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Concepts on Torque and Hanging Masses

Shown below are six figures in which a student is holding a meter stick horizontally. In these figures, the length of the meter stick is denoted as L. All of the meter sticks are identical, but the objects hanging from the sticks vary in mass and position. The objects have masses of 500 g, 750 g or 1000 g as indicated in the figure below.
Some of the masses hang from the end of the stick (distance L from the hand) and some hang at the midpoint of the stick (distance L/2 from the hand).
In all cases, the student is keeping the meter stick from rotating downward by applying a torque at the end of the stick.

The meter stick may be "harder" or "easier" to hold in different cases, depending upon the torque exerted by the student.

Which of the following statements are true about the situations depicted in the figures above? (Give ALL correct answers)

A) The torque due to the masses in figure C is 1500L
B) The torques exerted by all of the masses are counterclockwise
C) Stick D is harder to hold than stick B because the hanging mass is larger
D) The sticks in figures C and D are both the hardest to hold
E) In figure C, the left mass exerts more torque than the right mass


Solution Preview

Torque is defined as a measure of how much a force acting on an object causes that object to rotate. The formula for torque is Tau = L x F where L is the length to the pivot point and F is the force being applied. Note this is a cross product, so a more general formula is
<br>Tau = LFsin(Theta) where theta is the angle between L and F. In the case we have here, all the forces are perpendicular to the stick, so the first equation will ...