find the work done in the figure below: figure depicts a Force with an arrow on cartesian coordinate system going in positive y and x quadrant and the angle the goes from the force along negative x axis and represents the displacement which is -6 m, the angle made is 120 degrees. The magnitude of the force is 40N 

To find the work done (\(W\)) by a force acting on an object, we use the formula:

\[
W = F \cdot d \cdot \cos\theta
\]

Where:
- \(F = 40 \, \text{N}\) (magnitude of the force),
- \(d = 6 \, \text{m}\) (displacement, given as -6 m, but magnitude is used in the formula),
- \(\theta = 120^\circ\) (angle between the force and displacement).

### Step-by-Step Solution:

1. **Substitute the given values into the formula**:
   \[
   W = 40 \cdot 6 \cdot \cos(120^\circ)
   \]

2. **Find \(\cos(120^\circ)\)**:
   \(\cos(120^\circ) = -\frac{1}{2}\) (using trigonometric properties of angles).

3. **Compute the work done**:
   \[
   W = 40 \cdot 6 \cdot \left(-\frac{1}{2}\right)
   \]

   \[
   W = 40 \cdot 6 \cdot -0.5 = -120 \, \text{J}
   \]

### Final Answer:
The work done is:

\[
W = -120 \, \text{J}
\]

The negative sign indicates that the force does work *against* the displacement.

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Would you like further clarification or graphical illustrations of this problem?  

Here are 5 related questions to deepen your understanding:
1. How does the angle between force and displacement affect the work done?
2. What happens to the work done if the angle changes to \(90^\circ\)?
3. How is the sign of work interpreted in physical situations?
4. What would be the work done if the force magnitude doubled?
5. Can work done ever be zero? Under what conditions?

**Tip:** Always consider the direction of force and displacement when solving work-related problems; angles greater than \(90^\circ\) typically

Find the work done in the figure below: the figure depicts a Force with an arrow on a Cartesian coordinate system going in the positive y and x quadrant. The angle from the force along the negative x-axis represents the displacement, which is -6 m. The angle made is 120 degrees. The magnitude of the force is 40 N.

Understand how to calculate the work done by a force of 40 N acting at an angle of 120 degrees to a displacement of -6 m. Learn key concepts such as the vector dot product and trigonometric functions, with step-by-step solutions. Suitable for high school students in Grades 10-12.

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