Edexcel A-Level Mathematics AS M1.4.1 Concept of a Force Questions

Practise modelling forces as scalars or vectors, combining components, and applying F = ma to find accelerations, masses or unknown force constants.

Exam points

form F = ma with the correct mass after resolving or adding force vectors
equate i and j components to find unknown constants in a resultant force

[Maximum number: 3]

[In this question i and j are horizontal perpendicular unit vectors.]

A particle P of mass 2 kg moves on a smooth horizontal surface under the action of two forces $\mathbf{F}_{1}$ and $\mathbf{F}_{2}$ , where $\mathbf{F}_{1}=(-2 \mathbf{i}+3 \mathbf{j}) \mathrm{N}$ and $\mathbf{F}_{2}=(4 \mathbf{i}+2 \mathbf{j}) \mathrm{N}$ .

Find the acceleration of P.

At time t=0, the velocity of P is $(3 \mathbf{i}-4 \mathbf{j}) \mathrm{ms}^{-1}$

Resultant force
$=(-2 \mathbf{i}+3 \mathbf{j}+4 \mathbf{i}+2 \mathbf{j})=(2 \mathbf{i}+5 \mathbf{j})(\mathrm{N})$
Seen or implied

Correct use of F=m a
Must have added the forces

Acceleration
$=(\mathbf{i}+2.5 \mathbf{j})\left(\mathrm{ms}^{-2}\right)$
Isw if they find the
magnitude

[3]

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Edexcel A-Level Mathematics AS M1.4.1 Concept of a Force Questions question 1