Answer to Question #138817 in Mechanics | Relativity for Saja

Question

 Two people pull a wagon using 2 ropes with an angle 500 between them. If one person 

pulls with 110 N and the other with 115 N, what is the resulting force on the wagon? 

Answer 1

Put the angle of $500$ degrees into a convenient view, therefore $\alpha = 500-360 = 140 °$ this is our angle.

According to Newton's second law, we find the resulting force in the projection on the horizontal, for this we find the projection of the force $110$ N and it is equal to $F_{2x}=\cos {40 }\times 110 = 84.26$ N

Since the projection of force $110$ N is oppositely directed to force vector $115$ N, the resulting horizontal force $F_x=115-84.26=30.74$ N

And for the vertical projection, the resulting force is equal to $F_y=F_2\times\cos {50} = 110\times\cos {50} = 70.71$ N.

Therefore, the resultant force according to the parallelogram rule is $F =\sqrt {F _ y ^ 2 + F _ x ^ 2} =\sqrt {70.71 ^ 2 + 30.74 ^ 2} = 77.1$ N.