1009080706050403020100

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Student ID number

What is the best approximation of the class average on this exam?

A. 80B. 60C. 40D. 20

1009080706050403020100

1009080706050403020100

avg = 85

Exam Scores

The same scores are rearranged in ascending order below.

What is the best approximation of the class average on this exam?

A. 80 B. 60C. 40 D. 20

velo

city

, v

velo

city

, v

time (seconds) time (seconds)

velo

city

, v

velo

city

, v

time (seconds) time (seconds)

Which of the graphs above could represent an object freely falling from rest?

A. B.

C. D.

velo

city

, vve

loci

ty, v

time (seconds)

time (seconds)

velo

city

, vve

loci

ty, v

time (seconds)

time (seconds)

For the moving object graphed at left

A. vavg < vmax

vmax

vmax

vmax

vmax

12

B. vavg = vmax12

C. vavg > vmax12

vmax12

vmin

For the moving object graphed at left

A. vavg < vmax12

B. vavg = vmax12

C. vavg > vmax12

vmax12

Weight Support (floor)

Adding all these supporting forces together

some pull left,some pull right,some pull forward,some pull back

all tend to pull UP!

(a tug-of-war balancing)

Styrofoam bridge

weighted at center

Pressure applied to rigid glass bar

x x

x

Nat

ural

leng

th

x

Springs may be compressed (shortening their “natural length”) until the “restoring force” itcounters with in an attempt to regain its original shape exactly balances the applied force.

W

F

Springs may be elongated (beyond their “natural length”) until the “restoring force”exactly balances the force pulling it open.

Note: F x

x

Compound bowsuse systems of

pulleys and camsto maintain a

fairly constantresistance force

over the full distance drawn.

Otherwise, for a moreconventional recurve or simple longbow

Forceto holdin place

distancebow isdrawn

For

ce

Displacement, x

F x

Also means: F = kx

“spring constant” in units of N/m

The restoring force grows so many Newtons for every meter stretched.

The weight of a 1250 kg car is evenly distributed over 4 coil springs with strength

k = 32000 N/m.When carrying 5 passengers (each, on

average 73.0 kg) how much lower does thecar ride?

The empty car already compresses each spring:

kFx /¼th total weight, empty car

mN

smkg

/32000

)/8.9)(1250)(4/1( 2

= 0.096 m = 9.6 cm

With everyone on board:

mN

smkgkgx

/32000

)/8.9)(3651250)(4/1( 2

= 0.124 m = 12.4 cm

It rides about 2.8 cm (a little more than 1 inch) lower.

snapped garage door spring

sprung bicycleseat spring

crackedsuspensioncoil spring

permanetlydeformed

Slinky!

For

ce

Displacement, x

elastic range

failure

plastic deformation

proportionalitylimit

For

ce

Displacement, x

Work done against an elastic force

starting with force 0

ending with force = kx

W = Favg d

= xFmax

2

= k(x)212

F d

The “full draw weight’ of this bow is 20 pounds (90 Newtons) at the 24 inches (0.60 meter) that this archer has drawn it. What is its effective spring constant?

How much work was done in drawing the bow back?

If all the energy goes into the 400 grain (26 gram) arrow’s kinetic energy, what speed will it leave the bow with?

mNmNxFk /5.160.0/90/

2

212

21 )60.0)(/5.1()( mmNxkW

mN 27.0

2

212

21 )026.0(27.0 vkg mvNm

222 /77.20 secmv secmv /56.4

TotalWeight

A tennis ball rebounds straight up from the ground with speed 4.8 m/sec.

How high will it climb?

atvv 0

It will climb until its speed drops to zero!

final speed = 0g = 9.8 m/sec2

sec

smsmt

490.0

)/8.9()/8.4( 2

and in that much timeit will rise a distance

2

21

0attvd

22

21 )490.0)(/8.9(

)490.0)(/8.4(

ssm

ssmd

m d 176.1

orsince time up = time down

the distance it falls from rest in 0.49 sec:

22

21 )490.0)(/8.9( ssmd

2

21 atd

m d 176.1

A tennis ball rebounds straight up from the ground with speed 4.8 m/sec.

How high will it climb?

2

21 mv

It will climb until all its kinetic energy has transformed into gravitational potential energy!

mgh=

h g

v

2

2

)/8.9(2

)/8.4(2

2

sm

sm h

= 1.176 meter

A skier starts from rest down a slope with a 33.33% grade (it drops

a foot for every 3horizontally).h

3hThe icy surface is nearly frictionless. How fast is he traveling by the bottom of the 15-meter horizontal drop?

W

The long way: The accelerating force down along the slope is in the same proportion to the

weight W as the horizontal drop h is to the hypotenuse he rides:

F

10

1

109 22

h

h

hh

h

W

F

WF10

1 ga10

1

The slope is meters hh 434.479 22 long

So it takes him 2

21 atd adt /22

sec ghght 533.5/20)10//()10(2

During which he builds to a final speed:

secm atvvg

hg /146.17))((0 20100

A skier starts from rest down a slope with a 33.33% grade (it drops

a foot for every 3horizontally).h

3hThe icy surface is nearly frictionless. How fast is he traveling by the bottom of the 15-meter horizontal drop?

W

The short way: The gravitational potential energy he has at the top of the slope will convert

entirely to kinetic energy by the time he reaches the bottom.

F

2

21 mv mgh

gh v 22

msm v 15)/8.9(2 2

= 17.146 m/sec

h

3h 3h

2h

½h

1.5hh

The bottom of the run faces a slope with twice the grade (steepness).

Neglecting friction, the skier has just enough energy to coast how high?

A

B

C

D

We know rubber tires are easily deformedby the enormous weight of the car theysupport…but not permanently. They

regain their round shape when removed.

This “spring-like” resiliency explainsthe rebound of all sorts of balls.

Racquetballrebounding

from concrete.

Tennis ballrebounding

from concrete.

Airtrack bumper carts:

Notice that if the spring bumbersreverberate (ring) this would haveto represent some energy that did

not get returned to forward motion!

This represents a fractional loss in kinetic energy!

A purely ELASTIC COLLISION is defined as one which conserve kinetic energy.

Unlike the stored potential of the compressed bumpers, this is not a “potential” energy that can ever be recovered as kinetic energy.

Look how a racquetballstill undulates after leaving the floor!

These vibrationsare a wasted form ofenergy!