PHYS 2108 Lecture Notes - Lecture 5: Kinematics, Waste Heat, Inclinometer
5-1
LAB 5:
Work and Energy
In a somewhat circular set of definitions, work is the transfer of energy and energy is the ability to do
work. In accelerating a baseball from rest to some final speed, you must apply a force to the baseball
though soe aeleatio distae. I the ed, ou’e gie something to the baseball by increasing its
speed. That something is stored energy from your body ou’e gie to the baseball by doing some
positive work on it, and the resulting energy possessed by the baseball is of the kinetic variety.
In the converse case, a catcher slowing a thrown baseball to rest must do negative work on the ball to
pull its kinetic energy out. Unfortunately for the catcher, that removed energy is transferred into heat
ad a’t e saed fo late use.
In all cases, it is impossible to exert a force into a direction of distance without doing some amount of
work in the process. Work is defined as the product between the component of a force parallel to the
direction of motion and the distance over which the force acts.
Eqn. 5-1:
Work due to a Constant Force
The units Newton-meters have a special name: Joules (J).
Storing Energy
In the example above of throwing a baseball, it seems that the final kinetic energy originated
somewhere within you before being transferred to the baseball. Potential Energy comes in many forms:
elastic, electric, chemical, nuclear, gravitational and more. Potential energy is stored energy that can be
converted to other useful forms. In the above example, the baseball pitcher converted stored chemical
eeg ito the aseall’s kieti eeg though the atio of doig ok.
Consider an example wherein we lift a heavy book from the ground to a tabletop. We must use a force
eual to the ook’s eight, mg, in order to lift it without giving it an acceleration or final kinetic energy.
If we apply this force from the ground to the final height, h, the work done is mg times change in height.
Beause thee’s o kieti eeg at the top of the lift, the work you put into the book must have gone
somewhere else. The energy was stored by the interaction with the gravitational field, and will
expectedly come out as kinetic energy if we were to drop the book. Your study of kinematics tells you
that the ook aeleates ith ieasig speed util it stikes the goud. Up util ipat, the ook’s
gravitational potential energy was completely converted to kinetic energy associated with its final
speed. These two ideas are summarized in the following equations.
Eqn. 5-2:
Gravitational Potential Energy
Eqn. 5-3:
Kinetic Energy
This convertibility of energy from one form to another is a universal constant called the Law of
Conservation of Energy which states: energy cannot be created or destroyed, only converted from one
form to another. This means that energy is never truly lost in an interaction, and that physics is basically
glorified accounting. Follow the energies and balance the checkbooks.
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5-2
Coseatio is aothe od ith diffeet eaigs i eeda speeh ad siee. Wheeas i
Eglish oseatio is used to ea saig fo late, i siee oseatio stitl eas ot lost.
Whe e sa eeg is oseed e ea all of the energy before an event is accounted for after the
event.
Friction
A second question comes up in our baseball example involving the catcher. The pitcher converted
potential energy into kinetic; however, when the catcher did negative work to pull the kinetic energy
out of the ball, the catcher did not convert it into stored potential energy. Where did the energy go?
According to the Law of Conservation of Energy, the energy extracted from the baseball still exists. As
the muscles contract and resist the all’s foad otio, the usle fies u agaist oe aothe ad
produce heat due to friction. Other forms of energy may have also come out (sound from slapping the
mitt, deformations in the ball, etc.), and the total net sum of all their contributions must add up to the
original kinetic energy of the baseball.
Ou odies do’t hae a ehais fo oetig ehaial o kieti eeg into stored potential
eeg. A spig ould hae stoed the all’s eeg as it opesses, ut ee that amount would
oe up a little shot due to soe slight heatig. Alost all eeg oesios epeiee soe
inefficiency and appear not to be conserved. We tend to make a distinction between energy that can do
useful ok ad eeg that is aste. In the analogy between energy and accounting, think about
a eeg oesio as a puhase ith soe assoiated ta.
A usual suspet fo lost eeg is fo fitio. Fitioal foes geeall ae i the opposite dietio
of applied forces (and the direction of motion) so these frictional forces are doing negative work. You
put work into a system while friction is taking work away in the form of waste heat. The magnitude of
friction depends upon two important parameters: the coefficient of friction μ and the normal force
(FN). The oeffiiet is a paaete of ho stik the sufae is etee to uig ojets. The
oal foe is ho had the to sufaes ae pessed agaist oe aothe ad is the agitude of
the force perpendicular to the touching surfaces. Frictional forces (Ff) are given as:
Eqn. 5-4:
Magnitude of Frictional Force
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Document Summary
In a somewhat circular set of definitions, work is the transfer of energy and energy is the ability to do work. In accelerating a baseball from rest to some final speed, you must apply a force to the baseball th(cid:396)ough so(cid:373)e a(cid:272)(cid:272)ele(cid:396)atio(cid:374) dista(cid:374)(cid:272)e. i(cid:374) the e(cid:374)d, (cid:455)ou"(cid:448)e gi(cid:448)e(cid:374) something to the baseball by increasing its speed. That something is stored energy from your body (cid:455)ou"(cid:448)e gi(cid:448)e(cid:374) to the baseball by doing some positive work on it, and the resulting energy possessed by the baseball is of the kinetic variety. In the converse case, a catcher slowing a thrown baseball to rest must do negative work on the ball to pull its kinetic energy out. Unfortunately for the catcher, that removed energy is transferred into heat a(cid:374)d (cid:272)a(cid:374)"t (cid:271)e sa(cid:448)ed fo(cid:396) late(cid:396) use. In all cases, it is impossible to exert a force into a direction of distance without doing some amount of work in the process.
