Tray Plate
A lunch tray is being held in one hand, as the drawing illustrates. The mass of the tray itself is 0.140 kg?
A lunch tray is being held in one hand, as the drawing illustrates. The mass of the tray itself is 0.140 kg, and its center of gravity is located at its geometrical center. On the tray is a 1.00 kg plate of food and a 0.350 kg cup of coffee. Obtain the force T exerted by the thumb and the force F exerted by the four fingers. Both forces act perpendicular to the tray, which is being held parallel to the ground.
The length of the tray is .4m. The cup is .38m from the end. Plate is .24m from end. Fingers are .1m from the end and the thumb is .06m from the end. The force of the tumb is going down and the force of the fingers are going up.
♠ balance of torques around tray edge (g=9.8m/s^2)
B1+B2+B3+B4+B5=0; where B1=0.14g*(0.4/2) is torq of tray, 0.14g being weight of tray, 0.4/2 being arm of mass center of tray; also plate B2=1*g*0.24, cup B3=0.35g*0.38, fingers B4=F*0.1, thumb B5=T*0.06; Thus
0.14g*(0.4/2) +1*g*0.24 +0.35g*0.38 +F*0.1 +T*0.06=0;
0.401g +F*0.1 +T*0.06 =0;
♣ balance of forces
F+ T +0.14g +1*g +0.35g =0, hence F=-(T+1.49g);
♦ thus 0.401g -(T+1.49g)*0.1 +T*0.06 =0; hence
T=(0.401 -0.149)g/(0.1-0.06) =6.3g Newtons; and
F= -7.79g, minus means UP;
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