Choose which statement describes a process in which an external force does negative work on the system. The person is not part of the system.
(a) A person slowly lifts a box from the floor to a tabletop.
(b) A person slowly lowers a box from a tabletop to the floor.
(c) A person carries a bag of groceries horizontally from one location to
another.
(d) A person holds a heavy suitcase.
The correct answer and explanation is :
Correct Answer:
(b) A person slowly lowers a box from a tabletop to the floor.
Explanation:
In physics, work is defined as the transfer of energy due to a force applied over a displacement. The work done on a system is given by the equation:
[
W = F d \cos(\theta)
]
where:
- ( W ) is the work done,
- ( F ) is the force applied,
- ( d ) is the displacement, and
- ( \theta ) is the angle between the force and displacement vectors.
For negative work to occur, the force applied must oppose the displacement.
Analysis of Each Option:
- (a) A person slowly lifts a box from the floor to a tabletop.
The person exerts an upward force on the box, and the displacement is also upward. Since the force and displacement are in the same direction, the work done by the person is positive, meaning the external force does not do negative work. - (b) A person slowly lowers a box from a tabletop to the floor.
The force exerted by the person is upward to counteract gravity, but the displacement is downward. Since the force applied is in the opposite direction of displacement, work done by the external force (person) is negative. This matches the condition in the question. - (c) A person carries a bag of groceries horizontally.
The force applied by the person is vertical (upward to support the weight of the groceries), while displacement is horizontal. Since the force and displacement are perpendicular ((\theta = 90^\circ)), the work done is zero. - (d) A person holds a heavy suitcase.
There is no displacement, so work done is zero because ( W = F d \cos(\theta) ) and ( d = 0 ).
Thus, the correct answer is (b) lowering the box since the external force does negative work.
