Physics 111: Lecture 9. Today s Agenda

Physics 111: Lecture 9 Today’s Agenda     Work & Energy  Discussion  Definition Work of a constant force  Work/kinetic energy theorem Work of...
Author: Matthew Joseph
0 downloads 1 Views 1MB Size
Physics 111: Lecture 9 Today’s Agenda 

  

Work & Energy  Discussion  Definition Work of a constant force  Work/kinetic energy theorem Work of multiple constant forces Comments

Physics 211: Lecture 9, Pg 1

Work & Energy 

One of the most important concepts in physics  Alternative approach to mechanics



Many applications beyond mechanics  Thermodynamics (movement of heat)  Quantum mechanics...



Very useful tools  You will learn new (sometimes much easier) ways to solve problems

Physics 211: Lecture 9, Pg 2

Forms of Energy 

Kinetic: Energy of motion.  A car on the highway has kinetic energy.

 We

have to remove this energy to stop it.  The brakes of a car get HOT!  This is an example of turning one form of energy into another (thermal energy).

Physics 211: Lecture 9, Pg 3

Energy Conservation

Returning Can



Energy cannot be destroyed or created.  Just changed from one form to another.



We say energy is conserved!  True for any closed system.  i.e. when we put on the brakes, the kinetic energy of the car is turned into heat using friction in the brakes. The total energy of the “car-brakes-road-atmosphere” system is the same.  The energy of the car “alone” is not conserved... » It is reduced by the braking.



Doing “work” on an isolated system will change its “energy”...

Physics 211: Lecture 9, Pg 5

Definition of Work: Ingredients: Force (F), displacement (r) Work, W, of a constant force F acting through a displacement r is: W = F r = F r cos  = Fr r

F 

Fr

r

“Dot Product”

Physics 211: Lecture 9, Pg 6

Definition of Work... Hairdryer 

Only the component of F along the displacement is doing work.  Example: Train on a track.

F 

r F cos 

Physics 211: Lecture 9, Pg 7

Back to the definition of Work: Inclined Plane Work, W, of a force F acting through a displacement  r is: W = F  r

F r

Physics 211: Lecture 9, Pg 12

Lecture 9, Act 1 Work & Energy 

A box is pulled up a rough (m > 0) incline by a rope-pulley-weight arrangement as shown below.  How

many forces are doing work on the box?

(a) 2 (b) 3

(c) 4

Physics 211: Lecture 9, Pg 13

Lecture 9, Act 1 Solution

Physics 211: Lecture 9, Pg 14

Work: 1-D Example (constant force) 

A force F = 10 N pushes a box across a frictionless floor for a distance x = 5 m.

F

x Work done by F on box :

Physics 211: Lecture 9, Pg 15

Units: Force x Distance = Work Newton x [M][L] / [T]2

mks N-m (Joule)

Meter = Joule [L] [M][L]2 / [T]2

cgs Dyne-cm (erg) = 10-7 J

other BTU calorie foot-lb eV

= 1054 J = 4.184 J = 1.356 J = 1.6x10-19 J

Physics 211: Lecture 9, Pg 16

Work & Kinetic Energy: 

A force F pushes a box across a frictionless floor for a distance x. The speed of the box is v1 before the push and v2 after the push.

v1

v2

F

m i

x Physics 211: Lecture 9, Pg 17

Work & Kinetic Energy... 

Since the force F is constant, acceleration a will be constant. We have shown that for constant a:  v22 - v12 = 2a(x2-x1) = 2ax. 1/ mv 2 - 1/ mv 2 = max  multiply by 1/2m: 2 2 2 1 1/ mv 2 - 1/ mv 2 = Fx  But F = ma 2 2 2 1

v1

v2

F

m

a i

x Physics 211: Lecture 9, Pg 18

Work & Kinetic Energy... 

So we find that  1/2mv22 - 1/2mv12 = Fx = WF



Define Kinetic Energy K: K = 1/2mv2  K2 - K1 = WF  WF = K (Work/kinetic energy theorem) v2

v1

F

m

a i

x Physics 211: Lecture 9, Pg 19

Work/Kinetic Energy Theorem: {Net Work done on object} = {change in kinetic energy of object}

Wnet  K  K 2  K1 



1 1 2 2 mv 2  mv1 2 2

We’ll prove this for a variable force later.

Physics 211: Lecture 9, Pg 20

Lecture 9, Act 2 Work & Energy 

Two blocks have masses m1 and m2, where m1 > m2. They are sliding on a frictionless floor and have the same kinetic energy when they encounter a long rough stretch (i.e. m > 0) which slows them down to a stop. Which one will go farther before stopping? (a) m1 (b) m2

(c) they will go the same distance

m1

m2

Physics 211: Lecture 9, Pg 21

Lecture 9, Act 2 Solution

m

Physics 211: Lecture 9, Pg 22

Lecture 9, Act 2 Solution

m

Physics 211: Lecture 9, Pg 23

Lecture 9, Act 2 Solution

m

Physics 211: Lecture 9, Pg 24

A simple application: Work done by gravity on a falling object 

What is the speed of an object after falling a distance H, assuming it starts at rest? v0 = 0

H

Physics 211: Lecture 9, Pg 25

What about multiple forces? Suppose FNET = F1 + F2 and the displacement is r. The work done by each force is: W1 = F1 r

W2 = F2  r

F1

FNET

WTOT = W1 + W2 = F1 r + F2 r = (F1 + F2 ) r

WTOT = FTOT r

r

F2

It’s the total force that matters!! Physics 211: Lecture 9, Pg 26

Comments: 

Time interval not relevant  Run up the stairs quickly or slowly...same W

Since W = F r 

No work is done if: F = 0 or  r = 0 or   = 90o

Physics 211: Lecture 9, Pg 27

Comments... W = F r 

No work done if  = 90o.  No

T

work done by T.

v

No work done by N.

v N

Physics 211: Lecture 9, Pg 28

Lecture 9, Act 3 Work & Energy 

An inclined plane is accelerating with constant acceleration a. A box resting on the plane is held in place by static friction. How many forces are doing work on the block?

a

(a) 1

(b) 2

(c) 3 Physics 211: Lecture 9, Pg 29

Lecture 9, Act 3 Solution

a

Physics 211: Lecture 9, Pg 30

Lecture 9, Act 3 Solution

a

Physics 211: Lecture 9, Pg 31

EXTRA EXAMPLE 1 

Return to ACT 2: m

Physics 211: Lecture 9, Pg 32

EXTRA EXAMPLE 2a 

Consider an inclined plane with no friction:

Physics 211: Lecture 9, Pg 33

EXTRA EXAMPLE 2a 

Consider an inclined plane with no friction:

Physics 211: Lecture 9, Pg 34

EXTRA EXAMPLE 2b 

Consider an inclined plane with friction:

Physics 211: Lecture 9, Pg 35

EXTRA EXAMPLE 2b 

Consider an inclined plane with friction:

Physics 211: Lecture 9, Pg 36

EXTRA EXAMPLE 2c 

Consider an inclined plane with friction:

Physics 211: Lecture 9, Pg 37

EXTRA EXAMPLE 2c 

Consider an inclined plane with friction:

Physics 211: Lecture 9, Pg 38

Recap of today’s lecture 



  

Work & Energy (Text: 6-1 and 7-4)  Discussion  Definition (Text: 6-1) Work of a constant force (Text: 7-1 and 7-2)  Work/kinetic energy theorem (Text: 6-1) Properties (units, time independence, etc.) Work of a multiple forces Comments

Physics 211: Lecture 9, Pg 39