Physics 1100

Final Exam

Part A Mulitple Choice Select the best response and indicate your choice on the

computer card provded. VALUE 20%

1. The kilogram is currently defined as:

A the mass of a platinum-iridium cylinder kept in Scves, FranceB the mass of 5.9786 x 1026 protonsC the mass of one liter of pure water, free of air, at standard temperature and pressureD the mass of a cube of pure water, free of air, 10 cm on each side, at standard temperature and pressure

2. How many significant figures are in 120.07 cm?

A 6 B 5 C 4 D 3

3. The Hoover Dam is 726 feet high. What is its height in kilometers? Note 1 km = 0.621 mi and 1 mi = 5280feet.

A 0.726 kmB 0.138 kmC 0.221 kmD 0.275 km

4. Figure 3 represents the velocity of a particle as it travels along the axis. In what direction is the acceleration at t = 0.5 s?

A toward the positive x-axis B toward the negative x-axis C there is no acceleration at t = 0.5 s D you need an ‘acceleration vs time’ graph to do this problem

5. At a given instant, the acceleration of a certain particle is zero. Does this mean that:

A the velocity is constantB the velocity is increasingC the velocity is decreasingD the velocity is not changing at that instant

6. Figure 2 represents the position of a particle as it travels along the x-axis. What is the magnitude of

the average velocity of the particle between t = 1 s and t = 4 s?

A 0.57 m/s B 0.67 m/s C 1.0 m/s

D 1.3 m/s

7. Vector M = 4.00 points eastward and vector N = 3.00 points northward. The resultant vector M + N is given by

A 5.00 m at an angle 71.6o north of east.

B 5.00 m at an angle 18.4o north of east C 5.00 m at an angle 53.1o north of east

D 5.00 m at an angle 36.9o north of east

8. What is the angle between the vectors A and –A when these vectoes are drawn from a common origin?

A 90o

B 0o

C 360o

D 180o

9. Mass is a vector quantity.

A True

B False

10. A boy kicks a football with an initial velocity of 20 m/s at an angle of 25o above the horizontal. The

acceleration of the ball while in flight is

A 20 m/s2

B -20 m/s2

C -9.8 m/s2

D 0

11. For which value of θ is the range of a projectile fired from ground level a maximum?

A 30o above the horizontal

B 45o above the horizontal

C 600 above the horizontal

D 90o above the horizontal

12. A rock is thrown from ground level at some angle above the horizontal with a certain velocity. It reaches its highest point and starts falling down. What is the magnitude of the velocity of the rock just before it hits the ground?

A it is equal to its initial vertical velocityB it is equal to its initial horizontal velocityC it is equal to the magnitude of its initial velocityD 0

13. An object moving along a curved path with constant speed does not have a net force acting on it.

A TrueB False

• An object is moving with constant velocity. Which of the following statements is true:

A a constant force is being applied in the direction of motionB there are no forces acting on the objectC the net force on the object is zeroD there is no frictional force acting on the object

13. What average net force is required to accelerate a car with a mass of 1200 kg from 0 to 27 m/s in 10 s?

A 444 NB 3240 NC 4355 ND 11760 N

16. A 55-kg box rests on a horizontal surface. The coefficient of static friction between the box and the surface is 0.30. A horizontal force of 156 N is applied to the box. Does the box move?

A yes B no

17. The SI unit of work is expressed as

A WattB NewtonC Newton/secondD Joule

18. A person carries a mass of 10 kg and walks along the +x-axis for a distance of 100 m with a constant velocity of 2 m/s. What is the work done by this person?

