To determine the work done by the man while carrying a suitcase up the stairs, we need to understand the concept of work and its direction.
Work:
Work is defined as the amount of energy transferred by a force acting on an object as it moves through a distance. Mathematically, work is calculated as the product of force and displacement, where the force and displacement are in the same direction.
In this scenario, the man is applying a force on the suitcase to lift it up the stairs. Let's analyze the possible directions of force and displacement:
Force:
The force applied by the man is directed upward, opposite to the force of gravity acting on the suitcase. This force is necessary to counteract the gravitational force and lift the suitcase.
Displacement:
The displacement of the suitcase is also directed upward, as the man is moving the suitcase vertically up the stairs.
Since the force and displacement are in the same direction, the work done by the man is positive. The man is exerting energy to lift the suitcase against gravity.
Therefore, the correct answer is Option A: positive.

Explanation:

When a man carries a suitcase in his hand and climbs up the stairs, he is doing work against gravity. In order to understand the work done by the man, we need to consider the definition of work and the forces involved.

Definition of Work:
Work is defined as the transfer of energy that occurs when a force is applied to an object and that object is displaced in the direction of the force.

Forces Involved:
In this scenario, the main force that the man is working against is gravity. As the man lifts the suitcase against gravity while climbing the stairs, he is applying an upward force on the suitcase.

Direction of Force:
The direction of the force applied by the man is opposite to the direction of displacement. The man is exerting an upward force on the suitcase, while the suitcase is moving upward along the stairs.

Calculation of Work:
Work is calculated using the formula: Work = Force × Distance × cos(θ), where θ is the angle between the force and the displacement.

In this case, the force applied by the man is in the upward direction, and the displacement of the suitcase is also in the upward direction, so θ = 0 degrees.

When the angle between the force and displacement is 0 degrees, the cos(0) = 1. Therefore, the work done by the man can be calculated as:

Work = Force × Distance × cos(0)
= Force × Distance × 1
= Force × Distance

Since both the force applied by the man and the displacement are in the upward direction, the work done by the man is positive.

Conclusion:
The correct answer is option 'A' - positive. The man is doing positive work by carrying the suitcase up the stairs as he is applying an upward force on the suitcase while it moves upward.