Transcript Physics 131: Lecture 14 Notes

Physics 151: Lecture 26
Today’s Agenda
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Today’s Topics
Statics (Chapter 12)
Physics 151: Lecture 26, Pg 1
See text: 12.1-3
Statics:

Objects are at rest (Static) when :
F  0
No translation
AND
  0
No rotation
When choosing axes about which to calculate torque, we
can be clever and make the problem easy....
Physics 151: Lecture 26, Pg 2
Example 2
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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
Physics 151: Lecture 26, Pg 3
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 :
Physics 151: Lecture 26, Pg 4
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.
b.
c.
d.
e.




610 lb
540 lb
640 lb
570 lb
2000 lb
Physics 151: Lecture 26, Pg 5
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 :
Physics 151: Lecture 26, Pg 6
Lecture 26, Act 1
Statics

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
1
(b) 2 & 3
(c) 3 only
2
3
Physics 151: Lecture 26, Pg 7
Lecture 26, Act 1
Addendum

What are the torques ??
(where do the forces act ?)
 switches sign
at critical point
 goes to zero at
critical point
 always zero
N
f
rG
mg
g 
rf
f  0
rN
N 
Physics 151: Lecture 26, Pg 8
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.
Physics 151: Lecture 26, Pg 9
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?
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a.
b.
c.
d.
e.
43 lb
34 lb
38 lb
47 lb
24 lb
Physics 151: Lecture 26, Pg 10
Recap of today’s lecture

Today’s Topics
Statics (Chapter 12)
Physics 151: Lecture 26, Pg 11
Lecture 24, Act 1
Statics
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 won’t precess
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Physics 151: Lecture 26, Pg 12
Lecture 24, Act 1
Statics
Remember that W  /L.
So what is ?
=rxF
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.
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Answer (c) it won’t precess
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Physics 151: Lecture 26, Pg 13