1. Tuesday, Sept. 30th, 9:30 AM – First exam –
Announcements
Thursday, Sept. 25th, 4 PM – Physics Colloquium by Professor Steven Vogel, James B. Duke Professor of Biology at Duke U. – will discuss the physics of muscles
Tuesday, Sept. 30th, 9:30 AM – First exam –
Covering Chapters 1-8 of HRW
May bring 1 equation sheet, your calculator to exam
If you have kept up with your HW, you may drop your lowest exam grade
Today – review work-kinetic energy theorem
– discuss power
– introduce notion of potential energy
11/14/2018
PHY Lecture 8

2. Wnet = Kf – Ki Work – kinetic energy relation: 11/14/2018
PHY Lecture 8

3. If Ftrack=0, then ½ mvt2=½ mgR Wnet = Kf – Ki  mg(h-2R)= ½ mvt2
-Ftrack-mg=-mvt2/R h v 2R
If Ftrack=0, then ½ mvt2=½ mgR
Wnet = Kf – Ki  mg(h-2R)= ½ mvt2
h=5/2R
11/14/2018
PHY Lecture 8

4. Hooke’s “law” (model force)
F = -kx xi xf
11/14/2018
PHY Lecture 8

5. A mass m with initial velocity v compresses a spring
Example problem:
A mass m with initial velocity v compresses a spring
with Hooke’s law constant k by a distance xf. What is xf when the mass momentarily comes to rest?
11/14/2018
PHY Lecture 8

6. Example: gravity and Hooke’s law work --yi yf
11/14/2018
PHY Lecture 8

7. Constant force with no acceleration
Power:
Units: 1 J/s  1 Watt
Special case:
Constant force with no acceleration
11/14/2018
PHY Lecture 8

8. Work-kinetic energy theorem:
Energy forms
Work:
Kinetic energy: K= ½ m v2
Work-kinetic energy theorem:
Different kinds of contribution to total work:
Conservative (reversible) -- gravity, Hooke’s law
Dissipative (irreversible) -- friction
11/14/2018
PHY Lecture 8

9. Conservative forces – reversible work
Consider the work done by gravity Fg = -mg j ri rf
yf-yi
Note that the work of gravity is: > 0 if yf < yi
< 0 if yf > yi
11/14/2018
PHY Lecture 8

10. Conservative forces – reversible work
Define potential energy:
Consider the work done by gravity: Fg = -mg j
 Ugravity(y) = mgy (assuming yref = 0)
Note: Depends only on position (y) (not on path)
11/14/2018
PHY Lecture 8

11. Conservative forces – reversible work – more examples
Define potential energy:
Consider the work done by Hooke’s law force: Fs = -kx i
 Us(x) = ½ kx2 (assuming xref = 0)
Note: Depends only on position (x) (not on path)
11/14/2018
PHY Lecture 8

12. Using gravitational potential energy in Work-Kinetic energy theorem
Suppose that the total work is done by conservative forces:
More generally:
total mechanical energy
11/14/2018
PHY Lecture 8

13. ½mvf2 + 0 = 0 + mgh + Wfriction
A child of mass m=20kg starts from rest at the top of a 2m slide and has a speed of vf=3m/s at the end of the ride. How much friction energy does the child generate?
½mvf = mgh + Wfriction
½(20kg)(3m/s)2 = (20kg)(9.8m/s2)(2m)+Wfriction
Wfriction = -302 J
11/14/2018
PHY Lecture 8

14. Spring force: Fspring = -k(x-x0)
½mvf2+0=0+½k(xi-x0)2+0
11/14/2018
PHY Lecture 8

15. Review -- Work-Kinetic energy theorem:
Analyzing work in terms of “conservative” and “non-conservative”:
Rearranging terms to form total mechanical energy:
Statement of conservation of energy: If
11/14/2018
PHY Lecture 8

16. If Ftrack=0, then ½ mvt2=½ mgR
-Ftrack-mg=-mvt2/R
If Ftrack=0, then ½ mvt2=½ mgR h v 2R
11/14/2018
PHY Lecture 8

17. Example: gravity and Hooke’s law work --yi yf
11/14/2018
PHY Lecture 8

18. More on Hooke’s law -- U = ½ k x2
U(x)
E = ½ mv2 + ½ k x2 E
xmax
xmin
11/14/2018
PHY Lecture 8