What Is the Realistic Horsepower of a Truck Climbing Rabbit Ears Pass?

[pippintook]

A 40,000 kg truck traveling on I-70 leaves Denver (elevation 5280', mile marker 244) and goes over Rabbit Ears pass (elevation 11,840', mile marker 238) while maintaining 50 mph. What is the horse power rating on his engine?


The formulas I used are as follows:

power = work/time

work = (mass)(gravity)(height)

746 watts = 1 horsepower

To solve for time I did 50 miles/60 minutes = 6 miles/x minutes and got 7.2 minutes (or 432 seconds).

After putting in all of these numbers I got 57,442 horsepower. This doesn't seem to make sense though, as that is a LOT of horsepower. I think the problem may be the height, since I put in the change of height (6560 feet). Help please? Suggestions?

 

[mgb_phys]

Put everything into metres, seconds and kg, I suspect you have got the units mixed up.

Hint - you only care about the vertical speed.

 

[thomate1]

I would first like to clarify that the term "horsepower" is a unit of power, not a measure of the actual power produced by a horse. It was originally defined by James Watt as the amount of power needed to lift 550 pounds at a rate of one foot per second. In modern terms, one horsepower is equivalent to 746 watts.

Now, let's address the calculation you have done. It is true that power is equal to work divided by time, and that work is equal to mass times gravity times height. However, in this scenario, we are not given any information about the work being done by the truck. We are only given its mass, speed, and change in elevation.

To calculate the power of the truck's engine, we need to consider the force needed to maintain its speed and overcome the effects of gravity and air resistance. This can be calculated using the formula:

power = force x velocity

The force acting on the truck is the sum of its weight (mg) and the force of air resistance (Fd), where F is the coefficient of drag and d is the distance traveled. We can estimate the coefficient of drag for a truck to be around 0.7, and the distance traveled in this scenario is 6 miles.

Using these values, we can calculate the power of the truck's engine to be approximately 375 horsepower. This is a more reasonable and realistic estimate compared to the 57,442 horsepower calculated previously.

In conclusion, it is important to consider all relevant factors and use the appropriate formulas when making calculations in science. The horsepower rating of a truck's engine is determined by many factors, including its mass, speed, and the forces acting on it. It is not simply a matter of calculating work and time.