Question 3.SP.3: A 30-lb force acts on the end of the 3-ft lever, as shown. D...
A 30-lb force acts on the end of the 3-ft lever, as shown. Determine the moment of the force about O.
STRATEGY: Resolving the force into components that are perpendicular and parallel to the axis of the lever greatly simplifies the moment calculation.
MODELING and ANALYSIS: Replace the force by two components: one component P in the direction of OA and the other component Q perpendicular to OA (Fig. 1). Because O is on the line of action of P, the moment of P about O is zero. Thus, the moment of the 30-lb force reduces to the moment of Q, which is clockwise and can be represented by a negative scalar.
Q = (30 lb) sin 20° = 10.26 lb
M_O = −Q(3 ft)= −(10.26 lb)(3 ft)= −30.8 lb⋅ft
Because the value obtained for the scalar M_O is negative, the moment \pmb{M}_O points into the page.
You can write it as
M_O=30.8 lb⋅ft\circlearrowrightREFLECT and THINK: Always be alert for simplifications that can reduce the amount of computation.