A 0 J B 20 J C 200 J D none of the other answers given is correct

• On a force vs position graph, the area under the curve is a representation of

A ForceB PositionC Kinetic EnergyD Work

20. An object of mass 4.0 kg is moved from a point A to a point C as follows: 0.80 m vertically from A to B, and then 0.60 m horizontally from B to C. What is the amount of work done as the object is moved from point A to C? A 1.3 J from A to B and 16 J from B to C B 2.2 J from A to B and 32 J from B to C C 32 J from A to B and 0 J from B to C D 4.0 J from A to B and 16 J from B to C

21. The center of mass for a continuous, uniform object is located at the geometric center of the object.

A TrueB False

22. What is the correct expression for torque, in terms of the magnitude of the force , F, the radial distance from the axis of rotation, r, and the angle θ between the force and the radial line?

A γ = F r sin θ B γ = F r cos θ C γ = F r tan θ D γ = F r θ

23. A 55-kg box rests on a horizontal surface. The coefficient of static friction between the box and the surface is 0.30. A 140-N horizontal force is applied to the box. What is the frictional force on the box?

A 162 N B 540 N C 140 N D Since the box is not accelerating the frictional force is 0

• Vector A is initially pointing eastwards. This vector is rotated clockwise by an angle of 1100. Which of the following statements is correct regarding the final position of vector A?

A It is pointing 200 west of south B it is pointing 700 south of west C it is pointing 200 south of west D it is pointing 700 east of south

PART B Problems Do ten (10) out of the twelve (12) given problems. Mark a large X through the two (2) problems that you choose to omit. Your solutions must be organized and complete for full credit. VALUE 60%

1. A 55.0 kg skateboarder starts from rest at the top of a 10.0-m ramp with a height of 2.00 m. The coefficient of friction is 0.12 on the ramp, and on the horizontal parking lot at the bottom.

A Using energy principles, find the skateboarder’s speed at the bottom of the ramp. (4)

ANS. We set the height of parking lot as h =0 for GPE

ncf WEEi

fffii WUKUK

dFmvmgh ffi 2

2

1

dumgmghm

dFmghm

V ifif )cos(2

)(2

)0.10

00.212.000.2)(81.9(2)cos(2

2 m

mm

s

muhgV if

223.6s

mV f

2.00m

10.00m

θ

B If the skateboarder continues moving in a straight line across the parking lot until she coasts to a stop, use energy principles to find how far she travels. 2

ANS. We have a net force since there’s accelartion. This work on the object changes the mechanical (kinetic) energy of the object. Work Energy Theorm:

df

Fnet

WorkKE

umgi

mv

fF

iKE

fKE

fF

KEd

22

1

m

sm

sm

ugi

vd 9.6

)281.9)(12.0(2

20.4

2

2

2. A ball is thrown horizontally from the roof of a building 45.0 m tall and lands 24.0 m from the base.

A How long was the ball in the air?

ANS: We consider the vertical motion of the Ball

myo 0.45

0ov

ga

?t

?v

0y

2

2

1attvyy oo

2

2

100 atyo

281.9

)0.45(22

sm

m

a

yt o

st 0.3

B What was the ball’s initial speed?

ANS We consider the horizontal motion of the ball

?ov

0ox

?v

0.24x

0a st 0.3

2

2

1attvxx oo

00 tvx o

t

xvo

s

mvo 0.3

0.24

s

mvo 0.8

3. A book of mass 1.7 kg rests on the rear window shelf of a car that’s rounding a flat curve in the road that has a radius of curvature of 98m. The coefficient of static friction between the book and the car is 0.24.

A Find the magnitude and give the direction of the frictional force between the shelf and book while the car is rounding the curve at a speed of 36 km/h.

ANS Centripetal force to keep the book going in a circular motion is supplied by the static friction the book and the shelf. Static friction varies from 0 to μs mg.

Note that μsfn=μsmg is the maximum static frictional force possible.

Static frictioanl force =

ms

mkg

r

mvmacp 98

)6.3

36)(7.1( 2

2

N7.1

B What is the maximum speed of the car on the curve before the book begins to slide? free body diagram for book

mg

Ff

FN

fx FFVectors

maFNewton x

maxfFma

Nscp Fuma

mgur

mvs

2

)81.9)(98)(24.0(2s

mmrguv s

s

mv 15

4. A stone is launched straight up by a slingshot. It’s initial speed is 19.6 m/s and the stone is 1.50 m above the ground when launched.

