# Tractive effort of a car

1. May 17, 2010

### jamieengine

1. The problem statement, all variables and given/known data
A car of a mass 1200Kg accelerate frm 2.5ms to 5.0ms while travelling up slope of 1 in 10 through a distance of 60m if the resistance to motion is 105N determine using both a energy method and d'alembert principle. any help would be much appreciated.

2. Relevant equations

Pe=mgh
ke=1/2mv²
inertia resistance (ma)
frictional resistance (Fr)
Gravitational force (mg sinΘ )

3. The attempt at a solution
600x6.25=3750
600x25=1500

1200x9.81x60sin3.71
11772x5.97=70274.19
ke=15000
pe-70274.10

Last edited: May 17, 2010
2. May 17, 2010

### PhanthomJay

this is the initial KE, in joules
this is the final KE, in joules
this is the final PE in joules.

Now you must apply conservation of energy to solve for the traction force. You must list the equation that applies when work is being done by non-conservative forces. Are you familiar with the conservation of energy equation? Then, for the alternate approach, you must use kinematics to solve for the acceleration, then apply Newton's 2nd law (I gather using d'alembert principle, according tho the problem) to solve for the traction force.

3. May 17, 2010

### jamieengine

hi jay, thankyou for the help i really appreciate it, and no, i am really struggling with this question, any help i would be so gratefull because i cant make head or tails of it.

4. May 17, 2010

### PhanthomJay

well, if you are asked to solve the problem using energy methods, you must first know the conservation of energy equation. Is it in your text or notes or somewhere, anywhere? Does the equation $$W_{nc} = \Delta KE + \Delta PE$$ look at all familiar? If not, it's no small wonder that you are struggling. $$W_{nc}$$ is the work done by non-conservative forces like traction forces, air drag, friction, etc. Can you calculate or define the work done by the 105N retarding force, and the work done by the traction force, T? Solve for T, and then check your result using kinematics, a free body diagram, and Newton 2.

5. May 18, 2010

### jamieengine

hi. thankyou for your quick reply and no! it dosent look familiar, but i will give it ago. what is the equation for tractive effort then? Also with consersvation of energy, is it all off the kinetic and potenial energy. i.e. 3750+ 15000+70274.6.

Also i dont know how to work out work done, tractive effort,friction etc.

6. May 18, 2010

### jamieengine

Also i cant find a time thats it taken for accelration etc. And could i not use F=ma 105/1200=0.0875ms ?

7. May 18, 2010

### PhanthomJay

I'm afraid I am not going to be of much help if you don't have a basic understanding of work, work-energy methods, and Newton's laws (let alone D'alembert's principle which makes use of ficticious inertial forces). I don't know how you can be attempting this problem without such knowledge or use of reference material.

8. May 19, 2010

### jamieengine

i do know about them but dont know what order to put um in

9. May 19, 2010

### PhanthomJay

No, the initial energy of the system, plus the work done on the system by the traction (t) and resistive (r) forces, must equal the final energy of the system. To put the equation in another form, W_t +W_r + KE_i + PE_i = KE_f + PE_f. You need to calculate the work done by the tractive and resistive forces. The tractive force acts up the plane and parallel to it (it is the force of traction between the tires of the driving wheels and the ground), and the resistive force acts down the plane and parallel to it. Please look into your notes for the definition of work.