How Long Should a Ramp Be to Stop a Ford Ranger with Brake Failure?

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Homework Help Overview

The problem involves a Ford Ranger experiencing brake failure while traveling down a mountain road, requiring the use of a runaway truck ramp to stop the vehicle. The ramp has a specified incline, and the discussion centers around calculating the minimum length needed for the ramp based on energy principles, specifically kinetic and potential energy.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the conversion of kinetic energy to potential energy to determine the ramp length. There is a focus on the calculations involving height and the use of trigonometric relationships to find the ramp length. Some participants question the relevance of mass in the calculations.

Discussion Status

The discussion includes attempts to verify calculations related to energy conservation. Some guidance has been offered regarding simplifying the problem by noting the irrelevance of mass in this context. However, there is no explicit consensus on the correctness of the final ramp length calculation.

Contextual Notes

Participants are operating under forum rules that require showing attempts before receiving help, which has influenced the flow of the discussion. The problem also neglects friction and air resistance, which is a critical assumption in the calculations being discussed.

Tiffaney Sporl
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A Ford Ranger with a mass of 2430 kg is traveling at a velocity of 85 mph down a mountain road. The brakes fail and the driver elects to use a "run away" truck ramp to stop the vehicle. The ramp has an incline of 15.0 degrees. What is the minimum length the ramp must be in order for this strategy to stop the truck? Neglect friction and air resistance.

I found the KE at 1.75 x 10^6 J then set it equal to PE (mgh). This gave me a height of 73.559m. I used SOH to get a length of 284m. Is this correct?
 
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Forum rules require you to show your own attempt to solve the problem before help given.
 
CWatters said:
Forum rules require you to show your own attempt to solve the problem before help given.

Sorry I just added my attempt
 
Tiffaney Sporl said:
I found the KE at 1.75 x 10^6 J then set it equal to PE (mgh). This gave me a height of 73.559m. I used SOH to get a length of 284m. Is this correct?
Yes. You can make the working a bit simpler by noticing that the mass is irrelevant.
 

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