Download Chapter 3

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C7 – Some Potential Energy Functions
C8 – Force and Energy
General Physics
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Two Minute Problems – C7T.1
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The electrostatic potential energy
between the proton and electron in a
normal hydrogen atom (with the
conventional choice of reference
separation) is
A. negative
B. zero
C. positive
D. any of the above
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Two Minute Problems – C7T.4
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The following graph shows the potential energy function of a
certain interaction. The interaction is
A. always attractive
B. always repulsive
C. attractive for small r, repulsive for large r
D. repulsive for small r, attractive for large r
E. there is not enough information for a meaningful answer
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Two Minute Problems – C8T.1
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Two hockey pucks are initially at rest on a horizontal
plane of frictionless ice. Puck A has twice the mass of
puck B. Imagine that we apply the same constant
force to each puck for the same interval of time dt.
How do the pucks’ kinetic energies compare at the end
of this interval?
A. KA = 4 KB
B. KA = 2 KB
C. KA = KB
D. KB = 2 KA
E.. KB = 4 KA
F. Other
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Two Minute Problems – C8T.5
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When an object slides down a frictionless incline, the
cotact interaction between the object and the incline
does not contribute to the object’s kinetic energy,
true (T) or false (F)?
This means that it also does not transfer any
momentum to the object, T or F?
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Potential Energy Functions
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Electromagnetic Interaction
q1q2
V r    k
r
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Gravitational Interaction
m1 m2
V r   G
r
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reference separation :
V r   0 when r  
reference separation :
V r   0 when r  
Potential Energy of a Spring
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V r   k s r  r0 
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reference separation :
V r   0 when r  r0
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Attractive and Repulsive Interactions
q1q2
V r    k
r
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m1 m2
V r   G
r
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Interaction with a spring
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Dot Product
 
u  w  uwcos
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Kinetic Energy
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Kinetic energy is the dot product of velocity and
momentum
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dK  v  dp when dp  p
dK  vp cos 
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The kinetic energy of each interaction of the
objects in the system contribute to the overall
kinetic energy of the object
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 
 
dK  v  dpA  v  dpB  v  dpC  ...
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An Interaction’s contribution to dK
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Impulses are small changes in momentum
that contribute to the total momentum of a
particle
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dp  dpA  dpB  dpC  ...
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By analogy, k-work values are small
changes in kinetic energy that contribute to
the total kinetic energy of a particle
dK  dK A  dK B  dK C  ...
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K-work
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Each interaction’s contribution to dK is the tiny
amount of k-work the interaction contributes to
the particle during the time it takes the particle to
move a tiny displacement.
 
dK  F  dr
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F is the force exerted on the particle by the
interaction and dr is the small displacement the
particle moves
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K-work and impulse are like cash
transactions
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Momentum and kinetic energy are analogous
to your bank account.
Impulse and k-work analogous to cash
transactions into and out of your bank
account
Impulse has the same units as momentum
K-work has the same units as kinetic energy
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One big difference…
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The impulse that an interaction between two
particles delivers to one particle’s momentum
comes directly out of the other particle’s
momentum account.
The k-work represents a transaction between
a particle’s kinetic energy and the
interaction’s potential energy, NOT the other
particle’s kinetic energy
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Gravitational potential – both particles are
increasing their kinetic energy at the expense of
the potential energy
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Force Laws
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The definition
 
dK  F  dr
Provides a link between force and energy
We can determine the force an interaction
exerts on a particle
Gravitational force
Spring force
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Fgz  mg
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GmA mB
Fg  
rˆ
2
r
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Fsp  k s r  r0 rˆ
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Contact interactions
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Perpendicular interactions don’t contribute
to kinetic energy
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dK   FN  dr  0
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Group Problems
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C8B.5
C8S.6
C8S.7
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Classroom whiteboards
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