Transcript fall7Thus.ppt

Fall wk 7 – Thus.11.Nov.04
• Welcome, roll, questions,
announcements
• Energy, work, and forces
• Review derivatives
• Spring workshop
Energy Systems, EJZ
Energy review
Kinetic energy = ½ mv2
Potential energy due to gravity = mgh (near Earth’s
surface)
Potential energy due to gravitational attraction between
two masses = -GmM/r
Conceptest: review kinetic energy
Review energy,work, and forces
Recall that force = - gradient of potential energy
Fx= - dU/dx
Recall that work = force * displacement. Only the
component of force parallel to the displacement does
work:
W=F.d
Conceptests from Calculus Ch.2.4, 2.
Conceptest: work and force
Work done by constant forces
Quick experiment:
• Pull a mass along the table with force meter
• Measure force (F) and distance pulled (x)
• How much work (W) did you do at each point?
• How does it depend on the mass (m)?
• Graph F(x) and W(x)
Ch.7 #12 (p.160)
Work done by variable forces
W=F.d assumes that the force F is constant.
What if the force varies?
Investigate this with springs:
1. Add small masses to spring  calculate Ug
2. Measure force Fi exerted by each mass
increment mi
3. Measure incremental displacements di of spring
4. Calculate incremental work done Wi at each step
5. Graph Fi(x), Wi(x), U(x) and compare
Variable forces: data
mi
di
x
Ui
Fi
F(x)
Variable forces: results
F
x
W
x
Variable forces: questions
5. Graph Fi(x), Wi(x), U(x) and compare
1.
2.
3.
4.
QUESTIONS:
What relationship do you see between the spring force
at each point and the work done on the spring by
gravity?
What is the slope of the F(x) curve? What does it tell
you about your spring?
How does the potential energy stored in the spring
depend on the distance stretched?
How could you describe the potential energy stored in
the spring, algebraically?
Calculating variable forces
Uspring=1/2 kx2, F=-dU/dx=____
Ch.7 Fig.7-11 (p.150): Prob.# 27, 28, 61 (p.161)
Applying calculus: If U=-GmM/r, find F
Ch.8 # 38 (p.192), 72 (p.295)
Phys 7 HW 2
Ch.7 #12, 27, 28, 61
Ch.8 # 16, 38, 72
You can now calculate the force due to a known potential
energy, using derivatives.
After we learn integration in calculus, you will also be
able to calculate the potential energy for a known force.
This is useful, because it is easier to measure forces, and it
is easier to do calculations with energy conservation.