What is the Work Done on a Car Traveling Up a Slope?

[jamieengine]

Homework Statement

A car of a mass 1200Kg accelerate frm 2.5ms to 5.0ms while traveling 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.

Homework Equations

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

The Attempt at a Solution

600x6.25=3750
600x25=1500

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

 

[PhanthomJay]

Homework Statement

A car of a mass 1200Kg accelerate frm 2.5ms to 5.0ms while traveling 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.

Homework Equations

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

The Attempt at a Solution

600x6.25=3750

this is the initial KE, in joules

600x25=15000[/color]

this is the final KE, in joules

1200x9.81x60sin3.71
11772x5.97=70274.19

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.

 

[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 can't make head or tails of it.

 

[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.

 

[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 don't know how to work out work done, tractive effort,friction etc.

 

[jamieengine]

Also i can't find a time that's it taken for accelration etc. And could i not use F=ma 105/1200=0.0875ms ?

 

[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.

 

[jamieengine]

i do know about them but don't know what order to put um in

 

[PhanthomJay]

with consersvation of energy, is it all off the kinetic and potenial energy. i.e. 3750+ 15000+70274.6.

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.