The mechanics of this kind of problem – fundamentally, a
work problem - are pretty simple.
The energy available in a 1 kg mass at a height of 0.1 m is about
This must equal the work of the car moving distance
with a force of friction
, so
.
Rearranging,
So, if we measure the rolling resistance of the loaded car – say by pulling it with a scale – and the mechanical resistance of its various pulleys – a tougher measurement, but in principle doable with scales – add them together to get the total resistance
, and divide our 0.98 J energy by it, we get the distance it should travel.
For example, if the total resistance is 0.1 N, we expect it to travel about 9.8 m.
Notice that how fast it goes, or how much of the distance it coasts after the weight has dropped its full distance, doesn’t effect the total distance traveled, except that
is likely to be higher for higher rolling speeds, and less when coasting (the pulleys etc. won’t be contributing as much drag then). It also doesn’t matter how the car converts the gravitational potential energy of the weight into work for moving the car, except that some schemes will have more or less friction than others, affecting
.
Also notice that, as
won’t be truely constant, a more precise calculation would be more complicated. However, with most low-speed, every-day smooth-surface rolling machines, rolling resistance is nearly constant regardless of speed, so the simple calculation above is likely to be adequate.
