Question

A 320 N bench is 2.40m long. The legs are .30m from each end and weigh 15.0 N each. If 3 persons weighing in order ,500 N, 750N, and 1000N sit .40m, 1.20m, and 2m respectively from one end of the bench, what downward force must each set of legs exert on the floor?

Answer 1

weight = 320+ 4*15 + 500 + 750 + 1000 = total force up

moments around one end
Ff=force up from floor at far end
Fn = force up at near end

320(1.2)-Fn*.3+30*.3+500*.4+750*1.2
+1000*2 +30*2.1-Ff*2.1 = 0
but Fn = (total force up - Ff)