Work done & force-distance graphs
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Question
Define work done.
Answer
The **energy transferred** when a **force moves something through a distance**. Unit: the **joule (J)**.
Question
What is the equation for work done?
Answer
$W = Fs\cos\theta$ — force × distance × the cosine of the angle between them. (Given in the data booklet.)
Question
In W = Fs cos θ, what is θ?
Answer
The **angle between the force and the direction of motion**. If the force is along the motion, θ = 0 and cos 0 = 1, so W = Fs.
Question
How much work does a force at 90° to the motion do?
Answer
**Zero** — cos 90° = 0, so W = 0. (e.g. the normal force on a block sliding along a floor.)
Question
What does the area under a force–distance graph represent?
Answer
The **work done** by the force.
Question
What is the unit of work?
Answer
The **joule (J)** — the same unit as all forms of energy.
Question
Push a wall that doesn't move — how much work do you do on it?
Answer
**Zero** — no movement means no distance, so no work, however hard you push.
Question
How do you get a final speed from the work done (object starting from rest)?
Answer
The work becomes kinetic energy: set **W = ½mv²** and solve for **v**.
Question
What is kinetic energy and its equation?
Answer
The energy of a moving object: $E_k = \tfrac{1}{2}mv^{2}$ (m = mass, v = speed). Given in the data booklet.
Question
A 9.0 N net force acts over 4.0 m on an object from rest. Work done?
Answer
W = Fs = 9.0 × 4.0 = **36 J** (which equals the kinetic energy gained).
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Topic 1.3 hub
Work, energy and power
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