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February 1, 2012
Physics for Scientists&Engineers 1
1
Physics for Scientists &
Engineers 1
Spring Semester 2012
Lecture 12
Applications of Newton’s Laws
Two Pulleys
Ropes and pulleys can be combined to lift objects
that are too heavy to lift otherwise
Let’s consider the case of two pulleys
One pulley is tied to the ceiling and the other is
movable
A mass
m
is hung from the movable pulley
We pull down on the rope to lift the movable pulley
We assume that the pulleys are massless and
frictionless
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Two Pulleys (1)
Mass
m
hung from a system of two pulleys
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Two Pulleys (2)
First observation:
tension in string is the same
everywhere!
Freebody diagram of block (in
y
direction):
Freebody diagram of pulley
B
above block (also
direction):
F
g
−
T
3
=
0
T
3
=
F
g
=
mg
2
T
1
−
T
3
=
0
T
1
=
1
2
T
3
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Two Pulleys (3)
Combine these two equations:
=> Important result:
If you use this pulley system,
you only need to apply a force equal to 1/2 of the
weight of the object.
The pulley A only serves to redirect the force
T
1
in
this example:
T
1
=
1
2
T
3
=
1
2
mg
2
T
1
−
T
2
=
0
T
2
=
2
T
1
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Two Pulleys (4)
Final remark:
•
Combining all equations, we arrive
at the conclusion:
•
This means that the ceiling mount
of the upper pulley carries the
entire weight of the block
(compare green circles)
•
The entire force acting on the
ceiling is exactly the same as the
downward force on the rope, plus
the weight of the block (see
orange ovals)
T
2
=
2
T
1
=
2(
1
2
T
3
)
=
T
3
=
F
g
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February 1, 2012
Physics for Scientists&Engineers 1
7
Force Multiplier
We can also use the same rope
in loops and guide it over the
same pulley multiple times
•
In this example: 3 loops
•
We have six force vectors pointing
up, all with string tension
T
•
The object suspended from this
pulley then can have a weight of
6
T
In general for
n
loops:
T
=
1
2
n
mg
Applying Newton’s Laws
Newton’s Laws allow to solve various kinds of
problems involving force, mass, and acceleration
Newton’s Second Law enables us to solve a wide
range of calculations involving motion and
acceleration
Let’s consider an object of mass
m
located on a
plane that is inclined by an angle
θ
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This note was uploaded on 04/02/2012 for the course PHY 183 taught by Professor Wolf during the Spring '08 term at Michigan State University.
 Spring '08
 Wolf
 Physics, Mass

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