Roads going up mountains are formed into switchbacks, with the road weaving back and forth along the face of the slope such that there is only a gentle rise on any portion of the roadway.
(a) Compare the work done by a car climbing the mountain using a road with switchbacks to the work done by a car on a roadway that goes straight up the slope.
(b) The answer to (a) might be confusing to the non-physicist. Explain, then, why switchbacks are used.
(a) Compare the work done by a car climbing the mountain using a road with switchbacks to the work done by a car on a roadway that goes straight up the slope.
(b) The answer to (a) might be confusing to the non-physicist. Explain, then, why switchbacks are used.
-
a) The work is the same, regardless of the distance travelled. They both end up at the same height.
b) A road straight up a mountain could be steep and dangerous to travel, or just impossible to use.
By making switchbacks, the distance travelled is longer, but the slope is much more manageable.
It can be likened to pushing a heavy load up a ramp, which can require much less effort, rather than the effort of lifting the load vertically, which may be impossible for you. You use a large effort over a short distance, or a small effort over a larger distance. Both are the same work (ignoring friction on a ramp).
b) A road straight up a mountain could be steep and dangerous to travel, or just impossible to use.
By making switchbacks, the distance travelled is longer, but the slope is much more manageable.
It can be likened to pushing a heavy load up a ramp, which can require much less effort, rather than the effort of lifting the load vertically, which may be impossible for you. You use a large effort over a short distance, or a small effort over a larger distance. Both are the same work (ignoring friction on a ramp).
-
a)
Work = the amount of force required to move an object over a distance
Work = F*d
The amount of work required for a car to drive straight up a mountain is the exact same as the amount of work required for the same car to drive up the mountain via switchback.
b)
Because of this fact, switchbacks are a great choice for getting to much higher grounds. Steep inclines are very dangerous ( snow and ice in the winter, maybe rocks and dirt in the summer). But switchbacks aren't much different than driving on a regular road. The best part is, your car will not have to do any more work than if it were to climb straight up the mountain!
Work = the amount of force required to move an object over a distance
Work = F*d
The amount of work required for a car to drive straight up a mountain is the exact same as the amount of work required for the same car to drive up the mountain via switchback.
b)
Because of this fact, switchbacks are a great choice for getting to much higher grounds. Steep inclines are very dangerous ( snow and ice in the winter, maybe rocks and dirt in the summer). But switchbacks aren't much different than driving on a regular road. The best part is, your car will not have to do any more work than if it were to climb straight up the mountain!
-
(a) Total work done = mgH + fS
where H is the height of the hill and S is the path length and f mu mgcos theta force of friction. Naturally S increases as f increases (or theta decreases) for screw like ride. With switch back it is double the work against the force of friction.
(b) we cannot make theta above a particular value to avoid slide back of the vehicle in the event of brake failure or gear breakage.
where H is the height of the hill and S is the path length and f mu mgcos theta force of friction. Naturally S increases as f increases (or theta decreases) for screw like ride. With switch back it is double the work against the force of friction.
(b) we cannot make theta above a particular value to avoid slide back of the vehicle in the event of brake failure or gear breakage.