PHYS16 – Lecture 14
Ch. 7 Work and Energy
Announcements
• Interested in Biophysics Research?
– Come hear me give a talk on Thursday 4:45 pm in
Merrill 2
– “Using Lasers to Observe the Mechanics of Life”
Ch. 7 Work and Energy
• Mechanical Energy
– Potential Energy
– Kinetic Energy
• Work
– Constant Force → Dot Product
– Variable Force → Integral
• Work-Mechanical Energy theorem
Energy pre-question
• A projectile is shot at an angle of θ with an initial
speed of v0. What is the kinetic energy of the
projectile at the top of the arc?
A)
B)
C)
1 2
mv0
2
1 2 2
mv0 sin ( )
2
1 2
mv0 cos 2 ( )
2
0
D)
E) None of the above
Energy pre-question
• Some forces in nature depend on the inversesquare of the distance between objects (1/r2). If
you were to calculate the potential for this force
it would depend on:
A)
B)
C)
D)
E)
1/r
1/r3
r
r2
None of the above
Cheat Sheet
• Mechanical Energy
– Potential Energy, Gravitational U  mgh
1 2
– Potential Energy, Spring U  kx
2
– Kinetic Energy K  1 mv 2
2
• Work
 
W  F x cos
– Constant Force
– Variable Force W  Fx dx  Fy dy  ...


Review of Work
• Back to Jorge and his crate… Jorge pushes on a
10-kg crate 5 m with a 50 N force at 21
degrees. The coefficient of kinetic friction is
0.2. What is the total work?
http://www.wsu.edu/~jtd/Physics205/Chap4/Image189.gif
Discussion: Does the normal force do work?
• How much work is done by friction in the
Jorge/crate example? How much work is done
by the normal force?
• I push on a wall. Does the normal force do
work? Why am I tired?
• I push on a wall while on a skateboard, does
the normal force do work?
• Does the normal force ever do work?
Discussion: Mechanical Advantage and Work
• If I increase my mechanical advantage do I
decrease the amount of work I do?
• What is the mechanical advantage for the
incline? What is the work?
Discussion: Mechanical Advantage and Work
• What about for a pulley?
θ = 60 degrees
F
mass
Work-Mechanical Energy Theorem
Energy can be transformed
• Wyle E. Coyote
• http://www.youtube.com/watch?v=Jnj8mc04r9E&feature=related
Work – Mechanical Energy Theorem
• Work = the transfer of Energy
• Energy = the ability to do work
W  K
W  U
Work done by system
is negative
Work and grav. potential energy
• If I lift an object, how much work did I do on the object?
• Use work-energy theorem to derive gravitational potential
energy
W   U
 
  F  dx  U
Notice Sign
yf
  mg (dy)  U
yi
 mg ( y f  yi )  U
Discussion: Denver vs. Boston
• So if I drop a 1-kg ball from 2 m then the
change in the potential energy is 20 J. What if
this classroom where in Denver instead of in
Boston, a mile higher, would the potential
energy change?
http://upload.wikimedia.org/wikipedia/commons/c/c8/ReliefUSA_map.gif
Zero of Potential Energy
• Wherever you set your zero point for potential
energy will determine your coordinate system
– U=0 J at y=0 point for gravitational pot. energy
– U=0 J at equilibrium point for spring pot. Energy
• All calculations of ΔU will be relative so it
won’t matter where you put 0 J just make sure
not to switch back and forth!!!
Conclusion
• Mechanical Energy
– Potential Energy, Gravitational U  mgh
– Potential Energy, Spring U  1 kx2
2
– Kinetic Energy
1 2
K
• Work
2
mv
 
W  F x cos
– Constant Force
– Variable Force W  F dx  F dy  ...
 x  y
• Work-Mechanical Energy Thereom
W  K
W  U