A How high above the ground does the stone rise?

ANS We consider the upward motion of stone

Total height = 19.6m + 1.5m = 21.1

y

0v

?yga ?t

s

mVo 6.19

0oy

)(222

oo yyavv

)0(20 2 yavo

a

vy o

2

2

)81.9(2

)6.19(

2

2

s

ms

m

y

my 6.19

B How much time does the stone spend in the air?

We consider upward and downward motion

y s

mvo 6.19

0y

ga ?t

?v

0oy

2

2

1attvyy oo

2

2

100 attvo

a

vt o2

281.9

)6.19(2

s

ms

m

t

st 00.2

5. The maximum load that can be supported by a rope in an overhead hoist is 400.0 N.

A What is the maximum acceleration that can be safely be given to a 25.00-kg object being hoisted vertically upward?

ANS Freebody diagram of crate

FT

mg

a

mgFFVectors Ty

maFNewton y

mgFma T

m

mgFa T

kg

NNa

00.25

81.9*00.250.400

2190.6

s

ma

B What would be the tension in the rope if the load was being lowered at an acceleration of 3.000 m/s 2 ?

FT

mg

a

mgFma T

mgmaFT

)( gamFT

)81.9(00.3(00.2522 s

m

s

mkgFT

NFT 170

6. A 25.0-kg boy is wind sailing on his 10.0-kg sail-equipped cart. The wind pushes him and his cart at a constant speed up a 25.0- m-long incline that rises 5.00 m.

A Find the work done by the wind on the cart.

ANS Since the wind pushes the cart with a constant velocity, we know ∑ Fx = 0 ,Therefore FW = Wx =mg sinθ

)0.25

00.5)(81.9)(.100.25(

2 m

m

s

mkgkgFw

NFw 7.68

KJmNdFW ww 72.1)0.25)(7.68(

sinmgWF xw

B What is the power developed by the wind if the ride up the incline lasts 11.0 s?

Ws

KJ

T

WP 156

0.11

72.1

7. An experimental rocket car starting from rest reaches a speed of 560 km/h after a straight 400 m run on a level roadway.

A Assuming that acceleration is constant, what was the time of the run?

x

0oV

0oX

h

kmV 560

mX o 420

?a ?t

tVVXX oo )(2

1

tVVX o )(2

10

oVV

Xt

2

)6.3

5600(

)420(2

s

mm

t

st 4.5

B What is the magnitude of the acceleration?

atVV o

t

VVa o

ss

m

a4.5

06.3

560

28.28

s

ma

8. A swimming pool worker uses a uniform 3.45-m pole with a dip net at the far end to retrieve objects that fall in the pool. He holds it with his right hand at the end, and his left hand at the 50.0 cm mark. If the pole’s mass is 2.84 kg, and there is a 1.25-kg load in the dip net, find the size and direction of the force exerted by each hand when the pole is horizontal.

Note Fw = 2.84 * 9.81N = 27.9N FD = 1.25 * 9.81N = 12.3N Distance from center of pole to end is 3.45m/2 = 1.73m

Equilrium cond(i) …….. …………… Eq 1

cond(ii) use left end as pivot …………… Eq 2

From Eq 2

Subst. Into Eq 1

FR

FL

FW

FD

y

x

0yF 0 DWRL FFFF

0T

0 DDWwLL FRFRFR

m

NmN

R

FRFRF

L

DDWW

L 500.0

)3.12)(45.3()9.27)(73.1(

NFL 181

NNNNFFFF DWLR 1413.129.27181

9. A soccer player kicks a stationary ball, giving it a speed of 20.0 m/s at an angle of 15.00 to the horizontal

A What is the maximum height reached by the ball?

