Calculate θ for the bicycle in speed 12.0m/s and turning inradius of 30.0m
Question
Calculate θ for the bicycle in speed 12.0m/s and turning inradius of 30.0m
Solution
To calculate θ (the lean angle) for a bicycle, we can use the formula:
θ = arctan(v² / g*r)
where:
- v is the speed of the bicycle,
- g is the acceleration due to gravity (approximately 9.81 m/s² on Earth), and
- r is the turning radius.
Substituting the given values into the formula, we get:
θ = arctan((12.0 m/s)² / (9.81 m/s² * 30.0 m))
θ = arctan(144.0 m²/s² / 294.3 m²/s²)
θ = arctan(0.489)
Using a calculator to find the arctan of 0.489, we get:
θ ≈ 26.4 degrees
So, the lean angle of the bicycle is approximately 26.4 degrees.
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