Question

3. A 20 N cafeteria tray is being bussed by a waitress. The tray is 0.5 m long and the waitress is holding the tray at one end, using only one hand. A cup of coffee that weighs 12 N sits on the tray, centered 0.4 m from the end of the tray that the waitress is holding. In order to keep the tray horizontal, the waitress has to push up on the tray using her fingers which are extended 0.1 m from the end of the tray and push down on the tray using her thumb right at the end. Assume, the center of gravity of the tray is at its center. If the waitress wishes to keep the tray balanced and in static equilibrium then, a) (10 pts.) What force does the waitress need to exert using her fingers? b) (10 pts.) What force does the waitress need to exert using her thumb? 0.5 m 0.4 m 0.1 m 12N Figure 3

Answer 1

Use the rotational equilibrium and vertical equilibrium of the tray to find the required force exerted by fingers and thumb as shown below

a) Wer = ZON (wt. of tray) Wc = 12N (wt. of cup) force of thumb We tr Feh th = 0.25 E 'f ll " fingers { 0.4m = 0 Torque about the left end of tray =) Wer (0.25m) - Wc (0.4m) = FF (0-1m) - (200) 0.25mm) - 22N) (0.4m) - Fil0.1m) ' f S Ff = 98N from vestical equilibrium, Ff F th t Wert Wc => 990 = Ezu + 20N + 12N f = Fan = 66) N