Suppose in Figure 6.2 that +1.10 ×10^3 J of work is done by the force 𝐅 (magnitude =30.0 N ) in

step 1 So we have a force which is at an angle to the displacement. So we start by saying work is equal

Suppose in Figure 6.2 that +1.10 ×10^3 J of work is done by...

Suppose in Figure 6.2 that $+1.10 \times 10^{3}$ J of work is done by the force $\mathbf{F}$ (magnitude $=30.0 \mathrm{N}$ ) in moving the suitcase a distance of $50.0 \mathrm{m} .$ At what angle $\theta$ is the force oriented with respect to the ground?

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Key Concepts

Work

Work is the measure of energy transfer that occurs when an object is moved over a distance by an external force. It is calculated as the product of the force magnitude, the displacement magnitude, and the cosine of the angle between the force and displacement vectors, encapsulating how effectively the force contributes in the direction of movement.

Vector Dot Product

The vector dot product is a mathematical operation that takes two vectors and returns a scalar. It inherently includes the cosine of the angle between the vectors, which is critical for calculating quantities like work, where only the component of the force parallel to the displacement does work.

Force Components

Force components are the projections of a force vector along different directions, typically resolved into horizontal and vertical parts. Decomposing a force enables the determination of the effective portion that acts in the direction of displacement, which is essential for accurately computing work.

Trigonometric Relationships

Trigonometric relationships, particularly the cosine function, are used to link the angle of the applied force with its effective component in the direction of displacement. Understanding these relationships is key to solving problems where the orientation of the force must be determined from the work done.

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