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Check My Work Please

  1. Aug 26, 2004 #1
    Force and Momentum...Please Check My Work

    I have been having a bit of an argument (civil surprisingly) on a car site. I want to know if my physics reasoning is correct. I will provide some background to the argument. The issue is whether replacing the stock crankshaft pulley with a lighter and smaller pulley (UDP) will reduce gas mileage at constant speed or not. They submit that becuase the replacement pulley does not have as much inertia that it will require more power from the engine to keep at a constant speed. I submit that gas mileage does not change due to the lesser amount of inertia of the replacement pulley.

    To support their theory they submit reports of people dropping 4-5mpg after replacing the stock pulley with the UDP and reports of people telling them that a UDP will reduce gas mileage. I countered with fuel efficiency counting on so many variables that any one or a combination of those variables could have cuased the drop in mileage.

    My reasoning is as follows.
    1) The smaller size of the UDP creates a gear change multiplying the engines power thereby reducing the amount of power required to be produced by the engine to operate the accessories, with the draw back of a slower operating speed of the accessories.
    Ex. For every turn of the of the stock pulley the accesories' pullies turn once. Reducing the size of the of the crankshaft pulley by replacing the stock with the UDP will create a change making it for 1.25 turns of the UDP the accessories' pulleys turn once.

    2) The lesser inertia of the UDP causes no drop in gas mileage. There is no acceleration for the momentum of the UDP to resist so it has no effect at constant speed. Therefore no more force (in the form of fuel consumed) needed to keep the vehicle at constant speed.

    Here is a qoute from a post I made. Could you please check it for conceptual errors.

    "Here is an explanation of force as need to keep an object at constant speed leading up to why no more gas (power or force) is needed whether the pulley is lighter or heavier. An amount of force equal and opposite of the amount of resisting force must be applied to make net 0 (or balanced) force thereby keeping the spinning object at a constant speed. Note that that means an unbalanced force is required to create acceleration. Friction and the force required to operate the accessories are the resisting forces here. Momentum is not a resisting force at constant speed. The forces must remain constant to maintain constant speed. Any change in force will create an unbalance, which would then create acceleration. Force is related to momentum, similar to the way acceleration is related to velocity, in that force is a change in momentum. At constant speed momentum does not change. The fact that there is no change in momentum means that there is no extra acting force to resist the constant velocity. Since there is no more force applied then no more or less gas must be used. This one should do it for you."

    I appreciate your assistance.
    Last edited: Aug 26, 2004
  2. jcsd
  3. Mar 14, 2005 #2
    Less mass means faster acceleration. Less rotational mass means faster roational acceleration. And since F=ma, the force required accelerate the pulley to the same speed would be less for a less massive pulley. The difference of a few ounces on your crank puley isn't going to do anything at all, that isnt within the margin of error of ANY dynomometer. Now, the gearing reduction availible by using a smaller crank pulley size slows the speed of any accessory on that belt, which means less parasidic loss and greater fuel efficiancy and better acceleration. Of course, in the real world, these gains can be anywhere from negligent to fairly noticable, depending on each component.

    Similar in concept to reducing driveshaft mass, or getting lighter wheels. None do much, but a lot of little things add up ;) And to hell with spelling, I've been working on this damned massive cable/massless pulley problem all damn day... can't get this damned calc....
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