Question

20 multiple choice 1 point three different forces, a, b, and c act on a box as it slides to the right. each of the forces has the same magnitude, but they each have a different direction. rank the amount of work done by the forces on the box from greatest to least. a b c ∘ b > c > a ∘ b > a > c ∘ a = b = c ∘ c > a > b

Explanation:

Step1: Recall Work Formula

Work done by a force is given by \( W = Fd\cos\theta \), where \( F \) is force magnitude, \( d \) is displacement, and \( \theta \) is the angle between force and displacement. Here, \( F \) (magnitude) and \( d \) are same for all forces. So \( W \propto \cos\theta \).

Step2: Determine Angles for Each Force

• For Force B: The force is in the same direction as displacement (\( \theta = 0^\circ \)), so \( \cos(0^\circ) = 1 \).
• For Force A: The force is at an acute angle to displacement, so \( 0^\circ < \theta < 90^\circ \), and \( \cos\theta \) is between 0 and 1 (since \( \cos\theta \) decreases from 1 to 0 as \( \theta \) increases from 0 to 90).
• For Force C: The force is perpendicular to displacement (\( \theta = 90^\circ \)), so \( \cos(90^\circ) = 0 \).

Step3: Compare Work Done

Since \( W \propto \cos\theta \), and \( \cos(0^\circ) > \cos(\text{acute angle}) > \cos(90^\circ) \), the work done is \( W_B > W_A > W_C \).

Answer:

B > A > C (corresponding to the option "B > A > C")