as a hiker descends a hill, the work done by gravity on the hiker is
a.) positive and depends on the path taken
b.) negative and depends on the path taken
c) positive and indepedent of the path taken
d.)negative and independent of the path taken
The correct answer is c) positive and independent of the path taken.
When a hiker descends a hill, gravity is doing work on the hiker by exerting a downward force. The work done by gravity is given by the equation:
Work = Force x Displacement x cos(angle)
In this case, since the force of gravity is acting in the same direction as the displacement (downward), the angle between the force and displacement is 0 degrees, making cos(0) = 1.
Therefore, the work done by gravity is positive, indicating that energy is transferred from the gravitational potential energy to the kinetic energy of the hiker as they descend the hill.
Additionally, the path taken by the hiker does not affect the work done by gravity. The work is dependent only on the initial and final positions of the hiker and the vertical displacement, not the specific path taken. Therefore, the work done by gravity is independent of the path taken, as stated in option c).
To determine the work done by gravity on a hiker as they descend a hill, we need to consider the direction of the force of gravity and the displacement of the hiker.
The force of gravity always acts downward, while the displacement of the hiker is in the direction of their descent, which is also downward. Since both the force and displacement are in the same direction, the angle between them is 0 degrees.
The formula for calculating work is given by:
Work = Force × Displacement × cos(θ)
Because the angle cos(0) is equal to 1, the equation simplifies to:
Work = Force × Displacement
As the hiker descends the hill, gravity pulls them downwards, and their displacement is also in the same downward direction. Therefore, the work done by gravity is positive.
Now, regarding the path taken, it is important to note that the work done by gravity does not depend on the path taken. Gravity only depends on the initial and final positions of the hiker, not on the route they choose.
Based on this information, the correct answer is:
c) positive and independent of the path taken