Solve Dynamics Problem: Automobile Braking Force on 4 Degree Incline

  • Thread starter larryman210
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In summary, the problem involves finding the distance traveled by a 1400-kg automobile down a 4 degree incline, with a speed of 88 km/h and a braking force of 7500 Newtons being applied. The equation used is (1/2)*m*v1^2 + total work = (1/2)*m*v2^2, and the work done by gravity and friction are taken into account. Further calculations using PE + KE = 0 and integrating ax and ay are needed to find the magnitude of the resulting distance traveled.
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larryman210
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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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  • #2
>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.
 
  • #3
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.
 
  • #4
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)).
 

What is the equation for calculating the braking force on a 4 degree incline?

The equation for calculating the braking force on a 4 degree incline is Fb = mgsinθ, where Fb is the braking force, m is the mass of the automobile, g is the acceleration due to gravity, and θ is the angle of the incline.

How does the incline of a road affect the braking force of an automobile?

The incline of a road can greatly affect the braking force of an automobile. As the incline increases, the gravitational force acting on the automobile also increases, resulting in a higher braking force needed to stop the automobile.

What factors can impact the accuracy of calculating the braking force on a 4 degree incline?

There are several factors that can impact the accuracy of calculating the braking force on a 4 degree incline. These include variations in the mass of the automobile, changes in the angle of the incline, and external factors such as wind resistance.

Is the calculation of braking force on a 4 degree incline affected by the type of braking system in the automobile?

Yes, the type of braking system in the automobile can impact the calculation of braking force on a 4 degree incline. Different braking systems, such as disc brakes or drum brakes, have varying levels of efficiency and can affect the overall braking force required.

How can the knowledge of braking force on a 4 degree incline be applied in real-world situations?

The knowledge of braking force on a 4 degree incline can be applied in various real-world situations, such as designing and testing brakes for automobiles, determining the required braking force for vehicles on different road inclines, and calculating stopping distances for vehicles on hilly or mountainous roads.

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