Question

An adult and a child are on a seesaw 14 ft long. The adult weighs 175 lb, and the child weighs 70 lb. How many feet from the child must the fulcrum be placed so that the seesaw balances?

a) 8 ft
b) 9 ft
c) 10 ft
d) 11 ft

Answer 1

To balance the seesaw with an adult weighing 175 lb and a child weighing 70 lb, the child must sit 10 feet from the fulcrum as calculated using the principle of moments.

Step-by-step explanation:

To find out how many feet from the child the fulcrum must be placed so that the seesaw balances, we need to use the principle of moments which states that when an object is in equilibrium, the total clockwise moments about a pivot is equal to the total anti-clockwise moments about that pivot. This can be represented by the equation weight1 × distance1 = weight2 × distance2.

In the given problem, the adult weighs 175 lb and the child weighs 70 lb. Let's call the distance from the adult to the fulcrum d, and since the seesaw is 14 ft long, the distance from the child to the fulcrum is 14 - d.

Using the principle of moments: 175 × d = 70 × (14 - d).

Solving for d, we get:

175d = 980 - 70d

175d + 70d = 980

245d = 980

d = 980 / 245

d = 4

So, the adult should sit 4 feet from the fulcrum. Therefore, the child must sit 14 - 4 = 10 feet from the fulcrum. Hence, the correct answer is option c) 10 ft.