what angle to the table would the base be when it tips over?

Information

* Wine glass circular diameter 70mm
* Base of glass to centre of mass is 130mm

let W- as the weigth of the glass acting at the center of gravity(c.g) when the glass is at the upright
position.
W1=the component of glass weigth,W parallel to the base when the glass is tilted at an angle,Ѳ
W2=the component of glass weigth,W perpendicular to the base when the glass is tilted at an angle,Ѳ
Ѳ=angle of the shell side(assuming it is a right circular cylinder) of the glass to the table,otherwise it is an angle subtended by the glass centerline to horizontal table surface during tilting.

hence, W1= WcosѲ------eq.1
W2=WsinѲ--------eq.2

let P- the point where the tip of the glass is located,( or the tilting point)

∑@P=0, at equilibrium condition.

W1(130)= W2(70/2)
W2/W1= (130)/(70/2)=WsinѲ/WcosѲ= tanѲ
tanѲ= (130)(2)/(70)= 3.714

Ѳ=74.931 deg.

Angle of the the base of the glass with respect to the table= 90-Ѳ

At what angle to the table would the base be when it tips over, answer, Angle >(90-Ѳ=90-74.931)=15.069 deg.

Glass Center