Ch5 Circular Motion and Force

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Ch5Circular Motion and Force
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Centripetal Force - Swinging Ball

• Any body rotating about a fixed point will
  experience a centripetal (center seeking)
  acceleration.
• This acceleration is always directed inwards
  towards the center of the circle.
• If asked to find the centripetal force, then
  simply multiply the acceleration by the mass.
• When viewing Swinging Ball problems, note that
  the body has a force (tension, normal,) acting
  on it that is pulling the body towards the center
  of the circle at all times.

3

• You are looking down on a flail spinning in a
  horizontal circle.
• The chain breaks on the flail.
• Which flail (red, blue, or green) travels in the
  path that the flail would follow after the chain
  broke?

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Centripetal Force - Swinging Ball

• We will derive the equations relating the
  tensions in the top and bottom of a vertically
  swinging ball to the velocities of the ball at
  the top and bottom of its swing.
• Notice that the tension is pulling the ball
  towards the center of rotation at all times.
• Which tension would you expect to be the largest
  top or bottom? Why?
• Derive the tension for both cases

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Centripetal Force Ferris Wheel

• As the man riding the Ferris wheel is moving in a
  circle, he experiences a centripetal force (red)
  at all points as shown.
• The seat is also exerting an upward normal force
  on him (blue).
• Derive an expression for the weight of the boy at
  the top and bottom of the ride.

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Circular Motion and Force

• Synchronized jet fighters perform a perfect
  vertical circular loop maneuver.
• What is the apparent weight of the pilot at the
  top and bottom of the loop?

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Circular Motion and Force

• A test dummy (m 62.5 kg) rides freely in a
  high-speed roller coaster with a radius of
  curvature of r 52.00 m.
• What type of a problem is this one?
• A Ferris wheel problem.
• If the coaster was moving at vT 18.00 m/s
  at the top of the coaster, then what is the
  apparent weight of the test dummy at this point?
• What is the maximum safe
  speed of the roller coaster?

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Circular Motion and Force

• An airplane, whose engine failed, was gliding to
  the ground.
• Once the engine restarted, the pilot pulled up
  in order to keep the plane from crashing into the
  ground.
• The radius of curvature of the pull up is 175.0
  m, and the planes speed at the lowest point of
  this curve is 78.0 m/s.
• What is the apparent weight of the 58.2 kg pilot
  at this lowest point in flight?

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Friction Types for Rolling and Skidding Tires

• What type of friction acts between the road and a
  tire that is rolling without skidding?
• What type of friction acts between the road and a
  tire that is skidding?
• Watch the red dot on the tire below as it rolls
  and then slides.

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Skidding and Curves

• When an ATV safely negotiates a curve, the
  centripetal acceleration produced by the inward
  acting static friction is able to accelerate
  (change the direction of) the ATV.
• The tracks left behind by this ATV would look
  like the ones to the right.
• When an ATV goes around the curve at too high a
  speed, the tires begin to skid.
• The tracks left behind by this ATV would look
  like the ones to the right.

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Negotiating Curves

• Watch the animation to the right and explain what
  has happened.
• What force acted on the ATV that prevented it
  from slipping off the road during the first lap
  and in which direction was it acting?
• The static friction directed inwards towards the
  center of curvature.
• What forces were acting on the ATV when it
  slipped off the road?

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Negotiating Curves - Unbanked

• When a car negotiates an unbanked curve, the only
  force causing the centripetal acceleration is the
  static friction acting inwards along the radius
  of curvature.
• This static friction accelerates the car and
  causes it to turn.
• Derive an expression for the maximum speed the
  ATV can have to safely negotiate a curve of
  radius r when the coefficient of static friction
  between the tires and the road is ?s.