How Can D'Alembert's Principle Help Solve This Problem?

[Owen Griffiths]

Homework Statement

Just asking for a little help on this question

50kg object is pulled across a rough horizontal surface with a uniform force of 250N for 15m from rest, the surface has a frictional coefficient of 0.4, calculate the acceleration using dealemberts principle
But this results in a minus answer, so I'm lost, any help would be appreciated!

Homework Equations

Conservation of energy, d'alemberts principle

The Attempt at a Solution

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I have worked out the acceleration using conservation of energy using

PE+KE+Win = PE+KE+Wout+losses

To find the final velocity, and used

a=v^2-u^2/2s

To find acceleration which comes to 1.08m/s^2

Now the other part of the question is use d'alemberts principle to solve the same problem but I cannot for the life of me work this out, it's probably really simple but I just can't see it

I thought I would go down the route of force in minus the forces against = 0 to find the inertia force and use that to find acceleration, with F = -ma

But this results in a minus answer, so I'm lost, any help would be appreciated!

 

[Let'sthink]

I think you have already used the de Alembert's Principle in a way, after all how do you evaluate losses, Perhaps You think you have used Energy conservation Principle. But the principle that you have used, Newton's Laws of motion and de Alembert's principle are equivalent to each other and derivable from each other. Just think over. Solving a problem mechanically gives you pleasure may be but not insight. try to develop insight.

Also so called inertial force is not a force at all. That is also creating a conceptual problem, it is the name given to the product ma and because you think it is inertial you give it a minus sign but then you keep it on left hand side only try to equate the sum to zero. Sum of all forces including the so called inertial force = 0 is the principle. Personally I do not like the idea of inertial force at all. It creates more conceptual problems than solve them.

 

[Owen Griffiths]

Completely agree on insight, but I'm struggling atm, just a bit of back ground, I'm not a maths or physics student, I'm doing a career change atm and have to study mechanical principle at this level, we have to go through so many topics that I have to admit I very rarely understand the topics we do but rather answer most of the questions parrot fashion, which so far has been surprisingly successful!

But more into the working out
Car Mass: 50kg
Co-efficient of friction is 0.4
N = (mg) = 50 x 9.81 = 490
Frictional Resistance (Fr) = μN = 0.4x490 = 196N
Distance = 15 meters.

PE + KE + Win = PE + KE + Wout + Losses
0 + 0 + (F x Distance) = 0 + (1/2 mv^2)+ 0 + (Fr x distance)

(F x Distance) - (Fr x distance) = 1/2 x mv^2

(250N x 15 meters) – (196 x 15 meters) = 1/2 x 50v^2

(250 x 15 meters) – (196 x 15 meters) / (1/2 x 50) = v^2

32.4 = v^2

5.69 = V

Velocity is 5.69 m/s

 

[Owen Griffiths]

Then using

a=v^2-u^2/2s

I come to 1.08m/s^2

 

[Owen Griffiths]

Would it be simply

Force - frictional force

250-196= 54

F=ma

54 = 50a

a = 54/50

This equals 1.08 m/s^2 in my first answer

 

[Owen Griffiths]

However I thought I must use. F = -ma??

 

[Let'sthink]

That is the expression for inertial force. Newton's law do not hold good for accelerated frames. So it does not hold good in the frame of the particle where it is at rest. But if we introduce the concept of pseudo force which defined as -ma, where a is the acceleration of the particle in inertial frame, then the law can be made hold true. So in its own frame acceleration = 0 so net force including inertial force = 0 so
Fnet = Fnet in inertial frame - ma = 0 which is nothing but the expression of Newton's law F net = ma in inertial frame. But note that ma is not the result of any interaction. But all those forces thatyou talked about in this problem relate to some interaction except -ma!