# Calculating Tractive Force using two methods.

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1. Aug 5, 2016

### 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

2. Relevant equations
a)F=ma, mgsin(theta)
b) KE=1/2mv^2, PE=mgh

3. 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

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!

2. Aug 5, 2016

### PhanthomJay

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