Levers Algebra 1

Question

Where must the fulcrum be located if a 250-pound weight and a 300-pound weight balance when placed on each end of an 11-foot bar?

Answer 1

If I remember correctly:

Moment of mass about pivot = Mass × Displacement from pivot.

Let x be the center of mass:

So, ∑x_im_i (m1*x1+m2*m2)

x = ------------ = --------------------

∑ m_i m1 + m2

Or, to make it easier ( at least, to me), I assume that the center of the mass is at coordinate = 0, and let say, m1=250 is at -x so m2=300 is at 11-x, therefore:

250*-x + 300*(11-x) = 0

x = 60, so the balance is 6 feet away from 250lb and 5 from 300lb.

Answer 2

∑M=0

250x=300(11-x), thus x=6 ft and 11-x=5 ft

so the fulcrum must be located 6 ft from 250 lb and 5 ft from 300lb.