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.
P = mg; Γ = Fd
The Attempt at a Solution
g = 9,81 m/s2
d = 170 mm = 0,17 m
ω1 = 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 (Γ1):
Γ1 = F·d → Γ1 = 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 (Γ2) and output speed (ω2):
i1→2=(Z1) / (Z2) → i1→2=38/14 = 2,71
i1→2=(Γ1) / (Γ2) → Γ2 = (Γ1) / (i1→2 → Γ2=(100,062) / (2,71) = 36,86 N·m
i1→2=(ω2) / (ω1)→ω2=ω1·i1→2→ω2=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?