# D’Alembert’s principle and conservation of energy principles

Tags:
1. Dec 3, 2014

### lozoot96

1. The problem statement, all variables and given/known data
A load of 10 kg is pulled up a lubricated slideway, set at an angle of 30° to the horizontal, such that the load is accelerated from rest to a velocity of 1 m/s whilst travelling up the plane through a distance of 1 m. The frictional resistance to this motion is 10 N and g = 9.81 m/s2.

Using a) d’Alembert’s principle, then b) conservation of energy principles, find:

i) the work done in moving the load as described
ii) the maximum input power provided by the pulling device.

2. Relevant equations
honestly no idea.

3. The attempt at a solution
i have done my best to research d'Alembert's princeiples but i cant get a single hint anywhere.

2. Dec 3, 2014

### PhanthomJay

Well things can get rather complex using the full description of his principle, as you may have found out by googling it on the Wiki site.
D'Alembert's principle is good to use in certain cases, this not being one of them.
Essentially, however, his principle takes Newton's 2nd law, $F_{net} = ma$, and rearranges it to $F_{net} - ma = 0$ . Here, the system can be said to be in a state of dynamic equilibrium, where the '-ma' term is called the ficticious inertial force acting opposite to the real net force. In equilibrium, the net work done by all forces, including the inertial force, is 0. You'll have to calculate the acceleration using the kinematic equations. In calculating the work done by the pulling force, you'll have to subtract out the work done by gravity and friction. I don't like it. Try starting first using conservation of energy to see what you get.