Answer to Question #142796 in Mechanics | Relativity for Haddensen

Question

A 20.0-kg horizontal plank 4.00 m long rests on two supports, one at the left end and a second 1 .00 m right end. What is the magnitude of the force exerted on the plank by the support near the right end?

Answer 1

$L=4m \\mass \space of plank\space, m=20kg \\ take \space counterclockwise \space torques\space are positive\\ Apply\space torque \space equation\space about\space one\space end\\ F_{1}(0)-mg(\frac{L}{2})+F_{2}(L-1m)=0 \\F_{2}(L-1m)=mg(\frac{L}{2}) \\F_{2}=mg(\frac{L}{2(L-1)})\\ \quad=20kg\times 9.8m/s^{2}\times\frac{4m}{2(4m-1m)})\\ \quad=130.66N\\ \quad=131N$