We consider upward motion of the ball

θ

Vo Y

Vo=20.0 m/s

Vox

y

cosoox VV

)0.15cos()0.20(

s

mVox

s

mVox 3.19

sinooy VV

)0.15sin()0.20(

s

mVoy

s

mVoy 18.5

0yV

?y

ga ?t

s

mVoy 18.5

0oY

)(222

ooyy yyaVV

)0(20 2 yaVoy

)81.9(2

)18.5(

2

2

s

ms

m

y

a

Vy oy

2

)( 2

my 37.1

B What is the ball’s range?

g

VRange o 2sin2

2

2

81.9

)0.15*2sin()0.20(

s

ms

m

Range

mRange 4.20

10 .The ferris wheel at a circus has a diameter of 18.2 m and rotates once in 12.0 s.

A What is normal force exerted by the seat on a 57.5 kg rider when he is at maximum height?

Note the speed of Rider

y

X mg

FN

t

D

time

cedis

tan

s

m

0.12

)2.18(

s

m76.4

mgFFVectors Ny

cpy maFNewton

mgFma Ncp

mgmaF cpN

)( gamF cpN

)(2

gr

VmFN

2

2

81.9

2

2.18

)76.4()5.57(

s

mms

m

kgFN

NFN 421

Install a negative sign since acp

is negative when rider is at the top

B At what speed in m/s must the wheel rotate so that a rider feels 1.5 times his normal weight at the lowest position during the ride?

y

xFN

mg

mgFFVectors Ny

cpy maFNewton

mgFma Ncp

mgmgmacp 5.1

gr

v5.0

2

grv 5.0

)2

2.18)(81.9)(5.0(

2

m

s

mv

s

mv 7

11. The carton in the diagram below lies on a plane inclined at an angle of 22.00 to the horizontal. The coefficient of kinetic friction is 0.120.

A Determine the acceleration of the carton as it slides down the incline

9.30m

θ=22.0∙

mg x

mg

mgy

FfFN

y

x

fxx FmgFVectors

maFNewton x

fx Fmgma

yx mgmgma

yx gga

cossin gga

)cos(sin ga

)0.22cos120.00.22)(sin81.9(2

s

ma

258.2

s

ma

B If the carton starts from rest 9.30 m up the plane from its base, what will be the carton’s speed when it reaches the bottom of the incline?

x

yvo= 0

xo= 0

v= ?

x = 9.30 m

a = 2.58 m/s t = ?

)(222

oo xxavv

)0(202 xav

axv 2

)30.9)(58.2(2 ms

mv

s

mv 93.6

12. An aircraft that has an air speed of 225 km/h is to fly to a destination that lies in the direction 10.00 North ofEast. A steady wind of speed 45.0 km/h blows from the direction 15.00 East of North.

A Draw a relative velocity vector diagram.

10.0

15.0

Vpe

Vpa Vae

Note: P – plane

A – Air

E - Earth

n

ew

s

B Use vector components to find the velocity of the plane with respect to the earth during this flight

A

B

C

15.0

15.0

10.0 10.0

Using the same diagram as in part A. All angles are in degrees

0.1150.150.900.10 C

C

c

A

a

sinsin

CaAc sinsin

c

CaA

sinsin

)sin

(sin 1

c

CaA

h

kmh

km

A0.225

0.115sin0.45

sin 1

4.10A

4.204.100.10 PAVDirection

AEPAPE VVV

h

km

h

km4.784.20sin225

h

km

h

km2114.20cos225

h

km

h

km5.430.15cos0.45

h

km

h

km6.110.15sin0.45

h

km9.34

h

km199

VECTOR N-COMP E-COMP

VPA

VAE

VPE

22

PEEPENPE VVV 22 )199()9.34(h

km

h

km EofNat

h

km 0.10202

PART 3 Complete Question # 1 and ONE other question.Each Question Valued 10 for a total value of 20.

