Centripetal Force

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 isnt 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
mg tan q
mg
6
Period of Revolution

• The pendulum period is related to the speed and
  radius.

q
L
FT
r
mg tan 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 doesnt 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
Skidding

• 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/ ms g 64 m
• v2icy ms g r 120 m2/s2
• vicy 11 m/s 40 km/h

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.

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