Chapter 5: Applications of Newton’s Laws

Brent Royuk Phys-111

Concordia 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 Waal’s 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/Statics/friction/friction.htm

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Friction Load

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Kinetic Friction •  fk = µk N •  What is µk?

– Coefficients: Table 5.1, p. 165 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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Kinetic Friction Examples •  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 µk?

•  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? •  What does it mean that µs > µk ?

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Static Friction •  The static friction laws:

0 ≤ fs ≤ fs max fs max = µs 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 µs = 0.650?

–  If he keeps pulling with that force and µk = 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 θ. What is µs?

Strings and Springs •  String tension

–  Strings can’t push, can only pull –  Heavy vs. ideal

•  Ideal pulleys merely change direction •  Springs follow Hooke’s 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 •  Two blocks of mass m1 = 2.5 kg and m2 =

3.5 kg are side-by-side on a frictionless table and connected by a string. A horizontal force of 12.0 N is applied to the block on the left. Find the acceleration of the blocks and the tension of the connecting string.

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Examples •  Find T in terms of m, g and θ.

F θ

m T

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Examples •  Find the acceleration of Atwood’s

Machine 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, µk = 0.24. The box is moving up the plane. What is the acceleration?

•  Desk Problem: At a 30o angle, a box accelerates down an inclined plane at a rate of 0.85 m/s2.. Find µk.

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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 α v2

•  At terminal speed, Fdrag = mg

•  Equation:

•  ρ is the density of the fluid (1.2 kg/m3 for air), A is cross-sectional area, C is the shape coefficient, generally ranging from 0.5-1 (next slide)

€

vt =2mgCρA

F

drag= 1

2CρAv2

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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 (W’)? •  Scenarios:

•  at rest or constant speed: W’ = W = mg •  a = g/2 up •  a = g/2 down •  cable breaks •  a = 2g up •  a = 2g down

•  So could you jump at the last second in a free-falling elevator in order to survive?