5.1 Uniform Circular MotionAt what angle (relative to the horizontal) should a curve 52 m in radius be banked if no friction is required to prevent the car from slipping when traveling at 10 m/s? (g = 9.8 m/s2)Select one:a.32°b.28°c.11°d.16°
Question
5.1 Uniform Circular MotionAt what angle (relative to the horizontal) should a curve 52 m in radius be banked if no friction is required to prevent the car from slipping when traveling at 10 m/s? (g = 9.8 m/s2)Select one:a.32°b.28°c.11°d.16°
Solution
To solve this problem, we need to use the formula for the banking angle (θ) in uniform circular motion without friction:
tan(θ) = v²/rg
where: v = speed of the car = 10 m/s r = radius of the curve = 52 m g = acceleration due to gravity = 9.8 m/s²
Substituting these values into the formula, we get:
tan(θ) = (10 m/s)² / (52 m * 9.8 m/s²) tan(θ) = 100 m²/s² / 509.6 m²/s² tan(θ) = 0.196
To find the angle θ, we take the inverse tangent (arctan or tan^-1) of 0.196:
θ = arctan(0.196) θ = 11.13°
So, the closest answer is c. 11°.
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