A bicycle can go up a gentle incline with constant speed where the frictional force of ground pushing the rear wheel is $F_{2} = 4 N$ . With what force $F_{1}$ must the chain pull on the socket wheel if $R_{1} =$ 5 cm and $R_{2} =$ 30 cm ?

4 N

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24 N

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140 N

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\frac{35}{4} N

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Solution

The correct option is C $24 N$
Since the bicycle moves up the incline at a constant speed, net force is zero and net torque is zero.
Torque due to $F_{2} :$ $τ_{2} = r_{2} F_{2}$
Torque due to $F_{1} :$ $τ_{1} = r_{1} F_{1}$
$τ_{1} = τ_{2}$
$∴ r_{1} F_{1} = r_{2} F_{2}$
$\Rightarrow 5 F_{1} = 4 * 30$
$\Rightarrow F_{1} = 24 N$

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A bicycle can go up a gentle incline with constant speed where the frictional force of ground pushing the rear wheel is F2=4N . With what force F1 must the chain pull on the socket wheel if R1= 5 cm and R2= 30 cm ?

The correct option is C 24 NSince the bicycle moves up the incline at a constant speed, net force is zero and net torque is zero.Torque due to F2: τ2=r2F2 Torque due to F1: τ1=r1F1 τ1=τ2 ∴r1F1=r2F2⇒5F1=4∗30⇒F1=24N

A bicycle can go up a gentle incline with constant speed where the frictional force of ground pushing the rear wheel is $F_{2} = 4 N$ . With what force $F_{1}$ must the chain pull on the socket wheel if $R_{1} =$ 5 cm and $R_{2} =$ 30 cm ?