A cyclist is moving in a circular path of radius 10 m at a speed of 5 m/s. What is the angle of banking required to prevent slipping?

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Q: A cyclist is moving in a circular path of radius 10 m at a speed of 5 m/s. What is the angle of banking required to prevent slipping?

Solution: tan(θ) = v²/(rg) = (5²)/(10*9.8) = 0.25. θ = tan⁻¹(0.25) ≈ 14°.

Steps: 8

Step 1: Identify the given values. The radius (r) of the circular path is 10 meters, and the speed (v) of the cyclist is 5 meters per second.
Step 2: Recall the formula for the angle of banking (θ) to prevent slipping: tan(θ) = v² / (r * g), where g is the acceleration due to gravity (approximately 9.8 m/s²).
Step 3: Substitute the known values into the formula. Here, v = 5 m/s, r = 10 m, and g = 9.8 m/s².
Step 4: Calculate v², which is 5² = 25.
Step 5: Calculate r * g, which is 10 * 9.8 = 98.
Step 6: Now, divide v² by (r * g): 25 / 98 = 0.2551 (approximately 0.25).
Step 7: Use the arctangent function to find the angle θ: θ = tan⁻¹(0.25).
Step 8: Calculate θ using a calculator or trigonometric table, which gives approximately 14 degrees.