Work done by gravitational force on a man, in lifting a bucket out of ...
When the man pulls the bucket outside the well the gravitational potential of the man + bucket system increases and hence the work done by the gravitational force is negative.
Work done by gravitational force on a man, in lifting a bucket out of ...
**Answer:**
The work done by a force is given by the equation:
**Work done (W) = Force (F) × Displacement (d) × cosθ**
Where θ is the angle between the force vector and the displacement vector.
In this context, the gravitational force is acting vertically downwards, while the displacement is in the upward direction. Therefore, the angle θ between the force and displacement vectors is 180 degrees.
Let's analyze the options given:
a) Negative: If the angle between the force and displacement vectors is 180 degrees, then cosθ will be equal to -1. Since the force is acting in the opposite direction to the displacement, the work done will be negative.
b) Positive: If the angle between the force and displacement vectors is 0 degrees, then cosθ will be equal to 1. In this case, the force and displacement are in the same direction, so the work done will be positive.
c) Zero: If the angle between the force and displacement vectors is 90 degrees, then cosθ will be equal to 0. In this case, the force is perpendicular to the displacement, so no work is done.
d) Infinity: Work done is a scalar quantity and cannot be infinite.
Since the gravitational force and the upward displacement have an angle of 180 degrees between them, the correct answer is option 'a' - negative. The work done by the gravitational force on the man in lifting the bucket out of the well is negative because the force is acting in the opposite direction to the displacement. This means that the man is doing work against the gravitational force to lift the bucket. The negative sign indicates that the man is expending energy in doing this work.