Linearizing relationships & testing a law
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Flip to reveal answersWhat does 'linearizing' a relationship mean?
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Question
What does 'linearizing' a relationship mean?
Answer
**Re-plotting a curved law as a straight line** by choosing the right quantity for each axis (e.g. P against 1/V, or d against √P).
Question
What is the straight-line form you aim for?
Answer
**Y = mX + c** — match your two plotted quantities to Y and X; the gradient m and intercept c are physics quantities.
Question
What does a straight line through the origin show?
Answer
The two plotted quantities are **directly proportional**.
Question
Straight line, but it does NOT pass through the origin — what does that mean?
Answer
The relationship is **linear but NOT directly proportional** (there is a non-zero intercept c).
Question
How can you test 'directly proportional' from a table without a graph?
Answer
Check the **ratio Y/X is constant** across the rows. Different ratios → not proportional.
Question
To straighten a law like y = k·x², what do you plot?
Answer
**y (up) against x² (across)** — then the gradient is k.
Question
To straighten a law like y = k·√x, what do you plot?
Answer
**y (up) against √x (across)** — then the gradient is k.
Question
After linearizing, what is the gradient?
Answer
A **physics quantity** (a constant in the law) — quote it **with units**, never 'just a number'.
Question
Data booklet rule: uncertainty in y = ab/c?
Answer
Add **fractional** uncertainties: Δy/y = Δa/a + Δb/b + Δc/c.
Question
Data booklet rule: uncertainty in y = aⁿ?
Answer
Multiply the fractional uncertainty by |n|: Δy/y = |n·Δa/a| (e.g. ×½ for a square root).
Question
Why must the gradient line you choose make the graph straight?
Answer
A straight line has one gradient you can read directly; a curve has a changing slope you cannot read as a single value.
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Full study notes for Linearizing relationships & testing a law
Topic 6.1 hub
Experimental skills
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Physics exam skills
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