Question

An object thrown at a certain angle to the ground moves in a curved path and falls back to the ground. The initial and the final points of the path of the object lie on the same horizontal line. What is the work done by the force of gravity on the object?

Answer 1

The work done by the force of gravity on an object moving in a curved path, where the initial and final points lie on the same horizontal line, is given by:

Concept:

Work done by a force: \[ W = F \cdot d \cdot \cos \theta \] where \( F \) is the force, \( d \) is the displacement, and \( \theta \) is the angle between the force and displacement.

- Force of gravity acts vertically downward. 
- The horizontal displacement of the object is along the ground. 
- The vertical displacement of the object is zero (initial and final points are at the same height).
- Therefore, vertical displacement \( h = 0 \), and the work done by gravity: \[ W = m g h = m g \cdot 0 = 0 \]

Answer:

The work done by the force of gravity on the object = 0 J.

Note: Gravity only does work when there is a change in vertical height. Since the object starts and ends at the same height, no net work is done by gravity.