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Centripetal Force

Centripetal Force. Law of Action in Circles. Motion in a circle has a centripetal acceleration. For every acceleration there is a net force. There must be a centripetal force . Points to the center of the circle Magnitude is ma = mv 2 / r

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Centripetal Force

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  1. Centripetal Force

  2. Law of Action in Circles • Motion in a circle has a centripetal acceleration. • For every acceleration there is a net force. • There must be a centripetal force. • Points to the center of the circle • Magnitude is ma = mv2/r • The centrifugal force that we describe is just inertia. • It points in the opposite direction – to the outside • It isn’t a real force

  3. Conical Pendulum • A 200. g mass hung is from a 50. cm string as a conical pendulum. The period of the pendulum in a perfect circle is 1.4 s. What is the angle of the pendulum? What is the tension on the string? q FT

  4. Radial Net Force • The mass has a downward gravitational force, -mg. • There is tension in the string. • The vertical component must cancel gravity • FTy = mg • FT = mg / cos q • Tension: FT = mg / cos q = 2.0 N • Centripetal force: • FTr = mg sin q / cos q = mg tan q q FT cos q FT FT sin q mg

  5. Acceleration to Velocity • The acceleration and velocity on a circular path are related. q FT r mgtan q mg

  6. Period of Revolution • The pendulum period is related to the speed and radius. q L FT r mgtan q cos q = 0.973 q = 13°

  7. Vertical Curve • A loop-the-loop is a popular rollercoaster feature. • There are only two forces acting on the moving car. • Gravity • Normal force • There is a centripetal acceleration due to the loop. • Not uniform circular motion FN Fg

  8. Staying on Track • If the normal force becomes zero, the coaster will leave the track in a parabolic trajectory. • Projectile motion • At any point there must be enough velocity to maintain pressure of the car on the track. Fg

  9. Force at the Top • The forces of gravity and the normal force are both directed down. • Together these must match the centripetal force. • The minimum occurs with almost no normal force. • The maximum is at the bottom: a = v2 / r. Fg FN

  10. Horizontal Curve • A vehicle on a horizontal curve has a centripetal acceleration associated with the changing direction. • The curve doesn’t have to be a complete circle. • There is still a radius (r) associated with the curve • The force is still Fc = mv2/r directed inward r Fc

  11. Curves and Friction • On a turn the force of static friction provides the centripetal acceleration. • In the force diagram there is no other force acting in the centripetal direction. r Fc

  12. The limit of steering in a curve occurs when the centripetal acceleration equals the maximum static friction. A curve on a dry road (ms = 1.0) is safe at a speed of 90 km/h. What is the safe speed on the same curve with ice (ms = 0.2)? 90 km/h = 25 m/s rdry = v2/ msg = 64 m v2icy = msgr = 120 m2/s2 vicy = 11 m/s = 40 km/h Skidding

  13. Banking • Curves intended for higher speeds are banked. • Without friction a curve banked at an angle q can supply a centripetal force Fc = mg tan q. • The car can turn without any friction. next

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