Answer to Question #165296 in Mechanical Engineering for Terence

Question #165296

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.

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Expert's answer

conservation of energy is simpler as compared to D Alembert principle.

It accounts for loss of energy die to friction and there are no assumptions. It says that total energy of isolated system remains constant. Whereas for D Alembert it introduces the concept of virtual force.

Please look into the image for calculations.

Velocity comes out to be approximately 8.1 m/s2.

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