Answer:
15 feet
Step-by-step explanation:
Given : In this fulcrum, the weights are perfectly balanced.
To Find: How far must the fulcrum be located from the 60 pound weight if the bar is 24 feet long?
Solution:
To make the weights perfectly balanced torque must be equal
[tex]Torque = Force \times d[/tex]
Where [tex]Force = Mass \times Acceleration[/tex]
Let a be the acceleration
d= Distance between the pivot and the acting point.
Let x be the distance from 60 pound weight where fulcrum is located
Since we are given that Length of bar = 24 feet.
So,Distance of fulcrum from 100 pound weight = 24-x
Now torque for 60 pound weight :
[tex]Torque = 60a \times x[/tex]
Now torque for 100 pound weight.
[tex]Torque =100a \times (24-x)[/tex]
Now to maintain the equilibrium i.e. To make the weights perfectly balanced
[tex]60a \times x =100a \times (24-x)[/tex]
[tex]60x = 2400-100x[/tex]
[tex]160x = 2400[/tex]
[tex]x = \frac{2400}{160}[/tex]
[tex]x = 15[/tex]
Hence The fulcrum must be located 15 feet from the 60 pound weight if the bar is 24 feet long.
