Work done by a variable force is numerically equal to ...A... under... B„. displacement curve.

Options

A. force area
B. area force
C. force volume
D. work done area

Answer

To solve the question regarding the work done by a variable force, we need to understand the relationship between work, force, and displacement. Here’s a step-by-step solution:

### Step 1: Understand the concept of work done by a force
Work done (W) by a force is defined as the product of the force (F) and the displacement (s) in the direction of the force. Mathematically, it is expressed as:
\[ W = F \cdot s \]
However, when the force is variable, we need to consider the integral of the force over the displacement.

### Step 2: Define the work done by a variable force
For a variable force, the work done can be calculated using the integral of the force with respect to displacement. If the force varies with displacement, the work done can be expressed as:
\[ W = \int F(s) \, ds \]
where \( F(s) \) is the force as a function of displacement.

### Step 3: Relate work done to the area under the force-displacement curve
The work done by a variable force can be visualized graphically. If we plot the force (F) on the y-axis and the displacement (s) on the x-axis, the work done by the force is equal to the area under the curve of the force versus displacement graph.

### Step 4: Conclusion
Thus, we conclude that the work done by a variable force is numerically equal to the area under the force-displacement curve.

### Final Answer
The work done by a variable force is numerically equal to the area under the force-displacement curve.

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