Work and Energy. Chapter 6. Expectations. After Chapter 6, students will: understand and apply the definition of work. solve problems involving kinetic and potential energy. use the work-energy theorem to analyze physical situations.
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After Chapter 6, students will:
After Chapter 6, students will:
The woman in the picture exerts a force F on her suitcase, while it is displaced through a distance s. The force makes an angle q with the displacement vector.
The work done by the woman is:
Work is a scalar quantity. Dimensions: force·length
SI units: N·m = joule (J)
James Prescott Joule
December 24, 1818 –
October 11, 1889
English physicist, son of a wealthy brewer, born near Manchester. He was the first scientist to propose a kinetic theory of heat.
Notice that the component of the force vector parallel to the displacement vector is F cos q. We could say that the work is done entirely by the force parallel to the displacement.
Recalling the definition of the scalar product of two vectors, we could also write a vector equation:
Work can be either positive or negative.
In both (b) and (c), the man is doing work.
(b): q = 0°;
(c): q = 180°;
Let’s look at what happens when a net force F acts on an object whose mass is m, starting from rest over a distance s.
The object accelerates according to Newton’s second law:
Applying the fourth kinematic equation:
A closer look at that result:
We call the quantity kinetic energy.
In the equation we derived, it is equal to the work (Fs) done by the accelerating force.
Kinetic energy, like work, has the dimensions of force·length and SI units of joules.
The equation we derived is one form of the work-energy theorem. It states that the work done by a net force on an object is equal to the change in the object’s kinetic energy. More generally,
If the work is positive, the kinetic energy increases. Negative work decreases the kinetic energy.
A hand raises a book from height h0 to height hf, at
Work done by the hand force, F:
Work done by the gravitational force:
Total (net) force exerted
on the book: zero.
Total (net) work done
on the book: zero.
Change in book’s kinetic energy:
Now, we let the book fall freely
from rest at height hfto height h0.
Net force on the book: mg.
Work done by the gravitational
Calculate the book’s final kinetic
The book gained a kinetic energy equal
to the work done by the gravitational force
(per the work-energy theorem).
is both work done on the
book and kinetic energy gained by
it. We call this the gravitational
potential energy of the book.
The total work done by the
gravitational force does not
depend on the path the book takes.
The work done by the gravitational
force is path-independent. It
depends only on the relative
heights of the starting and
Over a closed path (starting and ending points the same), the total work done by the gravitational force is zero.
Compare with the frictional force. The longer the path, the more work the frictional force does. This is true even if the starting and ending points are the same. Think about dragging a sled around a race course.
The work done by
the frictional force
The gravitational force is an example of a conservative force:
Other examples of conservative forces:
The frictional force is an example of a nonconservative force:
Other examples of nonconservative forces:
A man lifts weights upward at a constant velocity.
He does positive work on the weights.
The gravitational force does equal negative work.
The net work done on
the weights is zero.
The gravitational potential energy of the weights
The work done by the nonconservative normal force of
the man’s hands on
the bar changed the
energy of the weights:
Work done on an object by nonconservative forces
changes its total mechanical energy.
If no (net) work is done by nonconservative forces, the
constant (is conserved):
This equation is another form of the work-energy theorem.
Note that it does not require both kinetic and potential energy to remain constant – only their sum. Work done by a conservative force often increases one while decreasing the other. Example: a freely-falling object.
“Energy is neither created nor destroyed.”
Work done by conservative forces conserves total mechanical energy. Energy may be interchanged between kinetic and potential forms.
Work done by nonconservative forces still conserves total energy. It often converts mechanical energy into other forms – notably, heat, light, or noise.
Power is defined as the
time rate of doing work.
Since power may not
be constant in time, we
define average power:
SI units: J/s = watt (W)
1736 – 1819
Invented the first efficient
steam engine, having a
separate condenser for the
Plot force vs. position (for a constant force):
Plot force vs. position (for a variable force):