Exam Sem 1, 2011 Questions and Answers.pdf PDF

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Exam Sem 1, 2011 Questions and Answers...

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The University of Melbourne Semester One Assessment 2011

School of Physics

PHYC10005 Physics 1: Fundamentals

Reading time:

15 minutes

Exam Duration:

3 hours

This paper has:

13 pages

Authorised Materials:

Calculators are permitted in accordance with the rules of the Faculty of Science. They may be used for the processing of numerical information only. They must not have been programmed nor should they store additional information.

Instructions to Invigilators:

The final three pages of this exam paper contain formulae and data for the use of candidates. These pages may be detached. This examination paper is to remain in the examination room.

Instructions to students:

Attempt ALL questions. The total number of marks is 150. Three pages containing formulae and data are included at the end of the exam paper. These pages may be detached.

Paper to be held by the University Library.

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PHYC10005 Physics 1: Fundamentals This page is intentionally left blank

PHYC10005

Semester 1, 2011

Page 2 of 13

PHYC10005 Physics 1: Fundamentals Question 1

14 marks

Please provide brief answers to the following questions. Approximately one paragraph for each part ought to be sufficient. (a)

A mother with a mass of 65 kg takes her daughter of mass 30 kg to a park to play on a see-saw. A see-saw consists of a long wooden plank which can pivot on a hinge around a 1 meter high bar placed underneath centre of the plank. The two find that by positioning themselves appropriately they can balance on the see-saw. How is this possible? Should the mother or daughter be closer to the centre of the see-saw?

(b)

According to Newton’s third law, when you push on a shopping trolley in the supermarket, the trolley pushes back on you with an equal and opposite force. Explain why it is that you can cause the trolley to move by pushing it, even though these forces are equal and opposite. Your explanation should refer to Newton’s laws and all of the forces involved.

(c)

In lectures we watched a video of a skater who set a world record for the fastest spin of 308 rpm. In the video we observed that after starting her initial rotation in the camel position no external torques acted upon her, yet we observed her rotation rate increase dramatically as she changed her body’s posture. Why did this happen? What principle did she use to set the world record?

(d)

People dive from high diving boards into swimming pools which are full of water without much risk of injury, but a person might well be killed if he dives into an empty swimming pool, even if he did it from the edge of the pool. Explain why the presence of the water makes so much difference. In your answer, include the terms ‘impulse’ and ‘average force’. [4 + 3 + 3 + 3 = 14 marks]

Question 2

8 marks

A car starts from rest and travels in a straight line under constant acceleration to reach 50 km/hour after 10 seconds. In the following 20 seconds the velocity of the car remains at 50 km/hour. Following this, the car accelerates at -2.0 m/s2 for 15 seconds. (a)

Draw to scale an acceleration-time graph for the duration of the trip.

(b)

Calculate the total displacement of the car after 40 seconds. [3 + 5 = 8 marks]

PHYC10005

Semester 1, 2011

Page 3 of 13

PHYC10005 Physics 1: Fundamentals

Question 3

14 marks

The world-record for the mens long-jump is 8.95 meters by Mike Powell of the USA. Assuming Mike Powell was travelling at 10 meters/second when he started his jump: (a) How long was Mike Powell in the air? (b) Assuming that he undergoes a perfect projectile motion by ignoring air resistance and his body movements while in the air, what was the maximum height of his centre of mass from the ground? (c) Assuming that he undergoes a perfect projectile motion by ignoring air resistance and his body movements while in the air, what was Mike Powell’s initial vertical velocity from his take-off jump? (d) World record jumps are only recognized if the wind velocity is under 2 ms-1 at the time of the jump. Can you think of a reason for this requirement? [2 + 6 + 4 + 2 = 14 marks]

Question 4

16 marks

A box in a warehouse is sliding slowly against friction down a ramp as shown in the diagram. The mass of the box is 1.5 kilograms. The coefficient of kinetic friction k between the box and the ramp is 0.20. The slope of the ramp is 30 degrees. (a) Draw a diagram in your exam booklet showing all the forces acting on the box. Label the forces in your diagram. (b) Calculate the size of the frictional force acting on the box. (c) Calculate the acceleration of the box down the ramp.

