Question 3.SP.3: A 30-lb force acts on the end of the 3-ft lever as shown. De......
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 one 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 M_{O} points into the page. You can write it as
M_{O} = 30.8 lb·ft ↻ ◂
REFLECT and THINK: Always be alert for simplifications that can reduce the amount of computation.
