Answer to Question #165082 in Mechanical Engineering for Terence

Question

Task 2 – Compare and contrast the use of D’Alembert’s principle with the principle of conservation of energy to solve an engineering problem A motor vehicle having a mass of 800 kg is at rest on an incline of 1 in 8 when the brakes are released. The vehicle travels 30 m down the incline against a constant frictional resistance to motion of 100 N where it reaches the bottom of the slope. a) Using the principle of conservation of energy, calculate the velocity of the vehicle at the bottom of the incline. b) Using an alternative method that does not involve a consideration of energy, cacluate the velocity of the vehicle at the bottom of the incline. c) Discuss the merits of the two methods you have used for parts a) and b) of this question. Justify the use of an energy method for these types of problems.

Answer 1

As per D alembert's principle- The impressed force acting on the body are in dynamic equilibrium with inertia forces of body under motion.

$\Sigma F - ma=0$ .

As per law of conservation of energy it says that energy remain conserved it transfer from one form to another form as in case of motion, work done in body for its motion is equal to change in its Kinetic energy.

(a) Apply law of conservation of energy

Kinetic energy of particles = Potential enegry - frictional work done

$\frac{1}{2}mv^2= mgh-work by frictional force$ , $h=30 sin\theta= 30\times (1/8)=30\times 0.125$

so we will put value of h in above relation we get

$0.5\times 800v^2= 800\times 9.8\times 30\times 0.125- 100\times 30$

$v=\sqrt{\frac{26400\times 2}{800}}=8.12 m/s$

(b) Using D alembert's relation we get

accelerated force = $mg sin\theta$ - frictional force

$800a= 800\times 9.8 \times 0.125-100$

$a=1.1 m/s2$

u=inital veocity = 0 m/s s= 30 m

now,

$v^2= u^2+2\times a\times s$

v=8.13 m/s2

So here we are not getting much difference using both concept

but conservation energy concept is good