Solve Dynamics Problem: Automobile Braking Force on 4 Degree Incline

[larryman210]

Homework Statement

A 1400-kg automobile is driven down a 4 degree incline at a speed of 88 km/h when the brakes are applied, causing a total braking force of 7500 Newtons to be applied to the automobile. determine the distance traveled by the automobile before it comes to a stop.

Homework Equations

(1/2)*m*v1^2 + total work = (1/2)*m*v2^2

The Attempt at a Solution

so far I have the equation (1/2)*m*v1^2 + total work = (1/2)*m*v2^2
so i have the work of weight which is -1400cos4, the work of friction which is -7500 and initial velocity of 88 km/h. I don't really know how to put this together. please help

 

[JaWiB]

>so i have the work of weight which is -1400cos4

Seems you should be using Work = Force * Distance, since all forces involved are constant. I see neither force nor distance in that answer.

 

[Chrisas]

Work = force vector dotted with translation vector.

First, check your trig. I think you have the wrong trig function for the work done by gravity. Gravity does work in pulling things down, not by moving them horizontally.

Also check your units. Force is Newtons, which is mass (kg) * acceleration (m/s^2). What is the force of gravity on an object?

For the work done by friction (braking), are any trig functions needed? Think about how the force direction and the translation direction are related.

 

[Topher925]

Try applying PE + KE = 0 in both the X and the Y and keep them separate. Then integrate ax and ay and find the magnitude (sqrt(ax^2 + ay^2)).