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Question
Define elastic potential energy.
Answer
The energy **stored in a spring** (or springy material) when it is **stretched or squashed**. Unit: the joule (J).
Question
Formula for elastic potential energy?
Answer
$E_H = \tfrac{1}{2}k\,\Delta x^{2}$ — half × spring constant × extension squared. (Also written E_p = ½kx².)
Question
What is the spring constant k?
Answer
How **stiff** a spring is — the force needed per metre of stretch. Unit: N m⁻¹ (newtons per metre).
Question
What does Δx mean in E_H = ½kΔx²?
Answer
The **extension or compression** — how far the spring is stretched or squashed from its natural length, in metres.
Question
You double a spring's extension — what happens to the stored energy?
Answer
It becomes **four times** as big, because the extension is squared (2² = 4).
Question
How do you find the energy stored in a spring-coupled collision?
Answer
By conservation of energy: **E_H = kinetic energy before − kinetic energy of the combined motion**.
Question
How do you find the carts' common speed in a spring collision?
Answer
From **conservation of momentum**: total momentum before = (combined mass) × common speed.
Question
What is the unit of elastic potential energy?
Answer
The **joule (J)** — the same unit as all other forms of energy.
Question
Find the energy stored: k = 300 N m⁻¹, Δx = 0.020 m.
Answer
E_H = ½ × 300 × 0.020² = ½ × 300 × 0.0004 = 0.060 J.
Question
A spring releases 0.60 J in 0.015 s. Find the average power.
Answer
Power = energy ÷ time = 0.60 ÷ 0.015 = 40 W.
Question
Elastic PE vs gravitational PE — what's the difference?
Answer
Elastic PE (½kΔx²) is stored by **stretching/squashing** a spring; gravitational PE (mgΔh) is stored by **lifting** a mass to a height. Both are in joules.
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