MATH SOLVE

4 months ago

Q:
# In this fulcrum, the weights are perfectly balanced. How far must the fulcrum be located from the 60 pound weight if the bar is 24 feet long?A) 9B) 15C) 12

Accepted Solution

A:

Answer:15 feetStep-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 accelerationd= Distance between the pivot and the acting point.Let x be the distance from 60 pound weight where fulcrum is locatedSince we are given that Length of bar = 24 feet.So,Distance of fulcrum from 100 pound weight = 24-xNow 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.