[3 + 9 + 4 = 16 marks]

PHYC10005

Semester 1, 2011

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PHYC10005 Physics 1: Fundamentals

Question 5

9 marks

At a carnival, a dodgem car (with two heavy occupants) of mass 220 kg, collides head-on with another car (with two lighter occupants) of mass 160 kg. Before the collision the heavier car is travelling 2 m/s, while the lighter one is travelling at 3 m/s in the opposite direction. After the collision the heavy car moves backwards along its original path at 1 m/s. (a) What is the velocity of the lighter car after the collision? (b) Compare the forces exerted by the two cars on each other during the collision. (c) Show that kinetic energy is not conserved in this collision.

[3 + 3 + 3 = 9 marks]

PHYC10005

Semester 1, 2011

Page 5 of 13

PHYC10005 Physics 1: Fundamentals

Question 6

14 marks

A Physicist of mass 70 kg rides a Ferris wheel of diameter 20m at a carnival.

The Ferris wheel has a uniform acceleration from rest to 0.2 rad/s in 10.0 seconds and from then on travels at constant speed.

(a) What is the magnitude of the angular acceleration in the first 10 seconds of the motion? (b) What is the direction of the torque in the first 10 seconds? (c) Through what total angle has the person travelled in the first 40 seconds of motion? (d) What distance has the person travelled in the first 40 seconds of motion?

The wheel continues to rotate at constant angular velocity of 0.2 rad/s (e) If, during this time of constant angular speed, the Physicist was standing on a set of scales and passed through point A, (halfway up the wheel as shown), what would the scales read? (Assume the scales are calibrated to read in kg) (f) The Physicist continues to point B, (at the top of the wheel), what do the scales read now? [2 + 2 + 2 + 2 +3 + 3= 14 marks]

PHYC10005

Semester 1, 2011

Page 6 of 13

PHYC10005 Physics 1: Fundamentals Question 7

14 marks

(a) Signora Bianca Castafiore is not loved by Captain Haddock. He is very irritated at her piercing ‘noise’. She is a loud soprano, who can produce a high C with a frequencies of 1000 Hz, 2000 Hz, 3000 Hz, … at an intensity level of 105 dB – 140 dB at a distance of 10 cm from her mouth. Explain why Haddock is particularly irritated by the sound, by referring to the figure below (the curves are of equal loudness).

(b) Signora Bianca Castafiore is claimed to break windows and wine glass with her voice. A typical wine glass might have a fundamental frequency of 900-1000 Hz. Does the breaking of a glass depend upon loudness or intensity? Explain how the wine glass might break (and ignore Mythbusters), as presented in lectures. (c) Haddock is also pretty loud, but is a bass. When he sings (or shouts) a low G, he produces harmonics at 100 Hz, 200 Hz, 300 Hz, … At 10 cm he can reach an intensity of 105 db at 100 Hz. Is it likely that he can break glasses just using his voice? Explain why or why not. (d) When looking at Castafiore’s high C or Haddock’s low G, there is an interesting pattern. The fundamental is very loud, the next is quite weak, and the third harmonic is very strong. Explain this in terms of organ pipes, and in particular explain whether the human voice is best represented by an open organ pipe or a half-closed organ pipe. [3 + 4 +2 + 5= 14 marks]

PHYC10005

Semester 1, 2011

Page 7 of 13

PHYC10005 Physics 1: Fundamentals Question 8

21 marks

(a) A single pulse wave shape is shown in the figure below for t = 0. Note that x is in centimetres, f(x) is in centimetres and t in seconds.

i)

A first year student claims that this shape is given by the function y=f(x+0.2t). Give the correct equation with correct dimensions.

