Question

Compare the use of D’Alembert’s Principle and the Principle of Conservation of Energy to solve the following problem. Use diagrams to illustrate your answers.


A car with a mass of 1200kg accelerates up a road with a slope of 1 in 6, increasing its speed from 10kmh-1 to 60kmh-1, while travelling along the road a distance of 120m, against a frictional resistance of 800N. Calculate the tractive effort (force) required to propel the car up the hill.

Answer 1

As per D'Alembert Principle, the sum of incremental virtual works done by all external forces (F) acting in conjunction with virtual displacement.

As per the question,

mass of the car $(m)=1200kg$

slop of the rod $(\tan \theta)=\dfrac{1}{6}$

$\sin \theta =\dfrac{1}{\sqrt{37}}$ ,

$\cos \theta=\dfrac{6}{\sqrt{37}}$

initial speed $(u)=10 kmph =10\times \dfrac{1000}{3600}=\dfrac{25}{9} m/sec$

final speed $(v)=60kmph =60\times \dfrac{1000}{3600}=\dfrac{50}{3} m/sec$

distance covered along the road $(d)=120m$

Frictional resistance force $(f)=800N$

acceleration of the block $=\dfrac{v^2-u^2}{2s}=\dfrac{(\dfrac{50}{3})^2-(\dfrac{25}{9})^2}{2\times 120}=\dfrac{268.27}{240}=1.12m/sec^2$

so F =ma

$F=1200\times 1.12 =1344 N$

Hence, work done $(W)=F.d = 1344\times 120=161280J$