Calculate the torque about the z-axis that is out of the page at the origin in the following figure, given that F1=3N,F2=2N,F3=3N,F4=1.8N.

Question

Calculate the torque about the z-axis that is out of the page at the origin in the following figure, given that F1=3N,F2=2N,F3=3N,F4=1.8N.

https://openstax.org/resources/c1c0f79ed0ff5625cf56b263f8187818a947a1d0

Answer 1

Forces are vectors. When calculating torques for forces, only the perpendicular component of the force to the line of action accounts for the resulting torque; therefore, starting with F₁:

1. T₁ = - ( 3m ) F₁ = - (3m) (3N) = - 9 Nm
2. T₂ = + ( 2m ) F₂ · cos ( 30⁰ ) = + (2m) (2N) cos(30⁰) = 3.464 Nm
3. T₃ = 0; this contributes nothing because it passes through the axis itself
4. T₄ = - ( 2m ) F₄ = - (2m) (1.8N) cos(20⁰) = - 3.383

The total torque is found by adding each of these torques:

1. T = T₁ + T₂ + T₃ + T₄
2. T = ( - 9 N·m ) + ( 3.464 N·m ) + 0 - ( 3.383 N·m)
3. T = - 8.92 N·m

Because the result is negative, the torque is into the paper.