1. A lab cart is set in motion, by hand, on a frictionless incline. Once the cart has been given its motion, only the force of gravity acts on it, and thus gravity controls its velovity on the incline.The three `velocity Vs time` curves presented in the graph below result from three different angles for the incline. The inlcine-angles, above the horizontal, are in random order, 10 ∙, 20 and 25 degrees.

Note that students are expected to associate each curve with its correct incline whose size is given in degrees above the horizontal

Question and answer on the next slide. You will have to flip back and forth to see graph and answer.

A Interpret the lab results from the previous page and complete the table below.

The initial section of each curve with negative slopes indicate the cart’s motion while being pushed. The nearly straight line sections with positive slope indicate the cart’s constant acceleration and down the incline. The bottom of the curves that end on the x-axis is where the cart was stopped and at the bottom of the incline.

sss

m

s

m

aincline55.185.2

)8.0(2.1)10(

2

8.1s

m

sss

m

s

m

aincline95.175.2

)0.1(50.1)20(

2

1.3s

m

sss

m

s

m

aincline25.185.1

)10.1(50.1)25(

2

3.4s

m

θ Sinθ Acceleration

10

20

25

0.1736

0.3420

0.4226

28.1

s

m

21.3

s

m

23.4

s

m

Mechanical theory proclaims that the acceleration of an object due to gravity on a frictionless incline is found usingthe relationship….

a = g sin θ where a - is the acceleration on the incline. θ - is the size of the incline in degrees g – is the acceleration due to gravity.

B Using the information from the table on the previous page, plot a curve a Vs sinθ on the gridbelow.

You should get a line something like this.

C Determine the slope of the above curve and using the accepted valve of g =9.8m/s2, find the % discrepancy for the experimental value for g .

12

12

xx

yySlope

1.5.

1.17.4

2

0.9s

m

%100*8.9

0.98.9%

yDiscrepanc %8

2. A car goes around a curve on a road that is banked at an angle of 30.0°. Even though the road is slick, the car will stay on the road without any friction between its tires and the road when its speed is 24.0 m/s. Note that we choose the positive y axis to point vertical and the positive x direction to point toward the center of the circular path.

Find the equation for r and calculate the radius of the curve for this car?

cos 0yF N mg

cos

mgN

cpsinxF N ma

cpsin sin

cos

N mga

m m

2

cp tanv

a gr

tan

2

g

vr

0.30tan)81.9(

)0.24(

2

2

s

ms

m

m102

The radius of the curve

The equation for r

3. When you arrive at Duke’s Dude Ranch, you are greeted by the large wooden sign shown in the figure below. The left end of the sign is held in place by a bolt, the right end is tied to a rope that makes an angle of 20.0° with the horizontal. If the sign is uniform, 3.20 m long, and has a mass of 16.0 kg, What is :(a) the tension in the rope(b) the horizontal and vertical components of the force, F, exerted by the bolt? (c) the Force on the bolt F?

note that from the sign’s point of view the situation is symmetric: it has a movable support at each end and doesn’t “know” whether the support is a wall or a wire. So, the force at the wall bolt is the same as it would be if the wall were instead a wire running up and to the right at 20.0° above horizontal. By symmetry, f = T and Fy 2T sin mg 0.

T mg

2sin

(16.0 kg) 9.81 ms

2 2 sin20.0

229 NFx F cos T cos (229.5 N) cos20.0 216 N

Fy F sin T sin mg

2

(16.0 kg) 9.81 ms2

2 78.5 N

4. A basketball is thrown horizontally with an initial speed of 4.20 m/s . A straight line drawn from the release point to the landing point makes an angle of 30.0° with the horizontal. What was the release height?

The horizontal distance the ball travels is given by and02h

x vg

tan .h

x

2

0

220

2

220

2ms 2

ms

2

tan

2

tan2

tan

2 4.20 tan (–30.0 )

9.81

1.20 m

h hv

g

v hh

g

vh

g