CAIE A-Level Mathematics 4.4.1 Newton's Second Law with Forces

Practise resolving tension, friction, thrust, resistance and weight and applying ΣF = ma to a constant-mass particle or vehicle moving along a line or inclined plane.

Exam points

resolve perpendicular to contact first when friction depends on the normal reaction
sum signed forces along the direction of motion and equate the result to ma
solve the force equation for tension, thrust, braking force or acceleration with correct units

[Maximum number: 4]

A particle P of mass 0.2 kg lies at rest on a rough horizontal plane. A horizontal force of 1.2 N is applied to P.

Given instead that the coefficient of friction between P and the plane is 0.3 , find the distance travelled by P in the third second of its motion.

$1.2-0.3 \times 0.2 g=0.2 a$

*M1

Resolve horizontally using
Newton's Second Law; 3 relevant
terms; allow sign errors; R=0.2 g
only.

a=3

A1

0.6=0.2 a only seen, allow with
BOD, but if 0.6 as friction being used as resultant force, this is
M0A0.

$s_{3}=0+\frac{1}{2} \times 3 \times 3^{2}[=13.5] s_{2}=0+\frac{1}{2} \times 3 \times 2^{2}[=6]$

DM1

For use of $s=u t+\frac{1}{2} a t^{2}$ (or a
complete method) to find a distance
at least once with u=0 and their
positive a and t=2 or t=3.

Distance $=13.5-6=7.5 \mathrm{~m}$

A1

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4.4.1—Forces question 1