Answer to Question #282834 in Physics for Sdff

Question

4 A uniform girder, of weight 14 kN and of length 8.0 m, rests horizontally on two wooden blocks, one at 1.0m from one end of the girder and the other at 0.5 m from the other end (as shown below). Calculate the force of the girder on each block.

Answer 1

1) Write equilibrium of forces:

$$-mg+R_1+R_2=0.$$

2) Write equilibrium of torques (think of R1 as a pivot point):

$$mg·\dfrac{1}{8}·\dfrac{1}{2}+R_1·0-mg\dfrac{6.5}{8}·\dfrac{6.5}{2}+R_26.5-mg\dfrac{0.5}8·\dfrac{0.5}{2}=0.$$

3) Solve this system of equations (keeping in mind that mg = 14 kN:

$$R_1=8413\text{ N},\\ R_2=5587\text{ N}.$$