Does it take more work to bike or walk uphill?

Question

Work is the amount of force needed to cause a displacement and is measured in joules. One joule = 1 Newton * meter.

Hence, here is the problem:

Take "Sam" deciding whether to walk or ride his bike uphill. This hill is steep, and has a 30 degree angle upward. There are 300 meters to travel on this hill with no change in the angle.

Sam weighs approximately 90 kilograms and his bike weighs 10 kilograms.

His bike is standard with multiple gear shifts for climbing uphill. Assume that he shifts to the "optimum" level to pedal continuously without stopping.

If possible, also answer which requires more calories? I would assume the one that requires more "work" requires more calories.

Don't give me any answer but something working out the math. I want a mathematical answer in Joules.

There must be a point at which the decreasing the angle tips the favor to biking as opposed to walking. What that might be?

Answer 1

Force with bike=100*sin30*10=500N
Force without bike= 0.9*500=450N
Thus, walking will save him 50*300=15000 joules.
But, don't forget that the bike has a bigger mechanical advantage or force multiplier that reduces the work. Suppose the MA is 4,then the force with bike will be 500/4=125N and hence work will be 15000/4=3750 J only. Therefore, riding is preferable.

Answer 2

chook7367 is right. When you ride a bike you are also doing work in transporting the bike up the hill. So in this case your doing work in transporting your body plus the work to transpor the bike.

But you might find it easier to climb the hill by riding on the bike. This is the effect of using a machine. Machine enhances the direction of the force such that it will effect the greatest effect. Also by changing the rate of doing the work (changing the gears) less force is required to do the job.

Answer 3

Assuming the weightless bike operates with no frictional loss (quite an assumption), they require the same amount of work. Another way of stating work is Force x Distance. In either one, he's overcoming the same force (his weight) the same distance up the hill. However, if he is on the bike, and still rolling when he reaches his destination, then that took more work than walking, because extra energy was put into the angular momentum stored in the wheels.

Answer 4

according to physics, the bike would take more "work" as the bike adds 10 kilos, now if you're trying to burn calories, the bike wins this round too, what do you know, the bike takes the title!

by the way, work is the force times the distance, not the amount of force, put fifty pounds of upward force on a forty pound object, it moves, you have done work. put fifty pounds upward force under a fifty pound object, it will not move, no work.

Answer 5

BIKE!.Without getting into mathematical formulas,if you alone walk up the hill,you will expend a certain amount of energy.You riding a bike means not only will you have to get yourself up the hill,but also the bike.Think about it???.

Answer 6

My brain hurts, and I'm going with bike due to friction considerations and how it helps minimize the work required to prevent yourself from going back down the hill.

Answer 7

Blah blah blah blah blah. Bike.