Length of ramp to stop vehicle

In summary, in order for the "run away" truck ramp to stop the Ford Ranger, it must be at least 284 meters long. This can be determined by setting the kinetic energy (calculated to be 1.75 x 10^6 J) equal to the potential energy at the top of the ramp (calculated to be 73.559m) and using SOH to solve for the length of the ramp.
  • #1
Tiffaney Sporl
3
0
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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  • #2
Forum rules require you to show your own attempt to solve the problem before help given.
 
  • #3
CWatters said:
Forum rules require you to show your own attempt to solve the problem before help given.

Sorry I just added my attempt
 
  • #4
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.
 

Related to Length of ramp to stop vehicle

1. What is the ideal length of a ramp to stop a vehicle?

The ideal length of a ramp to stop a vehicle depends on several factors such as the weight and speed of the vehicle, the angle of the ramp, and the coefficient of friction between the ramp surface and the vehicle's tires. A longer ramp will generally provide a longer stopping distance, but it is important to consider all of these factors when determining the ideal length.

2. How does the weight of the vehicle affect the length of the stopping ramp?

The weight of the vehicle plays a significant role in determining the length of the stopping ramp. A heavier vehicle will require a longer ramp to stop due to its greater momentum. It is important to consider the weight of the vehicle when designing a ramp for safe stopping.

3. Is there a specific angle that the ramp should be to effectively stop a vehicle?

The angle of the ramp can affect the length of the stopping distance. Generally, a steeper ramp will result in a shorter stopping distance, but it is important to consider other factors such as the weight and speed of the vehicle. A ramp that is too steep may also cause the vehicle to lose control and potentially cause an accident.

4. How does the coefficient of friction impact the length of the stopping ramp?

The coefficient of friction between the ramp surface and the vehicle's tires is an important factor in determining the length of the stopping ramp. A higher coefficient of friction will result in a shorter stopping distance, as the tires will have more grip on the ramp surface. It is important to use materials with a high coefficient of friction when designing a ramp for stopping a vehicle.

5. Are there any safety precautions to consider when designing a ramp for stopping a vehicle?

Yes, there are several safety precautions that should be considered when designing a ramp for stopping a vehicle. The ramp should be designed with a gradual incline to prevent the vehicle from losing control. It should also be made of materials with a high coefficient of friction to ensure the vehicle has enough traction to stop. Additionally, the ramp should be properly maintained and inspected regularly to ensure its safety and effectiveness.

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