Force and Motion-II

1
CHAPTER-6

• Force and Motion-II

2
Force and Motion-II

• Motion under frictional and centripetal forces
• Force of friction ( required for car motion out
  of a pit and out of a curve)
• Centripetal force (Radial force) (required to
  turn car in a circle

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Ch 6-2 Friction

• An external force F applied to a block resting on
  a rough surface
• No motion till F is less than static frictional
  force fs
• fs?sFN where FN Fg
• Body slides if F? fs
• When body start sliding static frictional force
  fs reduces to kinetic frictional force fk
• fk?kFN where FN Fg
• If lFllfkl body moves at constant speed
• If lFl ? lfkl body accelerates

4
Checkpoint 6-1

• A block lies on floor.
• (a) What is the magnitude of the frictional force
  on it from the floor?
• (b) If a horizontal force of 5 N is now applied
  to the block, but the block does not move, what
  is the magnitude of the frictional force on it?
• (c) If the maximum value fs,max of the static
  frictional force on the block is 10 N, will the
  block move if the magnitude of the horizontally
  applied force is 8 N?
• (d) If it is 12 N?
• (e) What is the magnitude of the frictional force
  in part (c)

• Ans
• (a) Zero
• (b) 5 N
• (c) No
• (d) Yes
• (e) 8 N

5
Checkpoint 6-2

• In the figure, horizontal force F1 of magnitude
  10 N is applied to a box on a floor, but the box
  does not slide. Then, as the magnitude of
  vertically applied force F2 is increased from
  zero but before the box begins to slide, do the
  following quantities increase, decrease, or stay
  the same.
• (a) magnitude of the frictional force on the box
• (b) the magnitude of the normal force on the box
  from the floor
• (c) the maximum value of fs,max of the static
  frictional force on the box?

• Ans
• (a) magnitude of the frictional force on the box
  remains same
• (b) the magnitude of the normal force on the box
  from the floor decreases
• (c) the maximum value of fs,max of the static
  frictional force on the box decreases

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Sample-Problem-6-2

• Loaded sled being pulled at constant speed, find
  T
• Since v is constant, then
• lTcos ?l lfkl ?kFN but
• FNTsin ?Fgmg
• FN mg-Tsin ?
• Then
• Tcos ? fk ?k FN
• ?k (mg-Tsin ?)
• Solve for T

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Sample-Problem-6-3

• Coefficient of static ?s friction for coin on
  verge of sliding down
• fs ?s FN ?s fs / FN
• ? Fx fs Fgsin?0
• fs Fg sin? mg sin?
• ? Fy FN Fg cos?0
• FN Fg cos?mg cos?
• ?s fs / FN
• mg sin? /mg cos?
• ?s tan ?

8
Ch 6-5 Uniform Circular Motion(Radial force and
friction force)

• Circular motion under the effect of centripetal
  force
• Centripetal force FR accelerates a body by
  changing the direction of the bodys velocity v
  without changing the bodys speed
• Constant centripetal acceleration aR, directed
  toward the center of the circle with radius R
• aRv2/R
• Centripetal force FRmaR
• m (v2/R)
• For puck tied to a string with tension T and
  moving in a circle
• FRTm (v2/R)

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Checkpoint 6-3

• Near the ground, is the speed of large raindrops
  greater than, or the same as the speed of small
  raindrops, assuming that all raindrops are
  spherical and have the same drag coefficient?

• Ans
• It takes longer time to attain the terminal
  velocity after falling for the larger raindrops
  as compared to the small drops. Under a constant
  acceleration, the large raindrops achieve larger
  value of terminal velocity than small raindrops.

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Sample-Problem-6-8

• Static frictional force fs prevent her from
  sliding down
• fsFg
• fs?sFN and normal force FN is provided by
  centripetal force FR
• Then FN FRm(v2/R)
• fs ?s FN ?sm(v2/R)Fgmg
• v2 Rg/ ?s

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Sample-Problem (Motion of car on a un-banked
curved road)

• Coefficient of static friction ?s when car is
  verge of sliding out of track
• -FR-mv2/R - fS -?s N
• -mv2/R - ?smg
• ?s v2/Rg

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Sample-Problem-6-10(Motion of car on a Banked
Curved Road)

• Calculate banking angle ? prevent sliding
• ? FX -FR-mv2/R - Nr -N sin ?
• -mv2/R -N sin ?..(1)
• ? FY NY -mg 0
• NY N cos ? mg .(2)
• Then
• (mv2/R)/(mg) (N sin ?)/(N cos ?)
• v2/Rg tan ?
• ? tan-1 (v2/Rg)