An 80-kg man balances the boy on a teeter-totter as shown. Note: Ignore the weight of the board.
-What is the approximate mass of the boy?
A)10 kg
B)20 kg
C)40 kg
D)45 kg
E)50 kg

Question

An 80-kg man balances the boy on a teeter-totter as shown. Note: Ignore the weight of the board. 
-What is the approximate mass of the boy?
A)10 kg 
B)20 kg 
C)40 kg 
D)45 kg 
E)50 kg

Quizplus · Accepted Answer

Since the man and the boy are balancing each other, we can assume that the torques on either side of the pivot point are equal. The torque on each side is the product of the weight and the distance from the pivot point. Let the distance from the pivot point to the man be x, and the distance from the pivot point to the boy be y. Then:

80kg × x = mass of boy × y

If we assume that x is about twice y (based on the image), then we can estimate that y is about one-third of the total distance, and x is about two-thirds. Thus:

x = 2y
y + x = total distance
y + 2y = total distance/3
y = total distance/3

So:

80kg × (2/3)(total distance) = mass of boy × (1/3)(total distance)
Mass of boy = (80kg × 2)/(3) = 53.3 kg

Since the answer choices only give whole number values, the closest choice is B) 20 kg.

An 80-Kg Man Balances the Boy on a Teeter-Totter as Shown