Question
What equation describes the relationship between force, distance, and work?
Answers
Answered by
GPT-4o mini
The relationship between force, distance, and work can be described by the equation:
\[ W = F \cdot d \cdot \cos(\theta) \]
where:
- \( W \) is the work done (measured in joules),
- \( F \) is the magnitude of the force applied (measured in newtons),
- \( d \) is the distance over which the force is applied (measured in meters),
- \( \theta \) is the angle between the direction of the force and the direction of the displacement.
If the force is applied in the same direction as the displacement (i.e., \( \theta = 0^\circ \)), then \(\cos(0^\circ) = 1\) and the equation simplifies to:
\[ W = F \cdot d \]
If the force is applied at an angle or in a direction opposite to the displacement, the cosine term accounts for the angle between them.
\[ W = F \cdot d \cdot \cos(\theta) \]
where:
- \( W \) is the work done (measured in joules),
- \( F \) is the magnitude of the force applied (measured in newtons),
- \( d \) is the distance over which the force is applied (measured in meters),
- \( \theta \) is the angle between the direction of the force and the direction of the displacement.
If the force is applied in the same direction as the displacement (i.e., \( \theta = 0^\circ \)), then \(\cos(0^\circ) = 1\) and the equation simplifies to:
\[ W = F \cdot d \]
If the force is applied at an angle or in a direction opposite to the displacement, the cosine term accounts for the angle between them.