Physics 151: Lecture 26 Today

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Physics 151 Lecture 26 Todays Agenda

• Todays Topics
• Statics (Chapter 12)

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Statics
See text 12.1-3

• Objects are at rest (Static) when

AND
No rotation
No translation
When choosing axes about which to calculate
torque, we can be clever and make the problem
easy....
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Example 2

• The diagrams below show forces applied to a wheel
  that weighs 20 N. The symbol W stands for the
  weight. In which diagram(s) is the wheel in
  equilibrium?
• a. A
• b. B
• c. C
• d. D
• e. A and C

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Example 4

• A bridge of length 50.0 m and mass 8.00 x 104 kg
  is supported on a smooth pier at each end as in
  Figure below. A truck of mass 3.00 x 104 kg is
  located 15.0 m from one end. What are the forces
  on the bridge at the points of support?

Solution
nA 5.98 x 105 N nB 4.80 x 105 N
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Example 5

• A 25-ft long crane supported at its lower end by
  a pin is elevated by a horizontal cable as shown
  in the figure. A 250-lb load is suspended from
  the outer end of the crane. The center of gravity
  of the crane is 10 ft from the pin, and the crane
  weighs 200 lb. What is the tension in the
  horizontal cable?
• a. 610 lb
• b. 540 lb
• c. 640 lb
• d. 570 lb
• e. 2000 lb

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Example 3

• A square of side L/2 is removed from one corner
  of a square sandwich that has sides of length L.
  The center of mass of the remainder of the
  sandwich moves from C to C. The distance from C
  to C is

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Lecture 26, Act 1Statics

• A box is placed on a ramp in the configurations
  shown below. Friction prevents it from sliding.
  The center of mass of the box is indicated by a
  white dot in each case.
• In which cases does the box tip over ?

(a) all (b) 2 3 (c) 3 only

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1
2
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Lecture 26, Act 1 Addendum

• What are the torques ??
• (where do the forces act ?)

t goes to zero at critical point
t switches sign at critical point
t always zero
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Example 7

• Two identical uniform bricks of length L are
  placed in a stack over the edge of a horizontal
  surface with the maximum overhang possible
  without falling, as in Figure below. Find the
  distance x.

• SOLUTION
• If the CM of the two bricks does not lie over the
  edge, then the bricks balance.

• If the lower brick is placed L/4 over the edge,
  then the second brick may be placed so that its
  end protrudes 3L/4 over the edge.

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Example 6

• A uniform ladder 15 ft long is leaning against a
  frictionless wall at an angle of 53 above the
  horizontal. The weight of the ladder is 30
  pounds. A 75-lb boy climbs 6.0-ft up the ladder.
  What is the magnitude of the friction force
  exerted on the ladder by the floor?
• a. 43 lb
• b. 34 lb
• c. 38 lb
• d. 47 lb
• e. 24 lb

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Recap of todays lecture

• Todays Topics
• Statics (Chapter 12)

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Lecture 24, Act 1Statics

• Suppose you have a gyroscope that is supported on
  a gymbals such that it is free to move in all
  angles, but the rotation axes all go through the
  center of mass. As pictured, looking down from
  the top, which way will the gyroscope precess?

(a) clockwise (b) counterclockwise (c) it
wont precess
?
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Lecture 24, Act 1Statics

• Remember that W t/L.
• So what is t?
• t r x F
• r in this case is zero. Why?
• Thus W is zero.
• It will not precess. At All. Even if you move the
  base.
• This is how you make a direction finder for an
  airplane.

Answer (c) it wont precess