3. A 25N cafeteria tray is being bussed by a waitress. The tray is 0.5m long and

Question

3. A 25N cafeteria tray is being bussed by a waitress. The tray is 0.5m long and the waitress is holding the tray at one end, using only one hand. A cup of coffee that weighs 10N sits on the tray, centered 0.4m from the end of the tray that waitress is holding. In order to keep the tray horizontal, the waitress has to push up on the tray using her fingers ( Ff ) which are extended 0.1m from the end of the tray and push down on the tray using her thumb (Ft) right at the end. a) Write Newton's second law for the tray in static equilibrium (Hint: Only two of the three equations for static equilibrium are necessary) b) What force does the waitress need to exert using her fingers (Ff )? c) What force does the waitress need to exert using her thumb (Ft)?

Explanation / Answer

Balancing forces on the tray,

Ft+mg+10-Ff=0

Ff-Ft=35N (1)

Balancing moments about the point where the thumb holds the plate,

Ff*0.1-25*0.25-10*0.4=0

Ff=102.5N

Ft=67.5N

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