Answer to Question #115148 in Classical Mechanics for asma ali

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 $(W)=F.d = 1344\times 120=161280J$