A-level · Forces & Newton's laws

Newton's laws and F = maExam-style questions

Newton's three laws and the one equation that runs all of dynamics — the RESULTANT force equals mass times acceleration — applied along a line and to forces given as 2-D vectors, why weight is mg and the normal reaction is whatever balances the rest, and how a lift problem is just F = ma done vertically.

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12 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4 Level 5

1
[In this question, $\mathbf{i}$ and $\mathbf{j}$ are horizontal unit vectors.]

A crate of mass 25 kg rests at the point $A$ on a horizontal floor. The crate is modelled as a particle and the floor is modelled as smooth.

Two workers start to pull the crate using two horizontal ropes. The forces exerted on the crate by the ropes are constant and are $(36\mathbf{i} + 15\mathbf{j})$ N and $(p\mathbf{i} + q\mathbf{j})$ N, where $p$ and $q$ are constants.

The crate moves in the direction of the vector $(2\mathbf{i} - \mathbf{j})$ .
(a) Show that $p + 2q + 66 = 0$

(4 marks)

Five seconds after the workers start to pull, the crate is at the point $B$ .

Given that $p = 4$
(b) find the distance $AB$ .

(5 marks)
Level 4 · 9 marksTry it