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Calculating the Force on a Bicycle Wheel

  1. May 14, 2015 #1
    I have been trying this problem for a while and can't seem to figure it out:

    A bicycle wheel has a radius R = 32.0 cm and a mass M = 1.82 kg which you may assume to be concentrated on the outside radius. A resistive force f = 137 N (due to the ground) is applied to the rim of the tire. A force F is applied to the sprocket at radius r such that the wheel has an angular acceleration of 4.50 rad/s^2. The tire does not slip.

    a. If the sprocket radius is 4.53 cm, what is the force, F (in Newtons)?
    b. If the sprocket radius is 2.88 cm, what is the force, F?
    c. What is the combined mass (kg) of the bicycle and rider?

    I know that the tangential acceleration a = rα where α is rotational acceleration.
    I also know the Kinetic energy must be K = ½ Iω^2+ ½Mv^2 where the first term is the rotational kinetic energy and the second term is the translational kinetic energy.
    Finally, I know that I which is the moment of inertia for a shell (the shape of the bicycle) is Mass*Radius^2.
    I've been doing the algebra with it and can't seem to get any meaningful results. Am I on the right track with this thinking? Thanks in advance for the help.
     
  2. jcsd
  3. May 14, 2015 #2

    mfb

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    Please show what you did (that's the point of the homework template - please do not delete it).

    Working with energy is possible, but using forces and torque everywhere is probably easier.
     
  4. May 14, 2015 #3

    haruspex

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    The linear KE cannot be interesting because you do not know the mass of the bicycle. Concentrate on torques and angular acceleration.
     
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