You pull a sled with force 100 N at some angle to the ground, moving it 10 m. Which single quantity decides how much work ( $\vec{F}\cdot\vec{d}$ ) you did?

Hints

$\vec{F}\cdot\vec{d} = Fd\cos\theta$ , everything but $\theta$ is fixed here.
Pull straight up ( $\theta = 90°$ ) and the sled goes nowhere: $\cos 90° = 0$ .

Show the answer

A. The angle of your pull

Why

The dot product is a projection: it pays only for the force component along the motion. At $0°$ you get all 1000 J; at $90°$ , nothing. Whenever physics asks "how much of this acts along that?", a dot product is the answer.

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You pull a sled with force 100 N at some angle to the ground, moving it 10 m. Which single quantity decides how much work (F⃗⋅d⃗\vec{F}\cdot\vec{d}F⋅d) you did?

Practise Dot Product, Cross Product, and Applications

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You pull a sled with force 100 N at some angle to the ground, moving it 10 m. Which single quantity decides how much work ( $\vec{F}\cdot\vec{d}$ ) you did?