Group Work

Rank the following scenarios from least work done to most work done.

10 m100 N

A.

100 m10 N

B.

100 m100 N

C.

100 N

100 mD.

100 N

0 mE.

Work

force is not all that matters

§ 6.1–6.2

What’s the point?

Energy is critically important to Nature.

Objectives

• Relate work to force and distance.

• Calculate the kinetic energy of a moving object.

Work

Formula

W = work = F·s

F = force applieds = displacement

Units of Work

J = Nm = kg m

m =s2

kg m2

s2

joule (J) = 1 newton along 1 meter

Group Work

Estimate the work done by the strong man in the video. Justify your estimates of force and distance.

Work is a Scalar

Source: Griffith, The Physics of Everyday Phenomena

component of force in direction of motion

Dot Product of Vectors

a·b = ab cos a

b

a

b

Commutative

Dot Product Geometrically

• Product of the projection of one vector onto the other

• “Overlap”

b cos

a cos

a

b

ab cos

Dot Product by Components

If

then

A·B = AxBx + AyBy + AzBz

A = Axi + Ayj + Azk

B = Bxi + Byj + Bzk

Dot Product Properties

• Positive if || < /2• Negative if || > /2

• Zero if vectors perpendicular (|| = /2)• Maximum magnitude if parallel or anti-

parallel

+–

Think Question

The piglet has a choice of three frictionless slides to descend. Along which slide is the greatest net force exerted on the piglet?

A B C

D. The net force is the same for all.

Think Question

The piglet has a choice of three frictionless slides to descend. Along which slide would the piglet slide the longest distance?

A B C

D. The distance is the same for all.

Think Question

The piglet has a choice of three frictionless slides to descend. Along which slide would the piglet finish soonest?

A B C

D. The time is the same for all.

Poll Question

The piglet has a choice of three frictionless slides to descend. Along which slide would gravity do the most work on the piglet?

A B CD. Same work for all. E. Need more information.

Example Problem

A luggage handler at the Laramie Airport pulls a 20-kg suitcase from rest up a ramp inclined at 25° above the horizontal with a force of 140 N parallel to the ramp. The coefficient of kinetic friction between the ramp and the box is k = 0.30. The suitcase travels 3.80 m along the ramp. Finda. the work done on the suitcase by the handlerb. the work done on the suitcase by gravityc. the work done on the suitcase by the normal forced. the work done on the suitcase by frictione. the total work done on the suitcasef. the final speed of the suitcase

s

Total (Net) Work

If several forces act on a moving object:

F1

F2

F3

F4

or

• W = (F)·s

• W = (F·s)

Poll Question

To accelerate an object from 10 to 20 m/s requires

A. more work than to accelerate from 0 to 10 m/s.

B. the same amount of work as to accelerate from 0 to 10 m/s.

C. less work than to accelerate from 0 to 10 m/s.

Work of Acceleration• To accelerate to speed v with constant force F

t

v

speed

time

mvtF = m (slope) =

12 d = vt

• Work = F·d

• Work = = mv212vt1

2mvt

slope = a = Fm

vt=

area = d

Another Perspective

• So, for the 0–10 vs. 10–20 m/s case:

• If same force, then same time– a’s and v’s are equal, so t’s are equal

• Average speeds are 5 vs. 15 m/s

• The 10–20 m/s case travels 3 as far

A Moving Object Can Do Work

Source: Griffith, The Physics of Everyday Phenomena

Kinetic Energy

the work to bring a motionless object to speed

K = 12 mv2

equivalent to

the work a moving object does in stopping

Which has more kinetic energy?

A.

B.

C.

D.

10 kg 10 m/s

5 kg 10 m/s

10 kg 20 m/s

40 m/s5 kg

Think Question

Poll Question

The piglet has a choice of three frictionless slides to descend. Along which slide would the piglet finish with the highest speed?

A B C

D. The final speed is the same for all.

Work-Energy Theorem

• If an amount of net work w is done on an otherwise isolated system, the system’s kinetic energy changes by an amount K = w.