Calculating Tractive Force using two methods

[Robert Forward]

1. A car accelerates 1800m down an incline of 1 in 4 at 0.4ms^2. The car has a mass of 4,000kg and the resistance to motion is 400N

Determine:

a) The Tractive effort required by using D'Alemberts principle
b) The Tractive effort required by using the conservation of energy

Homework Equations

a)F=ma, mgsin(theta)
b) KE=1/2mv^2, PE=mgh [/B]

The Attempt at a Solution

a) calculating intertial resistance
f=ma
4,000 x 0.4 = 1600N

calculating the angle of 1in 4
tan^-1(0.25)

calculating gravitational force
mgsin(theta)
4000 x 9.81 x sin(14.04)=9519.593816N[/B]

I'm stuck after this, do I add my two values and my resistance to motion or subtract them?

As for part b) I'm at a loss because I don't have any values for velocity to work out the change in KE nor do I have the height to work out PE. What am I missing here?

Thanks everyone!

 

[PhanthomJay]

1. A car accelerates 1800m down an incline of 1 in 4 at 0.4ms^2. The car has a mass of 4,000kg and the resistance to motion is 400N

Determine:

a) The Tractive effort required by using D'Alemberts principle
b) The Tractive effort required by using the conservation of energy

Homework Equations

a)F=ma, mgsin(theta)
b) KE=1/2mv^2, PE=mgh [/B]

The Attempt at a Solution

a) calculating intertial resistance
f=ma
4,000 x 0.4 = 1600N

calculating the angle of 1in 4
tan^-1(0.25)

calculating gravitational force
mgsin(theta)
4000 x 9.81 x sin(14.04)=9519.593816N[/B]

I'm stuck after this, do I add my two values and my resistance to motion or subtract them?

whether you add or subtract depends on the direction down or up the plane of the gravity force, resistance force, inertial force, and tractive force, which must sum to 0 using D'Alemberts principle. Once you establish the direction of the first 3, the direction and magnitude of the Tractive force will follow.

As for part b) I'm at a loss because I don't have any values for velocity to work out the change in KE nor do I have the height to work out PE. What am I missing here?

Use kinematic equations for finding V and trig for finding h. The length and slope of the incline is given.

 

[Alex Pegg]

Hi, I have something very similar to the original question and I have used D'Alemberts principle successfully for part a).
It is on part b) that I am also stuck.
Where you say use the kinematic equations this will not work as at the time you only know 2 of the values (Displacement and Acceleration). This is not enough to calculate a velocity.
I would be grateful for further explanation.

 

[PhanthomJay]

... you only know 2 of the values (Displacement and Acceleration). This is not enough to calculate a velocity.

Assuming that the car starts down the incline from rest, using one of the kinematic equations knowing d and a , you can solve for v_f. Which one?