ii) If this pulse is a wave on the beach, is it a transverse or a longitudinal wave? Explain. iii) Plot the function as a function of x for t = 3s. iv) Plot the function as a function of t for x = 10 cm. In your answers to parts (iii) and (iv) make sure that you clearly label your axes including the scale. (b) i) Unfortunately, you have just driven through a red light at 60 km/hour. More unfortunately, there was a stationary police car at the intersection watching you. They turn their siren on. Initially, the police car is stationary, and the siren corresponds to a frequency of 3000 Hz. What frequency do you hear the sound at as you travel away from the police car and the intersection? ii) The police car rapidly accelerates to your speed as it tails you down the road. What frequency do you hear during this pursuit while both speeds are 60 km/hour? iii) You naturally stop at the side of the road. The police car is still travelling at 60 km/hour towards you. What frequency do you hear now? (c) Professor C is the world’s greatest tuning fork musician, acclaimed the world over. Audiences and Oscilloscopes note that his tuning fork [note] is perfect. i)

Why are there no harmonics in the tuning fork?

ii) However, Professor C does not seem to get many requests for performances with the Melbourne Symphony Orchestra, even when he offers to play two tuning forks at once! Explain why an hour with Professor C would not necessarily compare favourably to an hour of a string orchestra. [9+8+4=21 marks]

PHYC10005

Semester 1, 2011

Page 8 of 13

PHYC10005 Physics 1: Fundamentals

Question 9

19 marks

(a) An 81 kg student is launched from a bridge by his best friends, some 50 metres above the river surface. Fortunately, he is attached to a 30 m bungee cord with a spring constant of 270 N/m. i) What is the equilibrium length of the bungee cord, including the force of gravity? ii) What velocity would the student have when he reaches the equilibrium position if he fell in free fall with no air resistance? iii) The student has a velocity of 23 m/s at the equilibrium position. Calculate the maximum extension of the spring from its equilibrium position. Is he safe? iv) What is his frequency of oscillation? What is his period of oscillation? v) In revenge at the experience, he gets his best friend, 121.5 kg, to jump from the same bungee cord off the same bridge. Explain what happens assuming that his velocity at the new equilibrium position is 24.5 m/s. [3+2+6+3+5=19 marks]

PHYC10005

Semester 1, 2011

Page 9 of 13

PHYC10005 Physics 1: Fundamentals Question 10

21 marks

a) (a) An object is located 80.0 cm from a converging lens with a focal length 30.0 cm. A mirror is a distance 80.0 cm behind the lens.

i)

Reproduce the figure above in your script book and draw three representative rays from a point on the object to a point on the initial image produced by the light refracted from the mirror. Explain your choice of rays by referring to the ‘rules’ of geometric optics and ray tracing.

ii) Is this image real or virtual? iii) Is this image upright or inverted? iv) How far from the lens is the image located? v) What is the linear magnification of the image relative to the object? vi) Draw rays from this image to the image produced by the mirror. How far from the lens is this image located? Is the image real or virtual? b) i)

A student is looking at an insect. Assume that the student has a near-point of 12 cm, and the magnifier has a focal length of 3.0 cm. A student uses the magnifier while keeping their vision relaxed. How much larger would the student perceive the object to be when using the magnifier, compared to when they place the object at their near point and use no visual aids?

c) i)

Explain how diffraction can affect the quality of images obtained using a microscope.

ii) Two small lights are placed 1.0 m from your head in a darkened room. Calculate the minimum separation of these lights such that you still recognise them as being two point sources. (Take the wavelength of light to be 550 nm and the pupil diameter to be 3.00 mm. Ignore the roles that photoreceptor spacing on the retina, refractive disorders or the refractive index of the eye may play in visual acuity). [12 + 2 + 7 = 21 marks]

End of examination questions Formula sheets follow

PHYC10005

Semester 1, 2011

Page 10 of 13

PHYC10005 Physics 1: Fundamentals Formula Sheet and Useful data for PHYC10005 Physics 1: Fundamentals

Constants Universal gravitational constant

G

6.673 × 10-11 kg-1 m3 s-2

Acceleration due to gravity at the Earth’s surface

g

9.8 m s-2

Speed of light in vacuum

c

3.00 × 108 m s-1 343 m s-1

Speed of sound in air (20 °C) Density of air

ρair

1.29 kg m-3

Avogadro number

NA

6.023 × 1023 kg mol-1

Elementary charge

e

1.602 × 10-19 C

Mass of electron

me

9.11 × 10-31 kg

Planck constant

h

6.626 × 10-34 J s

Molar gas constant

R

8.314 J mol-1 K-1

Boltzmann constant

kB

1.381 × 10-23 J K-1

Stefan-Boltzmann constant

σ

5.670 × 10-8 W m-2 K-4

Electron volt

eV

1 eV = 1.6 × 10-19 J.

