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During a testing process, a worker in a factory mounts a bicycle wheel on a stationary stand and applies a tangential resistive force of 115 N to the tire's rim. The mass of the wheel is 1.70 kg and, for the purpose of this problem, assume that all of this mass is concentrated on the outside radius of the wheel. The diameter of the wheel is 50.0 cm. A chain passes over a sprocket that has a diameter of 9.50 cm. In order for the wheel to have an angular acceleration of 4.90 rad/s2, what force, in Newtons, must be applied to the chain? (Enter the magnitude only.) N

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Answer:

616.223684211 N

Explanation:

[tex]F_r[/tex] = Resistive force on the wheel = 115 N

F = Force acting on sprocket

[tex]r_2[/tex] = Radius of sprocket = 4.75 cm

[tex]r_1[/tex] = Radius of wheel = 25 cm

Moment of inertia is given by

[tex]I=mr_1^2\\\Rightarrow I=1.7\times 0.25^2\\\Rightarrow I=0.10625\ kgm^2[/tex]

Torque

[tex]\tau=I\alpha\\\Rightarrow \tau=0.10625\times 4.9\\\Rightarrow \tau=0.520625\ Nm[/tex]

Torque is given by

[tex]\tau=Fr_2-F_rr_1\\\Rightarrow F=\dfrac{\tau+F_rr_1}{r_2}\\\Rightarrow F=\dfrac{0.520625+115\times 0.25}{0.0475}\\\Rightarrow F=616.223684211\ N[/tex]

The force on the chain is 616.223684211 N

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