Two children seat themselves on a seesaw.The one on the left has a weight of 300 N while the one on the right weighs 200 N.The fulcrum is at the midpoint of the seesaw.If the child on the right is not at the end but is 2.00 m from the fulcrum and the seesaw is balanced,what is the torque provided by the weight of the child on the left? (Take ccw as positive. )
A) -400 N·m
B) 400 N·m
C) 600 N·m
D) -600 N·m
E) 200 N·m

Question

Two children seat themselves on a seesaw.The one on the left has a weight of 300 N while the one on the right weighs 200 N.The fulcrum is at the midpoint of the seesaw.If the child on the right is not at the end but is 2.00 m from the fulcrum and the seesaw is balanced,what is the torque provided by the weight of the child on the left? (Take ccw as positive. )
A) -400 N·m
B) 400 N·m
C) 600 N·m
D) -600 N·m
E) ​200 N·m

Quizplus · Accepted Answer

Since the seesaw is balanced, the torque provided by the weight of the child on the left must be equal in magnitude and opposite in direction to the torque provided by the weight of the child on the right.

Let's use the equation torque = force x perpendicular distance from the fulcrum.

For the child on the left: 
torque_left = force_left x distance_left 
torque_left = 300 N x (2.00 m + 1.00 m)  [since the child is at the midpoint, their distance from the fulcrum is 1.00 m] 
torque_left = 900 N·m

For the child on the right: 
torque_right = force_right x distance_right 
torque_right = 200 N x (1.00 m)  [since the child is 1.00 m away from the fulcrum] 
torque_right = 200 N·m

Since the seesaw is balanced, torque_left = -torque_right. 
So torque_left = -200 N·m.

Therefore, the torque provided by the weight of the child on the left is 400 N·m in the counterclockwise direction (since torque is positive by convention when it causes counterclockwise rotation), which is answer choice B.

Two Children Seat Themselves on a Seesaw