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?

1. Scenario Description:
– The object is thrown at an angle to the ground and follows a curved path, ultimately falling back to the ground.
– The initial and final points of the object’s path lie on the same horizontal line.

2. Force of Gravity:
– The force of gravity acts vertically downward throughout the object’s motion.

3. Work Done Calculation:
– Work done (W) is given by the formula (W = Force x Displacement x cos(θ)).
– In this scenario, the force of gravity and the displacement of the object are perpendicular to each other.
– The angle between the force of gravity and the displacement is (90°).

4. Effect on Work Done:
– When the angle between the force and displacement vectors is (90°), the cosine of (90°) (cos(90°) = 0).
– Therefore, the work done by the force of gravity is zero in this situation.

5. Conclusion:
– In this described scenario where the object moves in a curved path and returns to its initial point horizontally, the work done by the force of gravity on the object is zero.

Understanding this concept helps to recognize that in cases where the force of gravity acts perpendicular to the displacement of an object (as in this curved path scenario), no work is done by gravity on the object.