Two boys weighing 60 pounds and 80 pounds balance a seesaw. How many feet from the fulcrum must the heavier boy sit if the lighter boy is 8 feet from the fulcrum ?
Dx80=8x60 or D=480/80=6 feet
To solve this problem, we can use the concept of moments. Moments depend on both the weight and the distance from the fulcrum.
The moment of the lighter boy can be calculated as the product of his weight (60 pounds) and his distance from the fulcrum (8 feet):
Moment of the lighter boy = 60 pounds × 8 feet
The moment of the heavier boy can be calculated as the product of his weight (80 pounds) and his distance from the fulcrum (let's call it x feet):
Moment of the heavier boy = 80 pounds × x feet
Since the seesaw is balanced, the moments on both sides of the fulcrum must be equal. Therefore, we can set up an equation:
60 pounds × 8 feet = 80 pounds × x feet
Now, we can solve for x:
480 feet × pounds = 80 pounds × x feet
480 feet = 80 x
480 ÷ 80 = x
6 = x
So, the heavier boy must sit 6 feet from the fulcrum in order to balance the seesaw when the lighter boy is 8 feet from the fulcrum.
To solve this problem, we can use the concept of moments or torque. The moment of an object is the product of its weight and its distance from the fulcrum. The seesaw will balance when the sum of the moments on either side is equal.
Let's first calculate the moment of the lighter boy. We'll call his weight W1 (60 pounds) and his distance from the fulcrum D1 (8 feet). So, the moment of the lighter boy will be W1 * D1.
Moment of lighter boy = W1 * D1 = 60 pounds * 8 feet = 480 pound-feet.
Since the seesaw is balanced, the moment of the heavier boy will also be equal to 480 pound-feet. We'll call his weight W2 (80 pounds) and his distance from the fulcrum D2. Therefore, the moment of the heavier boy is W2 * D2.
Moment of heavier boy = W2 * D2 = 80 pounds * D2.
We know that the sum of the moments on either side of the fulcrum is equal. So, we can write the equation:
W1 * D1 = W2 * D2.
Plugging in the known values:
60 pounds * 8 feet = 80 pounds * D2.
Now, let's solve for D2:
(60 * 8) / 80 = D2.
D2 = 6 feet.
Therefore, the heavier boy must sit 6 feet from the fulcrum in order to balance the seesaw with the lighter boy sitting 8 feet from the fulcrum.