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”

• Mechanical Energy– Potential Energy– Kinetic Energy

• Work– Constant Force → Dot Product– Variable Force → Integral

• Work-Mechanical Energy theorem

Ch. 7 Work and Energy

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)

D)E) None of the above

0

)(cos21

)(sin2121

220

220

20

mv

mv

mv

Energy pre-question

• Some forces in nature depend on the inverse-square of the distance between objects (1/r2). If you were to calculate the potential for this force it would depend on:

A) 1/rB) 1/r3

C) rD) r2

E) None of the above

Cheat Sheet

• Mechanical Energy– Potential Energy, Gravitational– Potential Energy, Spring– Kinetic Energy

• Work– Constant Force– Variable Force

cosxFW

...dyFdxFW yx

2

21 mvK

mghU 2

21 kxU

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?

F

θ = 60 degrees

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

UWKW

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

Uyymg

Udymg

UxdF

UW

if

y

y

f

i

)(

)(

Notice Sign

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– Potential Energy, Spring– Kinetic Energy

• Work– Constant Force– Variable Force

• Work-Mechanical Energy Thereom

cosxFW

...dyFdxFW yx

2

21 mvK

mghU 2

21 kxU

UWKW