Mass of Earth

ME

5.98 × 1024 kg

Radius of Earth

RE

6.38 × 106 m

PHYC10005

Semester 1, 2011

Page 11 of 13

PHYC10005 Physics 1: Fundamentals Mechanics

l  r ; v  r 

dx x ; v dt t

v av 

dv v ; a dt t

a av 

v f  v i  a t x 

1 x  v i t  a (t ) 2 2

2 ax  ( v f ) - (v i )

d  ;  dt t

 av 

d  ;  dt t

 f   i   t

1 v i  v f t 2

2

 av 

2

 

1  i  f t 2

   i  t 

1  ( t) 2 2

Fnet  ma

2  (  f ) 2 - ( i ) 2

Fsp   kx

 net  I

F L Y A L

  rF

k

YA L

v

  rF sin  N

2

i 1

  W  F  x  F ( x ) cos

f s  s N

P

v2 r

Fg 





I   m i ri

f k  k N

ac 



E t

E   K   U g   U s  Eth  ...  W  Q

Gm1 m 2 r2

2 r T

K

1 1 2 mv 2 ; K  I  2 2

U sp 

p  mv

1 2 kx 2

U g  mgy

J  Fav t  p xcom 

1 M

N

 m i xi i 1

L  I

PHYC10005

Semester 1, 2011

Page 12 of 13

PHYC10005 Physics 1: Fundamentals Oscillations, Waves and Sound

T  2

m L ; T  2 k g

v  f

2L n

nv fn  2L

4L n

nv fn  4L

n  n 

1 f T

 vsound  vo f ' f   v sound

y  f (x  vt )



v  f T

   

v  vo   f ' f  sound  vsound  vs 

  x        ft y( x ,t )  A sin 2        

I

P A

F

v

 v sound f ' f   v sound  v s

  

 I 

 10 log10  



I 0 

where

I 0 1012 W .m 2

I r ( 1v1   2v 2) 2  I i ( v  v ) 2 1 1 2 2 Optics

v

c n

1 n2  2 n1 n1 sin  1 n 2 sin  2

  N   f

PHYC10005

sin  

m a

m   1,  2, ...

L

L d

d

m m an integer

m  21 

sin  min  122 .

 1 1 1  ( n 1)   f R1 R2 

M 

m  0,  1,  2, ...

y dark 

n1 n 2 n2  n1   p q R

1 1 1   q f p

m d

ybright 

n |q| 2 | p| n1

P

sin  

xmin  1. 22 m 

q p

I 16mm  O p

m an integer

 d

 f  0.61 D NA





sin  tan   radians

small angles

c = f 

Semester 1, 2011

Page 13 of 13

Examination Answers – Semester 1, 2011 PHYC10005 Physics 1: Fundamentals These are answers to the exam questions, not complete solutions. Answers provided to questions requiring explanations do not represent complete solutions, and would in most cases not receive the full marks allocated on the exam paper. Many marks are given on the exam for ‘working’ (i.e. for showing that you understand the relevant physics), and a numerical answer alone is usually not sufficient to gain full marks. 1. (a)

The two position themselves so that the magnitudes of their respective torques about the hinge of the see-saw are equal. The mother should be closer to the centre.

(b)

The action/reaction pair of your force on the trolley and the trolley’s force on you act on two different objects. The trolley accelerates because it has a non-zero net force on it.

(c)

Changing her body posture changed her moment of inertia. Since angular momentum is conserved in this situation, reducing the moment of inertia meant that angular speed had to increase.

(d)

When landing (in water or on concrete), the diver has a certain momentum, which decreases to zero. This change in momentum is a fixed impulse. But if the time taken for the diver to slow to rest is increased, the average force on the diver is decreased, since impulse .

(a)

Graph required.

(b)

386 m.

(a)

0.895 s.

(b)

0.98 m.

2.

3.

(c)

.

(d)

If the wind speed is too high, the force of the air can add significantly to the distance of the jump.