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04-17-03, 09:35 AM
#19
hayneda
Carfree Retro Grouch

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Originally posted by ComPH
It's been some time since I thought of physics, but isn't that true that everytime you are riding up hill or against the wind, you are overcoming an opposing force? In that case, the forces you are creating by pedaling, in order to overcome the friction and gravity is Force=mass x acceleration. That would mean that even if you are riding at a constant speed, you are actually accelerating against decelerating forces while the mass is more or less constant. That would mean that you are actually accelerating more/less at all times. Of course these forces become much more significant when the hill is steep and/or the headwind is strong, neverheless you are constantly accelerating the bike against these decelerating forces, so that rotating mass is more significant practically at all times....
You on the right tract, but no that's not quite correct. When riding uphill at a constant speed, the work you are doing to lift the weight of the system (bike and rider) is mgh, where m is the mass, g is the gravitational acceleration, and h is the height through which you lift it. When I say acceleration with respect to the bike, I mean you are going from a slower to faster speed, i.e. you are increasing your velocity.

When you accelerate (speed up), you must put energy into two things beyond that needed for a constant speed for the given conditions (whether you are riding up and hill or on the level). First, you must accelerate the mass--good 'ol F=ma. That includes the mass of the bike, wheels and rider. This is called rectilliner acceleration or increasing the kinetic energy (linear momentum). Second, you must also provide for the rotational acceleration of the wheels--this is above the energy required just to accelerate the wheels in the direction of travel. This is called angular acceleration or increasing the angular momentum of the wheels.

For example, if you pick up a rock and throw it, while it's flying through the air it has kinetic energy--to slow it requires a force (drag or gravity). If you tie a string onto it and whirl it around in a circle, it has angular momentum and it takes energy to either speed up or slow down the rotation. Of course, when you let go of the string, the rotation energy is then converted into kinetic energy as the rock flies off in the straight path.

You can think of it this way: the wheels are kinda a double whammy cause you gotta both accelerate them forward, as well as "spin them up." But unless you're racing . . .

Climbing is simply lifting all the mass up through the earth's gravitational field. The more mass or the higher or faster you lift it, the more work is required.

Hope this helps,
Dave
Who in addition to being a rocket scientist dweep, also rides his bike