A lazy susan is a rotatable tray (a turntable) placed on top of a dining table t

Question

A lazy susan is a rotatable tray (a turntable) placed on top of a dining table to aid in serving (reputedly invented by Thomas Jefferson for his daughter Susan who complained that she was usually served last).

Mischievous Joey likes to play with his family's lazy susan (this drives Mom crazy because it is an antique). He puts the salt shaker near the edge and tries to spin the tray at a speed so that the shaker just barely goes around without slipping off. Joey finds that the shaker just barely stays on when the turntable is making one complete turn every two seconds. Joey's older sister measures the mass of the shaker to be 70 grams. She also measures the radius of the turntable to be 0.23 m, and she is able to calculate that the speed of the shaker as it successfully goes around in a circle is 0.7222 m/s.

(a) What is the magnitude of the horizontal part of the contact force on the shaker by the turntable? Give your answer in newtons.
N

(b) What is the magnitude of the vertical part of the contact force on the shaker by the turntable?
N

Explanation / Answer

A) Horizontal force:

F= Mass x acceleration

M= 0.070 kg

a= Change in speed / Change in time

Time= Distance / Speed
Time= 0.23 / 0.7222 = 0.318 sec

a= 0.7222 / 0.318= 2.27m/s^2

F= 0.070kg x 2.27

F= 0.158N

B( Vertical force (weight of the saltshaker):

W= Mass x gravitaional force

W= 0.070kg x 9.8 m/s^2

W= 0.686N

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