Rounding a flat curve – dynamics of circular motion problems and solutions

1. A 2000-kg car rounds a curve on a flat road of radius 150 m. The coefficient of static friction is 0.5. Determine the maximum speed so the car follows the curve and not skid. Acceleration due to gravity = 10 m/s².

Known :

Mass (m) = 2000 kg

Radius (r) = 150 meters

Coefficient of static friction (μ_s) = 0.5

Weight (w) = m g = (2000 kg)(10 m/s²) = 20,000 kg m/s² = 20,000 N

Force of static friction (F_s) = μ_s N = μ_s w = (0.7)(20,000 N) = 14,000 N

Wanted : v

Solution :

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1. Mass and weight
2. Normal force
3. Newton’s second law of motion
4. Friction force
5. Motion on the horizontal surface without friction force
6. The motion of two bodies with the same acceleration on the rough horizontal surface with the friction force
7. Motion on the inclined plane without friction force
8. Motion on the rough inclined plane with the friction force
9. Motion in an elevator
10. The motion of bodies connected by cord and pulley
11. Two bodies with the same magnitude of accelerations
12. Rounding a flat curve – dynamics of circular motion
13. Rounding a banked curve – dynamics of circular motion
14. Uniform motion in a horizontal circle
15. Centripetal force in uniform circular motion