Chapter 6: Applications of Newtons Laws

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Chapter 6 Applications of Newtons Laws

• Brent Royuk
• Phys-111Concordia University

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Friction

• Definition a _____ that opposes motion
• Three types
• Static Contact
• Kinetic Sliding
• Rolling
• Friction depends on two things
• The load
• Nature of the two surfaces
• Smooth vs. scratchy
• Real friction Van der Waals Forces
• Cold welding of metals
• Consider What would you do if you were on a
  completely frictionless surface?

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Friction

• http//www.engin.brown.edu/courses/en3/Notes/Stati
  cs/friction/friction.htm

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Kinetic Friction

• fk ?k N
• What is ?k?
• Coefficients Table 6-1, p. 143 and next slide
• Kinetic Friction is
• Proportional to N
• Independent of the relative speed of the surfaces
• Independent of the area of contact of the surfaces

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Friction Coefficients
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Kinetic Friction Examples

• Example 6-1 Someone at the other end of the
  table asks you to pass the salt. Feeling quite
  dashing, you slide the 50.0-g salt shaker in
  their direction, giving it an initial speed of
  1.15 m/s. If the shaker comes to rest with a
  constant acceleration in 0.840 m, what is ?k?
• Suppose you then lift up the table and incline it
  at an angle of 22o. Then you give the shaker a
  push. What acceleration does the shaker
  experience as it slides down the table?

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Static Friction

• What is the nature of friction between surfaces
  that are at rest with respect to each other?
• ?s gt ?k

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Static Friction

• The static friction laws
• 0 fs fs max
• fs max ?s N
• The Crate Problem
• A worker wishes to use a rope to pull a 40.0-kg
  crate across a floor. What force is necessary to
  get it moving if ?s 0.650?
• If he keeps pulling with that force and ?k
  0.450, what will the acceleration of the crate
  be?
• Rework the problem with the worker pulling at a
  30.0o angle.
• Place a penny on a board. Lift the board until
  the penny just starts to slide and measure the
  angle ?. What is ?s?

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Strings and Springs

• String tension
• Strings cant push, can only pull
• Heavy vs. ideal
• Figures 6-6, 6-7, p. 150
• Ideal pulleys merely change direction
• Conceptual Checkpoint 6-2, p. 152
• Springs follow Hookes Law
• F -kx
• The spring constant, k
• Units
• Meaning

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Examples

• A 10 kg weight and a 5 kg weight are hung from a
  string, one above another. An upward force of
  170 N is applied. What are the string tensions
  and the acceleration of the block?
• Standard Trick 1 vs. The Robot Method
• Two blocks of mass m1 2.5 kg and m2 3.5 kg
  are connected by a string as shown in in Figure
  6-10, p. 158. A horizontal force of 12.0 N is
  applied to the block on the right as shown. Find
  the acceleration of the blocks and the tension of
  the connecting string.

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Examples

• Find the acceleration of Atwoods Machine
  (Example 6-7, p. 161) in terms of its masses m1
  and m2. Find the string tension.
• Standard Trick 2
• Given m1 on an inclined plane at 32o, m2 hanging
  over a pulley at the top and pulling up the
  plane. m1 4.0 kg m2 3.5 kg, ?k .24.
  The box is moving up the plane. What is the
  acceleration?
• At a 30o angle, a box accelerates down an
  inclined plane at a rate of .85 m/s2.. Find ?k.

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The Drag Force

• An object moving through a fluid experiences a
  drag force.
• cannon ball sinking in water, car on highway,
  baseball, parachutist, dust, coffee filters
• Fdrag ? v2
• At terminal speed, Fdrag mg
• Equation
• ? is density of fluid (1.2 kg/m3 for air), A is
  cross-sectional area, C is a shape coefficient,
  generally ranging from .5-1

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Some Approximate Terminal Speeds

• Object Speed (m/s)
• cannonball 250
• 16-lb shot 145
• high caliber bullet 100
• sky diver 60-100
• baseball 42
• tennis ball 31
• basketball 20
• mouse 13
• ping-pong ball 9
• penny 9
• raindrop 7
• parachutist 5
• snowflake 1
• sheet of paper (flat) 0.5
• fluffy feather 0.4

You can drop a mouse down a thousand-yard mine
shaft and, on arriving at the bottom, it gets a
slight shock and walks away. A rat is killed, a
man is broken, a horse splashes. -J.B.S.
Haldane, British geneticist, 1892-1964
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Elevator Dynamics

• If you stand on a scale in an accelerating
  elevator, what does the scale read?
• Scenarios
• at rest or constant speed W? W
• a 4.9 m/s2 up
• a 4.9 m/s2 down
• cable breaks
• a 19.6 m/s2 down
• So could you jump at the last second in a
  free-falling elevator in order to survive?

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Circular Motion

• Uniform Circular Motion
• What is the nature of the speed, velocity and
  acceleration?
• What does centripetal mean?
• Derivation
• Small-angle approximation
• What is a centrifugal force?

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Circular Motion

• Swing a mass on a string, calculate and measure
  the centripetal force.
• A 1200-kg car rounds a corner of radius 45 m. If
  the coefficient of friction between the tires and
  road is 0.82, what is the greatest speed the car
  can have in the corner without skidding?
• What if the roadway is banked 18o?