CAIE A-Level Mathematics AS 4.4.1 Forces Questions

Practise modelling connected particles, rough surfaces and lifts using Newton’s laws.

Exam points

apply Newton’s second law to particles and connected systems
include friction, tension, normal reaction and weight in force models
solve mechanics problems involving lifts, planes and variable motion

[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
0.6=0.2 a only seen, allow with
BOD, but if 0.6 as friction being used as resultant force, this is
$s_{3}=0+\frac{1}{2} \times 3 \times 3^{2}[=13.5] s_{2}=0+\frac{1}{2} \times 3 \times 2^{2}[=6]$
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 $=13.5-6=7.5 \mathrm{~m}$
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CAIE A-Level Mathematics AS 4.4.1 Forces Questions question 1