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Physics
Work
It is done on a body when a force acts through a
distance. The definition of work involves the
force acting on the body (F), the distance
through which this force acts (S) and the angle
(θ) between the force vector and the distance
vector. In mathematical equation,
W  FS cos
units :
ft  lb
N  m or Joule(J)
Work
Sample work problems:
1. A puck lies on the horizontal air table. The air
table reduces the friction between the puck
and the table to almost zero since the puck
rides on a film of air. A player exerts a force of
70 lbs. on this puck through a distance of 0.5
feet, and he is careful that his force is in the
same direction as the distance through the
force is applied. The player has done 35 ft-lbs
of work on the puck.
Work
2. A sled is dragged over a horizontal snowy
surface by means of a rope attached to the
front of the sled. The rope makes an angle of
28˚ with the horizontal. The sled is displaced a
distance of 50 ft. The worker exerts a force of
35 pounds. How much work does the worker
do?
Work
Solution:
W  FS cos 
 (35lbs )(50 ft) cos 28
 1550 ft  lbs
0
Friction
It is a work done when as the surfaces rub
against each other. This work heats the
surfaces and always results in wasted work.
Previously, we talk about the weight (W), which
is the downward force due to gravitational
pull of the earth; and the normal force (N), the
upward push of the surface to itself on the
body. These two forces happens when a body
is at rest.
Friction
The W and the N are equal to each other in the
following condition.
Friction
Three kinds of friction:
1. Starting friction – the friction present at an
instant when a body has been at rest; just
before it begins to move under the application
of a force.
2. Sliding friction – the friction present as a
body is sliding over another surface. It is
present when the surface of the body and the
surface on which it slides are moving relative
to each other.
Friction
3. Rolling friction – the friction between a
rolling body and surface on which it rolls.
All the three cases, the friction equation the
same.
F  N

Friction
is the coefficient of friction is given in
the following table for different kinds
of material.
Material
μstart
μslide
Steel on steel
0.15
0.09
Steel on ice
0.03
0.01
Leather on wood
0.5
0.4
Oak on oak
0.5
0.3
Rubber on dry concrete
1.0
0.7
Rubber on wet concrete 0.7
0.5
Friction
Sample Problem:
A steel is weighing 100 lbs is resting on a
horizontal steel surface. How many pounds
force are necessary to start the body sliding?
What force is necessary to keep this body
sliding at constant speed?
Friction
Solution:
w  N  100lbs
F  N
Force to start sliding motion:
F  N
 (0.15)(100lbs )
 15lbs
Force to keep body sliding:
F  N
 (0.09)(100lbs )
Exercises
1. How much work is done by a person in raising a 45
lbs bucket of water from the bottom of a well that is
75 ft deep? Assume constant speed.
2. A block is dragged over a rough, horizontal surface
at a constant force of 78 lbs acting at an angle of
25˚above the horizontal. The block is displaced at a
distance of 45 ft. How much work is done by the
worker?
3. An aircraft with a weight of 85,000 lbs is towed over
a dry concrete surface. What force must the towing
vehicle exert to keep the airplane rolling?