recycle bin on the run

[lhorton]

Real life problem. I live on a 33% grade hill and took out my recycling bin to the curb. It tipped and went hurtling down the hill, taking out all curbed trash bins along the way with a deafening roar. I kept thinking, force = mass x acceleration. If the bin + recylables weighs 27 kg and the road is about 200 meters long, what is the force? How do you figure in the angle of the street?

 

[skeeter]

force of gravity on an incline ... \(\displaystyle \L F = mg\sin{\theta}\), where ...

m = mass of the object
g = acceleration due to gravity
\(\displaystyle \L \theta\) = angle of incline w/r to the horizontal

 

[Deleted member 4993]

Real life problem. I live on a 33% grade hill

Then sin(theta) = 0.33

 

[skeeter]

SK ... wouldn't it be tan(theta) = .33 ?

 

[Deleted member 4993]

Generally, grade of a road is expressed as sine - because it is easier to measure the "incline distance" directly and the height.

 

[galactus]

I have done the lay out on many roads and highways and horizontal distances are used. Stakes are normally put at 25 foot intervals for fine grading. Though, sine may very well be best with something this steep. You rarely see roads this steep. A driveway is another matter. Pipe, of course, can have grades this steep or steeper.