Work is a physical quantity that measures the energy transferred by a force acting on an object as it moves in the direction of that force. It is the product of the applied force and the distance moved in the direction of the force.
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Work is only done when a force is applied in the same direction as the displacement of the object.
The formula for work is $W = F \cdot d \cos \theta$, where $F$ is the force, $d$ is the displacement, and $\theta$ is the angle between the force and the displacement.
Positive work is done when the force and displacement are in the same direction, while negative work is done when the force and displacement are in opposite directions.
The SI unit of work is the joule (J), which is equivalent to a newton-meter (Nā m).
Work is a scalar quantity, meaning it has a magnitude but no direction.
Review Questions
Explain how the formula for work, $W = F \cdot d \cos \theta$, relates to the concept of work in the context of vectors.
The formula for work, $W = F \cdot d \cos \theta$, is directly related to the concept of work in the context of vectors. The force, $F$, and the displacement, $d$, are both vector quantities, meaning they have both magnitude and direction. The angle, $\theta$, between the force and the displacement is also a vector quantity. By including the cosine of the angle between the force and the displacement, the formula accounts for the fact that work is only done when the force is applied in the same direction as the displacement. This allows for the calculation of work in situations where the force and displacement are not perfectly aligned.
Describe how the direction of the force and displacement affect the sign of the work done.
The direction of the force and displacement relative to each other determines the sign of the work done. If the force and displacement are in the same direction, the work done is positive. If the force and displacement are in opposite directions, the work done is negative. This is because the cosine of the angle between the force and displacement is positive when they are in the same direction, and negative when they are in opposite directions. The sign of the work done is important in understanding the energy transfers and transformations that occur during a physical process.
Analyze how the concept of work relates to the conservation of energy principle.
The concept of work is closely tied to the conservation of energy principle, which states that energy can neither be created nor destroyed, but can only be transformed from one form to another. When work is done on an object, energy is transferred to that object, either increasing its kinetic energy, potential energy, or both. Conversely, when an object does work on its surroundings, it loses energy, which is then transferred to the surroundings. This exchange of energy through the performance of work is a fundamental aspect of the conservation of energy principle and is crucial for understanding the behavior of physical systems.