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

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SUMMARY

The minimum length of a runaway truck ramp required to stop a Ford Ranger with a mass of 2430 kg traveling at 85 mph is 284 meters. This calculation is based on the conversion of kinetic energy (KE) of 1.75 x 10^6 J into potential energy (PE) using the formula PE = mgh, where the height (h) is determined to be 73.559 meters. The incline of the ramp is 15.0 degrees, and the mass of the vehicle is irrelevant to the final length calculation.

PREREQUISITES
  • Understanding of kinetic energy (KE) and potential energy (PE) concepts
  • Familiarity with trigonometric functions, specifically SOH (sine, opposite, hypotenuse)
  • Basic knowledge of physics principles related to motion and forces
  • Ability to perform unit conversions and calculations involving mass and velocity
NEXT STEPS
  • Study the principles of energy conservation in physics
  • Learn more about the applications of trigonometry in real-world scenarios
  • Explore the design and safety standards for runaway truck ramps
  • Investigate the effects of friction and air resistance on vehicle stopping distances
USEFUL FOR

Physics students, automotive safety engineers, and anyone involved in vehicle dynamics and emergency stopping systems will benefit from this discussion.

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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