Answer to Question #73968 in Mechanics | Relativity for malelelo mishumo

Question

A meter stick of negligible mass is fixed horizonally at its 100 cm mark.imagine this meter stick used as a displayfor some fruits and vegetables with record-breaking masses.a lemon with mass of 3.9kg hangs from the 70cm mark and a cucumber with a mass of 9.1kg hangs from the xcm mark .what is the value of x if the net torque acting on the meter stick is 56N in the counter clockwise direction.

Answer 1

Given. l_0=100 cm=1 m; l_1=70 cm=0.7 m; m_1=3.9 kg; m_2=9.1 kg; τ_net=56 N∙m.
Find. l_2-?
Solution.
So,
τ_net=τ_1+τ_2=F_1∙d_1+F_2∙d_2=m_1 g(l_0-l_1 )+m_2 g(l_0-l_2 )→

(l_0-l_2 )=(τ_net-m_1 g(l_0-l_1 ))/(m_2 g) → l_2=l_0-(τ_net-m_1 g(l_0-l_1 ))/(m_2 g) →

l_2=l_0-(τ_net-m_1 g(l_0-l_1 ))/(m_2 g)=1-(56-3.9∙9.81∙(1-0.7))/(9.1∙9.81)=0.501 m=50.1 cm.

Answer. l_2=50.1 cm.