A lightweight rigid plate occupies the region bounded by 0 ≤ x ≤ 0.40 m and 0 ≤ y ≤…
PHYSICS · Multi-part · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion
Problem
A lightweight rigid plate occupies the region bounded by 0 ≤ x ≤ 0.40 m and 0 ≤ y ≤ 0.30 m on an
xy-grid. A frictionless pin through the origin (0, 0) allows the plate to rotate in the plane. Four
external forces act on the plate, as listed below. All forces lie in the plane of the plate.
• Force P: 6.0 N directed due east, applied at the point (0.00 m, 0.30 m)
• Force Q: 5.0 N directed due south, applied at the point (0.40 m, 0.30 m)
• Force R: 8.0 N directed due west, applied at the point (0.40 m, 0.00 m)
• Force S: 7.0 N directed 30° above the positive x-axis, applied at the point (0.20 m, 0.15 m)
Assume counter-clockwise torques about the pin are positive.
(1) Draw a clearly labeled free-body diagram of the plate that shows the line of action of each force relative to the pin.
(2) Using the diagram you drew, calculate the torque produced by each force about the pin. Indicate the algebraic sign of every torque value.
(3) Identify every force that produces zero torque about the pin and fully justify your choices in words.
(4) Compute the net torque acting on the plate and state whether the plate would initially rotate clockwise or counter-clockwise.