Solve Dynamics Problem: Automobile Braking Force on 4 Degree Incline

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Homework Help Overview

The problem involves a dynamics scenario where a 1400-kg automobile is descending a 4-degree incline at a speed of 88 km/h when brakes are applied, resulting in a braking force of 7500 Newtons. The objective is to determine the distance the automobile travels before coming to a stop.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the application of work-energy principles, specifically the equation relating kinetic energy and work done. There are questions regarding the correct application of trigonometric functions for calculating work done by gravity and friction. Some participants suggest reconsidering the relationship between force and distance in the context of constant forces.

Discussion Status

The discussion is ongoing, with participants providing guidance on checking trigonometric functions and ensuring unit consistency. Different approaches to separating potential and kinetic energy in the context of the incline are being explored, indicating a productive exchange of ideas without reaching a consensus.

Contextual Notes

Participants note the need to clarify the forces acting on the automobile, including gravitational force and the braking force, as well as the implications of the incline on these forces. There is an emphasis on ensuring the correct application of physics principles without providing direct solutions.

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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
 
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>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.
 
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.
 
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)).
 

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