https://file.aiquickdraw.com/mathbot/file/17280796202416kvhn5ik.jpg

To calculate the work done by the force, we need to use the concept of **work** from physics, which is defined as:

\[
W = \int F(x) \, dx
\]

Since the force varies with displacement, the work done is represented by the area under the force-displacement graph.

### Step-by-Step Solution:

1. **Look at the graph:**
   - The force \( F \) starts at \( 0 \, \text{N} \) when \( x = 0 \, \text{m} \), increases linearly to \( 4 \, \text{N} \) at \( x = 4 \, \text{m} \), and then decreases back to \( 0 \, \text{N} \) at \( x = 10 \, \text{m} \).
   - This forms a **triangle** from \( 0 \, \text{m} \) to \( 10 \, \text{m} \), with a peak at \( 4 \, \text{m} \) and \( 4 \, \text{N} \).

2. **Find the area of the triangle:**
   - The area under the curve will give the total work done.
   - The base of the triangle is \( 10.0 \, \text{m} \) (displacement), and the height is \( 4.0 \, \text{N} \) (force).

\[
\text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height}
\]
\[
\text{Area} = \frac{1}{2} \times 10.0 \, \text{m} \times 4.0 \, \text{N} = 20.0 \, \text{J}
\]

Thus, the **work done** by the force is **20.0 joules**.

Would you like more details or have any questions?

---

Here are 5 related questions:
1. How would the work done change if the peak force increased?
2. What if the displacement was increased but the force remained the same?
3. How does this calculation apply to non-linear force-displacement relationships?
4. What is the significance of the work done when the object starts and ends at rest?
5. How would you calculate work if the graph had multiple shapes?

**Tip:** The area under a force-displacement graph always represents the work done by the force over that displacement.

A horizontal force F applied to an object varies with its displacement as shown in the graph. Calculate the work done by the force when the object moves from x = 0 to x = 10.0 m.

Learn how to calculate the work done by a varying force using the area under a force-displacement graph. The force varies linearly with displacement, forming a triangle, and the work done is computed by finding the area under the curve. Suitable for high school physics students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation