Which of the following situations will increase the torque being produced on the left side of the balance beam shown here?

Question

a. If the mass (m) on the balance beam is moved farther from the fulcrum.
b. If the amount of mass (m) on the balance beam is increased.
c. If the mass on the opposite side of mass (m) (the right side of the fulcrum) is decreased.
d. If the mass and balance beam are taken to the Moon (where gravity is six times weaker).
e. None of these will increase torque on the left side of the fulcrum.
f. All of these will increase torque on the left side of the fulcrum.
g. Only A and B will increase torque.
h. Only A, B and C will increase torque.

Answer 1

I assume the fulcrum is to the right of m.  Let us look at each choice one at a time.

 

(a) If you move m farther to left (i.e. farther from the fulcrum), the torque increases, so (a) is good.

 

(b) Increasing m increases the force applied at the point where m is located, which increases the torque, so (b) is good.

 

(c) The sketch does not show another mass on the opposite side of the fulcrum.  But if there was a mass there, and if it was reduced, the applied force at that point is smaller, which reduces the torque on the right.  The net result is a stronger counterclockwise torque.  However, this situation does not produce more torque on the left; it reduces the opposing torque on the right.  Based on a very literal reading of the words of (c), I would not pick (c), because the torque applied on the left side is not changed.  This only reduces the opposing torque applied on the right side, which results in a net increase in counterclockwise torque.

 

(d) The torque is caused by weights applied at locations along the lever arm, perpendicular to the arm.  On the moon, the weights are lower, so the torques they cause are also lower, and therefore (d) is not good.

 

(e) is false.

 

(f) is false.

 

I suggest both (a) and (b), which is answer (g).  However, note my remarks on how to interpret the wording of (c).  It could still be (a), (b), and (c), which is answer (h).  I suggest (g) based on a very literal interpretation of (c).