A constant force of 8N acting on an object displaces it through a distance of 3.0 m in the direction of force. Calculate work-done by the force on the object.
The Correct Answer and Explanation is:
To calculate the work done by the force on the object, we can use the formula for work:
[
\text{Work} (W) = F \times d \times \cos(\theta)
]
Where:
- ( W ) is the work done,
- ( F ) is the applied force,
- ( d ) is the displacement, and
- ( \theta ) is the angle between the force and the displacement.
Given:
- Force, ( F = 8 \, \text{N} )
- Displacement, ( d = 3.0 \, \text{m} )
- The force is applied in the direction of the displacement, so the angle ( \theta = 0^\circ ).
Step-by-Step Calculation:
Since the force is in the same direction as the displacement, the cosine of the angle between the force and displacement is:
[
\cos(0^\circ) = 1
]
Substituting the known values into the work formula:
[
W = 8 \, \text{N} \times 3.0 \, \text{m} \times 1
]
[
W = 24 \, \text{J}
]
Conclusion:
The work done by the force on the object is 24 joules (J).
Explanation:
In physics, work is done when a force causes a displacement of an object in the direction of the force. The formula for work is dependent on three factors: the magnitude of the force applied, the distance over which the force acts, and the angle between the force and the displacement. When the force is applied in the same direction as the displacement (as in this case), the angle between the force and the displacement is 0 degrees, so the cosine of the angle is 1, and the formula simplifies to ( W = F \times d ).
In this scenario, the applied force is 8 newtons, and the object moves through a distance of 3 meters in the direction of that force. Multiplying these values gives a work done of 24 joules. Work is measured in joules, where 1 joule is equivalent to 1 newton-meter (N·m). Therefore, the work done is 24 J, meaning that the force transferred 24 joules of energy to the object, causing it to move.