Solving D'Alembert's Equation: Homework Help

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Discussion Overview

The discussion revolves around solving a physics homework problem related to D'Alembert's equation, focusing on a car's acceleration on a slope, the forces involved, and calculations for tractive effort, work done, and average power. The scope includes theoretical understanding and practical application of physics concepts.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant expresses uncertainty about solving the problem and mentions their tutor's lack of assistance.
  • Another participant emphasizes the need to understand kinematics, Newton's laws, and energy concepts, suggesting that the original poster make an attempt at the problem.
  • A participant proposes a calculation for tractive effort using D'Alembert's equation, stating it equals gravitational force plus inertia resistance and frictional resistance, but does not clarify the definitions used for these terms.
  • Concerns are raised about the accuracy of the gravitational force calculation, with a suggestion that the weight of the car should be calculated as mass times gravity, and that the component of weight acting down the slope should be considered.
  • There is a challenge to the definition of inertia force, indicating it should be mass times acceleration, and a suggestion to rework the first two terms of the tractive effort calculation.
  • Work done is calculated by one participant as force times distance, but another notes that net work should consider all forces acting on the car.
  • Average power is discussed, with one participant referencing an online source for the formula but expressing uncertainty about the calculations involved.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correct approach to solving the problem, with multiple competing views on the application of D'Alembert's equation versus Newton's laws, as well as differing interpretations of the forces involved.

Contextual Notes

Limitations include potential misunderstandings of the definitions of forces involved, the need for clarification on the component forces acting on the slope, and unresolved mathematical steps in the calculations presented.

Vancurt
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Homework Statement



Hey, this is the first time i have ever done this and i like to know how to solve it.

A car with a mass of 1350kg is tested by having it accelerated up a road with a slope of 1 in 5,increasing in speed from 2.5 to 12 m/s,covering a distance of 100m, agaisnt a frictional force of 750 N.

Determine:

The tracktive effort between driving wheels and the road surface.

The work done during period of the acceleration
The average power developed.

The Attempt at a Solution



My first time doing tracktive efforts and Alemberts equation, but from what i gathered on the internet:

My tutor does not seem to understand English either, we all asked for tips and guidance, he replied with 'ask your friends'.

100x1/5 =20m

1350x9.81x20= 264870.

Don't ask where the 9.81 came from, i saw quite a few answers with it in so i guessed.
 
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You need to understand kinematics, Newton's laws, free body diagrams, Work, and/or energy. g = 9.81 m/s^2, the acceleration of gravity. Please make an attempt.
 
Ok here is my attempt, possibly all wrong.

I guessed the tracktive effort is 2100.2

I got this by looking at the D'Alembert's equation:

Tracktive effort = gravitational force + inertia resistance + frictional resistance.

For Gravitational force, i put 1350 as that is mass and a force, the inertia resistance 1 over 5 as that is the resistance going up a slope and for the frictional force 750 because it says so.

Therefore 1350 + 1/5 + 750 = 2100.2

B) is work done so the equation: force x Distance = 750 x 100 = 75000

C) Average power i looked upon the internet for the equation which is: Integral power over time divided by time interval.

So just grasping at straws here: 75000 divided by 1/5 = 375000.
 
Vancurt said:
Ok here is my attempt, possibly all wrong.

I guessed the tracktive effort is 2100.2

I got this by looking at the D'Alembert's equation:

Tracktive effort = gravitational force + inertia resistance + frictional resistance.
Are you being asked to use D'Alembert's equation? It has merit for certain problems, but in general, stick with Newton's 2nd Law.
For Gravitational force, i put 1350 as that is mass and a force,
1350 kg is the mass...its weight is 1350(9.81) or approximately 13,200 N... but you should be looking at the component of the weight acting down the plane
the inertia resistance 1 over 5 as that is the resistance going up a slope
you have a wrong definition of the inertia force...it is mass times acceleration (ma)
and for the frictional force 750 because it says so.
, acting down the plane
Therefore 1350 + 1/5 + 750 = 2100.2
rework the first 2 terms
B) is work done so the equation: force x Distance = 750 x 100 = 75000
the net work done is the work done by all forces , that is, the work done by the net force acting on the car, if this is what the problem is asking
C) Average power i looked upon the internet for the equation which is: Integral power over time divided by time interval.

So just grasping at straws here: 75000 divided by 1/5 = 375000.
really grasping...average power is force times average speed///
 

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