Download 7-1 Work Done by a Constant Force The work done by a constant

Chapter 7
Work and Energy
6-4 Satellites and “Weightlessness”
Satellites are routinely put into orbit around the Earth.
The tangential speed must be high enough so that the
satellite does not return to Earth, but not so high that it
escapes Earth’s gravity altogether.
6-4 Satellites and “Weightlessness”
The satellite is kept in orbit by its speed—it is
continually falling, but the Earth curves from underneath
it.
Newton’s Law of Universal Gravitation and
satellites
• Satellites and planets are kept
in orbit by gravitational force
å F = ma =
Gmearthmsatellite
Gm1m2
F=
2
r
r2
We will treat the orbits as circular,
so the acceleration is towards the
center of the circle
å Fr = msat a r =
v =
Gmearthmsatellite
r2
Gmearth
r
= msat
v2
r
r
r
6-4 Satellites and “Weightlessness”
Objects in orbit are said to experience weightlessness. They do
have a gravitational force acting on them, though!
The satellite and all its contents are in free fall, so there is no
normal force. This is what leads to the experience of
weightlessness.
Problem 29
29.(II) What will a spring scale read for the weight
of a 53-kg woman in an elevator that moves (a)
upward with constant speed 5.0 m/s, (b) downward
with constant speed 5.0 m/s, (c) upward with
acceleration 0.33 g, (d) downward with acceleration
0.33 g, and (e) in free fall?
Apparent Weight
• Scale in an elevator: The apparent weight has a
magnitude of FN and points in the direction opposite
the normal force.
FN
6-4 Satellites and “Weightlessness”
More properly, this effect is called apparent weightlessness,
because the gravitational force still exists. It can be
experienced on Earth as well, but only briefly:
7-1 Work Done by a Constant Force
The work done by a constant force is defined as the distance
moved multiplied by the component of the force in the
direction of displacement:
W= Fd cos θ
If the force and the displacement are in the
same direction θ =0 and W=Fd
Question
A boy pulls a sled across the snow 10 m. The
work done on the sled by the normal
force is
A) Positive
B) Negative
Normal
C) Zero
Gravity
Question
A boy pulls a sled across a level field of
snow. The work done on the sled by
gravity is
A) Positive
B) Negative
C) Zero
Question
A boy pulls a sled across the snow 10 m. The
work done on the sled by the Boy is
A) Positive
B) Negative
Force Boy
C) Zero
Question
A pendulum bob is swinging back and forth in an arc
in the plane of the page as seen below. The
Tension force is 20 N, and the arc length is 5 m.
The Work done by the Tension force in one quarter
swing (up or down) is
A) Positive
B) Negative
C) Zero
T
D) Depends on the direction of the swing
Question
Alice lifts a 1 kg box 2 meters off the
ground at a constant speed where gravity
= 10m/s2
Work done by gravity is:
A) +20 Nm
B) -20 Nm
C) 0
D) -5 Nm
2m
E) +5 Nm

7-1 Work Done by a Constant Force
Work done on a crate.
A person pulls a 50-kg crate 40 m along a horizontal floor by
a constant force FP = 100 N, which acts at a 37° angle as
shown. The floor exerts a friction force Ffr=50N. Determine
(a) the work done by each force acting on the crate, and (b)
the net work done on the crate.
Problem 9
9.(II) A box of mass 6.0 kg is accelerated
from rest by a force across a floor at a rate
of 2m/s2 for 7.0 s. Find the net work done
on the box.
Problem 10
• 10.(II) (a) What magnitude force is required to give a
helicopter of mass M an acceleration of 0.10 g
upward? (b) What work is done by this force as the
helicopter moves a distance h upward?
7-1 Work Done by a Constant
Force
Example 7-2: Work on a backpack.
(a) Determine the work a hiker must do on a
15.0-kg backpack to carry it up a hill of
height h = 10.0 m, as shown. Determine also
(b) the work done by gravity on the
backpack, and (c) the net work done on the
backpack. For simplicity, assume the motion
is smooth and at constant velocity (i.e.,
acceleration is zero).
7-1 Work Done by a Constant Force
In the SI system, the units of work are joules:
Work is a scalar
As long as this person does not
lift or lower the bag of
groceries, he is doing no work
on it. The force he exerts has
no component in the direction of
motion.
Total Work or Net Work

When more than one force acts on an object, the
total work is the sum of the work done by each
force.
Wtotal = W1 + W2 + ....+ Wn
Airplane Example
N
W net = Wnormal + Wgravity + Wdrag
= 0 + 0 + W drag
Another way to look at it is….
Airplane Example
åF
åF
y
= N - mg = 0
x
= Fdrag
Fdrag
mg
7-1 Work Done by a Constant Force
Solving work problems:
1. Draw a free-body diagram.
2. Choose a coordinate system.
3. Apply Newton’s laws to determine any
unknown forces.
4. Find the work done by a specific force.
5. To find the net work, either
a) find the net force and then find the work
it does, or
b) find the work done by each force and add.
7-2 Scalar Product of Two Vectors
Definition of the scalar, or dot, product:
Therefore, we can write:
Scalar Product
• The scalar product is commutative
• The scalar product obeys the
distributive law of multiplication
• The scalar (dot) product is a scalar not
a vector
Dot Products of Unit Vectors
î  î  ĵ  ĵ  k̂  k̂  1
î  ĵ  î  k̂  ĵ  k̂  0
Using component form with
and
:
Dot Product: Problem 16
16.(I) What is the dot product of
A  2.0 x 2 ˆi  4.0 x ˆj  5.0 kˆ
and B  11.0 ˆi  2.5 x ˆj?