A uniform metre stick of negligible mass is pivoted at the 20 cm mark on a horizontal…

PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

A uniform metre stick of negligible mass is pivoted at the 20 cm mark on a horizontal friction-less support. Three forces act perpendicular to the stick in the vertical plane: •

F_{1}=8\,\text{N}

downward at the 0 cm mark. •

F_{2}=5\,\text{N}

upward at the 90 cm mark. • An unknown force

F_{3}

acts at the 60 cm mark in a direction to be determined. The stick is required to remain in rotational equilibrium. (i) Taking the upward direction as positive, write the algebraic expression for the net torque about the pivot in terms of

F_{3}

. (ii) Hence calculate the magnitude and sense (upward or downward) of

F_{3}

that will keep the stick in rotational equilibrium. (iii) If

F_{3}

is applied as found in part (ii), compute the net force acting on the stick and comment on whether translational equilibrium is also achieved.

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