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 object lie on the same horizontal line. What is the work done by the force of gravity on the object ?

Explanation

To solve the problem of calculating the work done by the force of gravity on an object thrown at a certain angle to the ground, we can follow these steps:

### Step 1: Understand the Motion of the Object
The object is thrown at an angle and follows a curved path (projectile motion) before returning to the ground. The initial point (A) and the final point (B) of the object's path are at the same horizontal level.

**Hint:** Remember that in projectile motion, the object moves up and then down, but the starting and ending heights are the same.

### Step 2: Identify the Forces Acting on the Object
The primary force acting on the object during its flight is gravity, which acts downwards with a force equal to \(mg\) (where \(m\) is the mass of the object and \(g\) is the acceleration due to gravity).

**Hint:** The force of gravity is constant and acts vertically downward throughout the motion.

### Step 3: Define Work Done by a Force
Work done by a force is calculated using the formula:
\[ \text{Work} = \text{Force} \times \text{Displacement} \times \cos(\theta) \]
where \(\theta\) is the angle between the force and the direction of displacement.

**Hint:** The direction of the force and the direction of displacement are crucial in determining the work done.

### Step 4: Analyze the Displacement in the Direction of Gravity
In this case, while the object moves from point A to point B, it returns to the same vertical position (height). Thus, the vertical displacement (which is in the direction of the gravitational force) is zero.

**Hint:** Displacement in the direction of gravity is the change in height. If the initial and final heights are the same, the displacement is zero.

### Step 5: Calculate the Work Done by Gravity
Since the vertical displacement is zero, we can substitute this into the work formula:
\[ \text{Work} = mg \times 0 \times \cos(0) = 0 \]
Thus, the work done by the force of gravity on the object is zero.

**Hint:** Remember that if there is no displacement in the direction of the force, the work done is always zero.

### Final Answer
The work done by the force of gravity on the object is **0 Joules**.