Energy expended cycle a hill - different grades/same height

[denverericj]

Please settle this "argument" between a fellow cyclist and I. If I am riding east up and over a pass will I use the same amount of energy as if I rode the opposite direction? His argument is that going from west to east, the climb is steeper so it is harder. I countered that it doesn't matter which direction you are going because the same amount of energy is stored and then released (potential and kinetic) as long as the vertical height you are "moving" the weight up is the same. You might go slower up the steep side but you will get there at the same time (theoritically). Neither direction is impassable meaning the rider has the power to climb them using different gearing.

 

The pass in question is Squaw Pass in Colorado just west of Denver but that is irrelevant. Neither of us are physicists/scientists or, in his case, not as smart as I thought he was...

 

Assumptions: Vertical feet climbed is 3000 feet. Rider and bike weigh 200 lbs. Distance from west to east is 17 miles to the peak and 13 miles to the bottom of the other side. You start and end at the same altitude.

 

Please help give me bragging rights. I will print this out and glue it to his car window!...Eric

Edited June 23, 2011 by denverericj

[J.C.MacSwell]

Please settle this "argument" between a fellow cyclist and I. If I am riding east up and over a pass will I use the same amount of energy as if I rode the opposite direction? His argument is that going from west to east, the climb is steeper so it is harder. I countered that it doesn't matter which direction you are going because the same amount of energy is stored and then released (potential and kinetic) as long as the vertical height you are "moving" the weight up is the same. You might go slower up the steep side but you will get there at the same time (theoritically). Neither direction is impassable meaning the rider has the power to climb them using different gearing.

 

The pass in question is Squaw Pass in Colorado just west of Denver but that is irrelevant. Neither of us are physicists/scientists or, in his case, not as smart as I thought he was...

 

Assumptions: Vertical feet climbed is 3000 feet. Rider and bike weigh 200 lbs. Distance from west to east is 17 miles to the peak and 13 miles to the bottom of the other side. You start and end at the same altitude.

 

Please help give me bragging rights. I will print this out and glue it to his car window!...Eric

 

 

Energy expended may not be the same. In each case, I'm sure you would both agree that the potential energy, PE, at the top is the same, and the kinetic energy, KE, as well if you arrive at the same speed still weighing the same (regardless who took how long to get there).

 

But in either case your energy expended will be much greater than your PE and KE at the top. Which took more energy depends on a lot of variables.

[denverericj]

OK, taking the variables out of the equation (efficiency of the bikes in different gears, wind resistance, rolling resistance, etc), why would the energy used be different? A simple experiment would be the amount of energy required to lift a 10 lb bowling ball up 1 foot vs the amount of energy used to move it up a 5 foot ramp to a height of 1 foot. Or, using a block and tackle to lift 500 lbs up 10 feet vs a simple pulley. Wouldn't that be the same? Thanks, Eric

[zapatos]

Not my specialty but I'll take a crack at it. Someone please correct me if I'm wrong.

 

The amount of energy to move the vertical distance will be the same regardless of whether you had a steep or shallow climb. But there is also the energy to travel the horizontal distance. Assuming a smooth descent on both sides that would allow you to coast all the way from the top to the end, the person who had the shorter horizontal distance to pedal during their climb should expend less energy.

[J.C.MacSwell]

OK, taking the variables out of the equation (efficiency of the bikes in different gears, wind resistance, rolling resistance, etc), why would the energy used be different? A simple experiment would be the amount of energy required to lift a 10 lb bowling ball up 1 foot vs the amount of energy used to move it up a 5 foot ramp to a height of 1 foot. Or, using a block and tackle to lift 500 lbs up 10 feet vs a simple pulley. Wouldn't that be the same? Thanks, Eric

 

The minimum work required is the same, so if you disregard inefficiencies and kinetic energies on arrival (assuming stationary start) you are correct.

 

That is very different from "energy expended" though, which may be your friends point (which he may be holding back?... and if it's not exactly East West he may have a trick!)