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## Homework Statement

We have a transmission system (plate-pinion), with a 38-tooth chainring and a 14-tooth sprocket. The distance between the crank (between the chainring and the pedal) is 170 mm and the pedal is overloaded with 60 kg and pedalled at a speed of 70 min

^{-1}.

## Homework Equations

P = mg; Γ = Fd

## The Attempt at a Solution

Data:

Z

_{1}=38

Z

_{2}=14

m=60 kg

g = 9,81 m/s

^{2}

d = 170 mm = 0,17 m

ω

_{1}= 70 min

^{-1}= 7,33 rad/s

The first step is to calculate the force (weight) applied to the pedal:

P = m·g → P = 60·9,81=588,6 N

Once we know the force, we have to calculate the input torque (Γ

_{1}):

Γ

_{1}= F·d → Γ

_{1}= 588,6 · 0,17 = 100,062 N·m

The next step is to calculate the gear ratio (i) using the number of teeth, and once calculated we can obtain the output torque (Γ

_{2}) and output speed (ω

_{2}):

i

_{1→2}=(Z

_{1}) / (Z

_{2}) → i

_{1→2}=38/14 = 2,71

i

_{1→2}=(Γ

_{1}) / (Γ

_{2}) → Γ

_{2}= (Γ

_{1}) / (i

_{1→2}→ Γ

_{2}=(100,062) / (2,71) = 36,86 N·m

i

_{1→2}=(ω

_{2}) / (ω

_{1})→ω

_{2}=ω

_{1}·i

_{1→2}→ω

_{2}=7,33·2,71=19,89 rad/s

Is the exercise well done? What could I add because the resolution was more physically correct? Any suggestions or ideas?