Physics 2211 Mechanics Review 2 Knight: Chapters 5'49

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Physics 2211 - MechanicsReview 2Knight
Chapters 5.4-9

• Dr. John Evans

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Chapter Summaries

• Chapters 5 - 9

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Chapter 5 Summary (1)
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Chapter 5 Summary (2)
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Terminal Velocity
An object falling in air accelerates until it
approaches a velocity at which the drag force and
weight are equal and opposite Dw
(in SI units only!)
A 75 kg sky diver who is 1.8 m tall and0.4
m wide will therefore reach a velocity of vterm
4(75 kg)(9.80 m/s2)/(1.8 m)(0.4 m)½ 64 m/s
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ExampleStopping Distances (1)
A 1500 kg car is traveling at 30 M/s when the
driver slams on the brakes and skids to a stop.
What is the stopping distance if the car is
heading up a 100 slope, down a 100 slope, and on
a level surface?
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ExampleStopping Distances (2)
Up 100 slope x1 48 m Down 100 slope x1
75 m On level surface x1 57 m
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Example Sliding Cargo
A 100 kg box of dimensions 50 cm by 50 cm by
50 cm is in the back of a flatbed truck. The
coefficients of friction between the box and bed
are ms0.4 and mk0.2. What is the maximum
acceleration that the truck can have without the
box slipping?
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Chapter 8 Summary (1)
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Chapter 8 Summary (2)
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Chapter 8 Summary (3)
Massless strings and ropes transmit and reverse
tension forces, changing the direction without
changing the magnitude. Remember that strings
can only pull along their length, not push or
make sideways forces. Massless and frictionless
pulleys are used to modify the direction of the
tension force without changing the magnitude.
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Example Accelerating Boxes
The hand pushes box A, which pushes box B
across a frictionless table. The mass of B is
greater than the mass of A. Rank the
horizontal forces.
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Example Towing a Car
A tow truck uses a rope to pull a car along a
horizontal road, as shown above. Identify all
action/reaction pairs, show them in a diagram,
and then draw free-body diagrams for the car, the
truck, and the rope.
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Example Stagecraft (1)
A 200 kg set used in a play is stored in a
loft above the stage. The rope holding the set
passes up and over a pulley, then is tied
backstage. The director tells a 100 kg stagehand
to lower the set. He unties the set, holds on to
the rope, and is hoisted into the loft. What
is his acceleration? (Assume a massless
rope and a massless frictionless pulley.)
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Example Stagecraft (2)
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Chapter 6 Summary (1)
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Chapter 6 Summary (2)
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Example A Home Run
A baseball is hit so that it leaves the bat
making a 300 angle with the ground. It crosses a
low fence at the boundary of the ballpark 100 m
from home plate at the same height that it was
struck. (Neglect air resistance.) What was
its velocity as it left the bat?
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Example A Ball Toss

• Mike throws a ball upward at a 630 angle
  with a speed of 22 m/s. Nancy rides past Mike on
  her bicycle at 10 m/s at the instant he releases
  the ball.
• What trajectory does Mike see?
• What trajectory does Nancy see?

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Chapter 7 Summary (1)
acentripetal v2/r w2r
Fcentripetal mv2/r mw2r
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Chapter 7 Summary (2)
Note the (r,t,z) coordinate system is a
non-inertial reference frame (because the origin
moves and accelerates with the rotation) and
therefore suspect. However, as long as the
quantities of interest are measured in an
inertial frame, the use of (r, t, z) coordinates
is OK.
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Chapter 7 Summary (3)
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Looping the Loop
Consider a roller coaster doing a vertical
loop-the-loop of radius r. This is not uniform
circular motion because the car goes faster at
the bottom than at the top. However, at the very
top and bottom points, the car is changing
direction at a constant speed, so uniform
circular motion applies andFnet mv2/r.
At the bottom,
At the top
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Losing the Loop
At the top of the loop
This can be negative, indicating the car will
fall off the track. The critical speed vc for
n0 is
The critical speed vc is the speed at which
the weight force alone is just sufficient to
cause circular motion at the top. There, wapp 0
and the rider momentarily will experience zero
gravity. At speeds less than vc, the car
will leave the track and follow a parabolic
trajectory to the ground.
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Review of Newtons Laws (1)
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Review of Newtons Laws (2)
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Chapter 9 Summary (1)
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Chapter 9 Summary (2)
Conservation of momentum p1f p2f p1i
p2iTherefore, p1f - p1i -(p2f - p2i) or
Dp1 -Dp2
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Chapter 9 Summary (3)
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Example Rolling Away
Bob sees a stationary cart 8.0 m in front of
him. He decides to run to the cart as fast as he
can, jump on, and roll down the street. Bob has
a mass of 75 kg and the carts mass is 25 kg.
If Bob accelerates at a steady 1.0 m/s2 before
jumping on, what is the carts speed just after
Bob jumps on?
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ExampleA Three-Piece Explosion (1)
A 10 g projectile is traveling east at 2.0
m/s when it suddenly explodes into three pieces.
A 3.0 g fragment is shot due west at 10 m/s,
while another 3.0 g fragment travels 400 north of
east at 12 m/s. What is the speed and the
direction of the third fragment?
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ExampleA Three-Piece Explosion (2)
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ExampleA Spinning Ice Skater (1)
An ice skater spins at 2.0 rev/s while
holding two 5.0 kg weights at arms length. He
begins to spin with his arms straight out from
his body and the weights 140 cm apart. He pulls
the weights in and holds them against his
shoulders so that they are separated by 50 cm.
Assuming the mass of the skater can be
neglected, how fast does the skater spin after
pulling in the weights?
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ExampleA Spinning Ice Skater (2)