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: 1]

A car has mass 1400 kg . When the speed of the car is $\mathrm{vms}^{-1}$ the magnitude of the resistance to motion is $k v^{2} \mathrm{~N}$ where k is a constant.

The car moves at a constant speed of $24 \mathrm{~m} \mathrm{~s}^{-1}$ up a hill inclined at an angle of $\alpha$ to the horizontal where $\sin \alpha=0.12$ . At this speed the magnitude of the resistance to motion is 480 N .

Find the value of k.

$\left[k \times 24^{2}=480 \Rightarrow\right] k=\frac{5}{6}$
OE, e.g. $\frac{480}{576}, 0.833$ or better.

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CAIE A-Level Mathematics AS 4.4.1 Forces Questions question 1