Question

As shown in the figure below, seven forces all with magnitude |F| = 57 N are applied to an irregularly shaped object. Each force is applied at a different location on the object, indicated by the tail of the arrow; the directions of the forces differ. The distances shown in the diagram have these values: w=7m, h=16 m, and d=12 m.

For each force, calculate the z component of the torque due to that force, relative to location A (x to the right, y up, z out of the page). Make sure you give the correct sign. 

Relative to location A, what is the z component of the net torque acting on this object? 

Answer 1

1 )

τ₁ = F*w +z = 57*7 = + 399 N*m

τ₂ = 0

τ₃ = 0  

becuse point is on location A in case of 2 and line of action is passing through point A in case of 3

τ₄ = - F*h = 57*16 = -912 N.m

τ₅ = - F*h = 57*16 = -912 N.m

τ₆ = - F*h = 57*16 = -912 N.m

τ_z at distance d = F*dsinθ = 57*12 =684 N.m

Total torque = add them all with sign = 399+ 3*-912 +684 = -1653 N.m

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