Physics 221 Chapter 6

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Physics 221Chapter 6
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Problem 1 . . . Round and round

• A red car goes counterclockwise around a track at
  a constant speed (see figure)
• A. The car is accelerating and Q shows the
  direction of the force on it
• B. The car is accelerating and P shows the
  direction of the force on it
• C. The car is not accelerating
• D. The car is accelerating but there is no force
  acting on it.

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Solution 1 . . . Round and round

• A red car goes counterclockwise around a track at
  a constant speed (see figure)
• A. The car is accelerating and Q shows the
  direction of the force on it.
• Centripetal Force changes the direction
• Centripetal Force does not change speed
• Centripetal Force points toward the center

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Problem 2 . . . Equation for C.F.

• The correct equation for centripetal force is
• A. F mv
• B. F mvr
• C. F mv / r
• D. F mv2 / r

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Solution 2 . . . Equation for C.F.

• The correct equation for centripetal force is
• F mv2 / r

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Problem 3 . . . Stoned and strung

• Dennis the menace ties a 250 g rock to a 160 cm.
  string and whirls it above his head. The string
  will break if the tension exceeds 90 N. What
  minimum speed will endanger the windshield on his
  neighbors car?

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Solution 3 . . . Dennis the Menace

• Centripetal Force is F mv2 / r
• 90 (0.25)(v2 / 1.6 )
• v 24 m/s

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Problem 4 . . . Slippery when wet!

• A car exits on a ramp (unbanked) of radius 20 m.
  The coefficient of friction is 0.6. The maximum
  speed before slipping starts is most nearly
• A. 10 m/s
• B. 20 m/s
• C. 40 m/s
• D. 120 m/s

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Solution 4 . . . Slippery when wet!

• Force of Friction Centripetal force
• (0.6)(m)(g) (m)(v2) / r
• v 11 m/s

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Problem 5 . . . Spaced out!

• Residents in a colony in outer space live in a
  cylindrical spaceship that has a diameter of 90 m
  and its speed at the rim is 15 m/s. The
  simulated g felt by the occupants is most
  nearly
• A. 0.5 g
• B. 1.0 g
• C. 2.0 g
• D. 5 g

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Solution 5 . . . Spaced out!

• (m)(v2) / r m g
• g v2 / r
• g (15)(15)/45
• g 5 m/s2
• g 0.5 g
• Correct answer is A.

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Satellites

• Many LEO (Low Earth Orbit) satellites are fairly
  close to the Earth. There is substantial g out
  there. Yet people feel weightless! This has
  to do with free-fall like when you are in an
  elevator and it accelerates down.
• Problem 8 How much would a 120 lb woman feel
  she weighs in an elevator decelerating at 2 m/s2 ?

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Satellites

• Solution8 F ma
• mg - T ma
• T mg - ma
• T 12 x 10 - 12 x 2
• T 120 - 24
• T 96 lbs.
• Note Satellites are in free-fall so the
  occupants feel weightless!

a
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Air Drag

• Free-fall acceleration is g 9.8 m/s2. However,
  if air resistance is taken into account then the
  acceleration keeps decreasing as the objects
  speed keeps increasing. This is because the
  resistive force of air drag increases as the
  speed increases. When the resistive force
  becomes equal to the force of gravity (weight)
  the object attains a constant speed. This final
  constant speed is called Terminal Velocity.

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What does drag depend on?

• Air Resistance (drag) is generally proportional
  to the square of the speed
• R Cv2
• R ½ D ? A v2
• R resistive force
• D Drag coefficient (0.5 to 2)
• ? density of air
• A cross-sectional area
• Generally in a liquid, the resistance is
  proportional to the speed
• R - bv

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• Thats all Folks!