Question

four machines in a factory are moving crates around. rank them from greatest (1) to least (4) work done. force: 3f displacement: d time: ½t force: f displacement: d time: t force: ½f displacement: d time: 3t force: ½f displacement: 3d time: t

Explanation:

Step1: Recall Work Formula

Work \( W \) is calculated as \( W = F \times d \) (force times displacement), time does not affect work (only power).

Step2: Calculate Work for Each Machine

• Machine 1: \( W_1 = 3F \times D = 3FD \)
• Machine 2: \( W_2 = F \times D = FD \)
• Machine 3: \( W_3 = \frac{1}{2}F \times D = \frac{1}{2}FD \)
• Machine 4: \( W_4 = \frac{1}{2}F \times 3D = \frac{3}{2}FD \)

Step3: Rank by Work Magnitude

Compare \( 3FD \), \( FD \), \( \frac{3}{2}FD \), \( \frac{1}{2}FD \). Order from greatest to least: \( 3FD \) (1st), \( \frac{3}{2}FD \) (2nd), \( FD \) (3rd), \( \frac{1}{2}FD \) (4th). So machines:

1. Force: \( 3F \), Displacement: \( D \)
2. Force: \( \frac{1}{2}F \), Displacement: \( 3D \)
3. Force: \( F \), Displacement: \( D \)
4. Force: \( \frac{1}{2}F \), Displacement: \( D \)

Answer:

1. Force: \( 3F \), Displacement: \( D \)
2. Force: \( \frac{1}{2}F \), Displacement: \( 3D \)
3. Force: \( F \), Displacement: \( D \)
4. Force: \( \frac{1}{2}F \), Displacement: \( D \)