The gravitational force on a body, W=mg, acting vertically downwards (in N).

Value of g near Earth's surface?

9.8 m s⁻² (or 9.81 m s⁻²).

Does mass change with location?

No. Mass is constant; weight changes because g changes.

Is g a universal constant?

No. It depends on location, e.g. about 1.6 m s⁻² on the Moon.

Tension when a lift moves at constant velocity?

T=mg (the resultant force is zero).

How do you handle forces given as vectors?

Add to find the resultant, then use \mathbf{F}=m\mathbf{a}.

Acceleration of a body falling freely?

g downwards, whatever its mass.

The constant acceleration equations?

v=u+at, s=ut+\frac12at^2, v^2=u^2+2as, s=\frac{u+v}{2}t

Units of force, mass and acceleration?

newton (N), kilogram (kg), m s⁻².

Newton's second law, weight and gravityAQA A-Level Maths: Flashcards

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State Newton's second law.

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State Newton's second law.: The resultant force on a particle equals its mass times its acceleration, $F=ma$ , in the direction of the resultant.
What is weight?: The gravitational force on a body, $W=mg$ , acting vertically downwards (in N).
Value of $g$ near Earth's surface?: $9.8$ m s⁻² (or $9.81$ m s⁻²).
Does mass change with location?: No. Mass is constant; weight changes because $g$ changes.
Is $g$ a universal constant?: No. It depends on location, e.g. about 1.6 m s⁻² on the Moon.
Force needed to give $8$ kg an acceleration of $2.5$ m s⁻²?: $20$ N
Tension when a lift of mass $m$ accelerates upwards at $a$ ?: $T-mg=ma$ , so $T=m(g+a)$ .
Tension when a lift moves at constant velocity?: $T=mg$ (the resultant force is zero).
How do you handle forces given as vectors?: Add to find the resultant, then use $\mathbf{F}=m\mathbf{a}$ .
Acceleration of a body falling freely?: $g$ downwards, whatever its mass.
The constant acceleration equations?: $v=u+at$ , $s=ut+\frac12at^2$ , $v^2=u^2+2as$ , $s=\frac{u+v}{2}t$
Units of force, mass and acceleration?: newton (N), kilogram (kg), m s⁻².

Exam questions on Newton's second law, weight and gravity

A box of mass $8$ kg is pulled across smooth horizontal ground by a constant horizontal force of $20$ N. The box starts from rest.
Find the distance travelled by the box in the first $4$ s.2 marks
A lift of mass $500$ kg is raised and lowered by a vertical cable. Take $g=9.8$ m s⁻² and ignore air resistance.
While the lift is moving upwards at $2$ m s⁻¹ the cable snaps. Find the further height the lift rises before it is instantaneously at rest.2 marks
A particle of mass $2$ kg is acted on by two forces $\mathbf{F}_1=(6\mathbf{i}-2\mathbf{j})$ N and $\mathbf{F}_2=(\mathbf{i}+8\mathbf{j})$ N, and no other forces. The vectors $\mathbf{i}$ and $\mathbf{j}$ are perpendicular unit vectors.
Find the acceleration of the particle.3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).