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?
thank you!!
80x isnt an answer
To solve this problem, we can use the principle of moments to find the distance from the fulcrum at which the heavier boy must sit.
The principle of moments states that the sum of the moments on one side of a lever (seesaw) is equal to the sum of the moments on the other side. The moment is calculated by multiplying the weight (force) by the distance from the fulcrum.
Let's denote the distances from the fulcrum for the lighter boy and the heavier boy as d1 and d2, respectively. We know that the weight of the lighter boy is 60 pounds, and he sits 8 feet from the fulcrum.
The weight (force) of the lighter boy multiplied by its distance from the fulcrum gives the moment:
Moment1 = Weight1 * Distance1
Moment1 = 60 pounds * 8 feet
Moment1 = 480 pound-feet
Now, let's consider the heavier boy. We know that his weight is 80 pounds, and we are trying to find his distance from the fulcrum, which we'll denote as d2.
Using the principle of moments, we can equate the moments of the lighter and heavier boys:
Moment1 = Moment2
Weight1 * Distance1 = Weight2 * Distance2
60 pounds * 8 feet = 80 pounds * Distance2
480 pound-feet = 80 pounds * Distance2
To find the distance from the fulcrum for the heavier boy, we rearrange the equation:
Distance2 = 480 pound-feet / 80 pounds
Distance2 = 6 feet
Therefore, the heavier boy must sit 6 feet from the fulcrum.
To solve this question, we can use the concept of torque. Torque is the measure of how effectively a force causes rotation around a fulcrum. It is given by the formula:
Torque = Force x Distance
In this case, the torque on both sides of the seesaw must be balanced for it to be in equilibrium.
Let's assume that the heavier boy sits 'x' feet from the fulcrum. Therefore, the lighter boy is 8 feet from the fulcrum.
The torque exerted by each boy can be calculated by multiplying their weight (in pounds) with their respective distance from the fulcrum (in feet).
For the lighter boy:
Torque (lighter boy) = Weight (lighter boy) x Distance (lighter boy)
= 60 pounds x 8 feet
For the heavier boy:
Torque (heavier boy) = Weight (heavier boy) x Distance (heavier boy)
= 80 pounds x x feet
Since the seesaw is balanced, the torque exerted by the lighter boy should be equal to that of the heavier boy. Therefore, we can write the equation:
Torque (lighter boy) = Torque (heavier boy)
60 pounds x 8 feet = 80 pounds x x feet
To solve for 'x', we can rearrange the equation:
60 x 8 = 80 x x
480 = 80x
x = 480/80
x = 6 feet
Therefore, the heavier boy must sit 6 feet from the fulcrum.
the product of weight and distance must be equal on both sides, so
60*8 = 80x