Shown below are six situations where a student is holding a meter stick at the l

Question

Shown below are six situations where a student is holding a meter stick at the left end at various angles. A 1000 g mass is hung on the meter sticks at different locations. All of the meter sticks are identical, but the distance along the meter stick at which the 1000 g mass is hung and the angles at which the student holds the meter stick vary. Specific values are given in each figure. (Ignore the mass of the meter stick.) Rank these situations, from hardest to easiest, on the basis of how difficult it would be for the student to hold the meter stick from the left end in the position shown. That is, put first the situation where it would be hardest to hold the meter stick at the angle shown and put last the situation where it would be easiest to hold it at the angle shown. Hardest 1_________ 2_________ 3________ 4_________ 5________ 6_________ Easiest Or, it would be equally difficult to hold all seven of these meter sticks as shown._______ Please carefully explain your reasoning.

Explanation / Answer

we try to find the torque. more torque means more difficult to hold the stick

torque= f r where r= perpendicular distnace betwen force and point of application of force

here force= weight =mg= 1(9.8) =9.8 N

A) Torque at hand = 9.8*1*cos30 = 8.487 Nm

B)Torque at hand = 9.8*0.5 = 4.9Nm

C)Torque at hand = 9.8*1*sin60 = 8.487Nm

D)Torque at hand = 9.8*1*cos45 = 6.93 Nm

E)Torque at hand = 9.8*0.75 = 7.35 Nm

F)Torque at hand = 9.8*1 = 9.8Nm

From hardest to easiest, the ranking is F>A=C>E>D>B

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