The work W done by a constant force F⃗ on an object that undergoes displacement s⃗ from point 1

The work W done by a constant force F⃗ on an object that...

The work $W$ done by a constant force $\vec{F}$ on an object that undergoes displacement $\vec{s}$ from point 1 to point 2 is $W=\vec{F} \cdot \vec{s} .$ For $F$ in newtons (N) and $s$ in meters $(\mathrm{m}), W$ is in joules $(J) .$ If, during a displacement of the object, $\vec{F}$ has constant direction $60.0^{\circ}$ above the $-x$ -axis and constant magnitude $5.00 \mathrm{~N}$ and if the displacement is $0.800 \mathrm{~m}$ in the $+x$ -direction, what is the work done by the force $\overrightarrow{\boldsymbol{F}} ?$

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Key Concepts

Work

Work is defined as the energy transferred when a force causes displacement. It is calculated as the dot product of the force and displacement vectors, which means that only the component of the force acting in the direction of the displacement does work.

Dot Product

The dot product is a mathematical operation that multiplies two vectors and results in a scalar. It involves multiplying the magnitudes of the vectors and the cosine of the angle between them, and it is crucial for calculating work since it directly relates the force component in the direction of displacement.

Vector Decomposition

Vector decomposition involves breaking a vector into its components relative to a coordinate system. This process is essential for analyzing forces and displacements in multiple dimensions, allowing each component to be handled separately when calculating work or other vector-related quantities.

Angle Between Vectors

The angle between two vectors determines the effectiveness of the force in causing displacement. In the context of work, the cosine of this angle is used in the dot product formula, directly affecting the amount of work done by the force.

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