Four workers each push an identical 25 kg crate along a level warehouse floor through the same 3.0 m displacement directed due east. In every case the crate moves at constant speed. Each worker applies a constant 200 N force to the crate, but the directions differ as follows:
• Case P: force directed due east (0° above the horizontal).
• Case Q: force directed 30° above the horizontal toward the east.
• Case R: force directed 30° below the horizontal toward the east.
• Case S: force directed due west (180° from the crate’s displacement).
Ignore any vertical motion of the crate; assume the floor is perfectly smooth except as needed to satisfy the motion conditions.
(1) For each case, calculate the numerical value and sign (positive, negative, or zero) of the work done by the worker’s applied force during the 3.0 m displacement.
(2) Rank the four cases from the greatest positive work to the greatest negative work by the applied force, clearly indicating any ties.
(3) Explain physically why the magnitudes and signs of work differ among the four cases even though the force magnitude is the same in every case.