Download 1 PHYSICS Level 3 AS 90521 3.4 Demonstrate understanding of

New Zealand Institute of Physics
PHYSICS
Level 3
AS 90521
3.4 Demonstrate understanding of Mechanical Systems
Credits: Six
Answer ALL the questions in the spaces provided.
For all numerical answers, full working must be shown and the answer should be rounded to the correct
number of significant figures and given with an SI unit.
For all ‘describe’ or ‘explain’ questions, the answer should be in complete sentences with all logic fully
explained.
Check that this booklet has pages 2-11 in the correct order and that none of these pages are blank.
You must hand this booklet to the supervisor at the end of the assessment.
Achievement Criteria
Achievement
For Assessor’s use only
Achievement
with Merit
Achievement
with Excellence
 Identify or describe aspects of
phenomena, concepts or
principles in an integrated
context.
 Give descriptions or
explanations in terms of
phenomena, concepts,
principles and/or relationships.
 Give concise explanations that
show clear understanding in
terms of phenomena, concepts,
principles and/or relationships.
 Solve straightforward problems.
 Solve problems.
 Solve complex problems.
Overall Level of Performance (all criteria within a column are met)
2
Formulae that you may find useful are given below
Fnet  ma
p  mv
W  Fd
EK (LIN )  12 mv 2
d  r


t
p  Ft
E p  mgh
v  r
a  r

  2f
f 
i  f  t
f  i  t

  
  Fr
Fg 
GMm
r2
Fc 
2
mv
r
1
T

t
EK (ROT )  12 2
f  i  2 
  i t  12 t 2
L  mvr
L  
2
2
2
l
g
E  12 ky2
F   ky
T  2
y  A sin t
v  A cos t
a   A2 sin t
y  A cos t
v   A sin t
a   A2 cos t
T  2
m
k
a   2 y
g = 9.81 ms-2
Physics 3.4: Mechanical Systems - Question and Answer Booklet 2005
Assessor’s
use only
3
You are advised to spend 60 minutes answering the questions in this booklet.
QUESTION ONE: SIMPLE HARMONIC MOTION AND CARS
In a car engine the piston moves up and down in the cylinder to power the engine. The
diagram below shows the piston-cylinder assembly. The motion of the piston in a car
engine is approximately simple harmonic.
The amplitude of the piston is 0.55m and its frequency of oscillation is 140Hz.
Cylinder
t=0
Piston
(a)
Explain the meaning of the term “simple harmonic motion”.
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(b)
Show that the value of the angular frequency for the piston is 880. State the
appropriate SI unit with your unrounded answer.
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________________________________________ Unit = ____________________
(c)
Calculate the total distance travelled by the piston in one complete cycle.
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________________________________ Total distance = ____________________
(d)
Calculate the maximum speed of the piston.
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__________________________________Maximum speed = _________________
Physics 3.4: Mechanical Systems - Question and Answer Booklet 2005
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(e)
On the axes provided below sketch, the shape of the velocity-time graph of the
piston’s motion for one complete cycle. Assume t=0 when the piston is at the
equilibrium position and moving upwards. Label any available values for time and
velocity.
Velocity (m/s)
Time
(s)
(f)
Calculate the maximum acceleration of the piston.
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_________________________ Maximum acceleration = ____________________
(g)
Where does the maximum acceleration take place during the motion of the piston?
Give a reason for your answer.
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A car is driven to test its suspension system. The mass of the car is 1250kg and the mass
of the driver is 80kg. The suspension system of the car is compressed by 0.020m, when
the driver sits on the seat. The car is now being pushed down and let go.
(h)
Show that the period of the oscillation of the car is 1.16s (3sf).
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Physics 3.4: Mechanical Systems - Question and Answer Booklet 2005
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(i)
Explain how the period of the oscillation in (h) would change if it is loaded with
another four adult passengers.
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(j)
The car is driven over a series of equally spaced bumps as shown in the diagram
below. The amplitude of oscillation becomes much larger when it is driven at
15 ms-1. Calculate the distance from the centre of one bump to the next one. The
period of the oscillation of the car is still 1.16s.
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____________________________________ Distance = ____________________
(k)
Explain why the amplitude of the oscillations becomes much larger at this particular
speed.
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Physics 3.4: Mechanical Systems - Question and Answer Booklet 2005
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Assessor’s
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QUESTION TWO: SPACE TRAVEL
During a space exploration a spacecraft flies past the planet Venus. The diagram below
shows the path taken by the spacecraft as it flies past the planet. Use the data given below
to answer the following questions.
P
DATA:
Mass of Venus = 5.41 x 1024 kg
Universal Gravitational constant,
G = 6.67 x10-11 Nm2kg-2
Mass of the spacecraft = 4.32 x104 kg
Venus
(a)
Spacecraf
t
The point P is 6.682 x 106 m above the centre of the planet Venus. Show that the
size of the gravitational force acting on the spacecraft at the instant when it is at P is
3.49 x 105 N.
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(b)
State the direction of the force experienced by the spacecraft when it is at the
point P.
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(c)
Calculate the orbital speed of the spacecraft at the point P. State your answer to
the correct number of significant figures.
__________________________________________________________________
__________________________________________________________________
__________________________________________________________________
_________________________________ Orbital speed = ____________________
Physics 3.4: Mechanical Systems - Question and Answer Booklet 2005
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QUESTION THREE: SATELLITE
An orbiting satellite has two sensors. When the sensors are fully extended as shown in the
diagram below, the rotational inertia of the system is 1.20 x 102 kgm2. The sensors can be
withdrawn back to the axis of rotation using an electric motor.
Sensor
Arm
(a)
The satellite is rotating with an angular velocity of 0.100 rads-1 when the sensors are
fully extended as shown in the above diagram. Calculate its rotational kinetic
energy.
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______________________ rotational kinetic energy = ______________________
(b)
The sensors are now withdrawn back to the axis of rotation using the electric motor.
Its new rotational inertia is 1.00 x 102 kgm2. Calculate its new angular velocity.
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____________________________ Angular velocity = ______________________
(c)
Explain the physics idea used to calculate the angular velocity in question (b).
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Physics 3.4: Mechanical Systems - Question and Answer Booklet 2005
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(d)
Each sensor has a mass of 2.00kg. Each of them is now extended to 1.50m from
the axis of rotation. The mass of the telescopic arms is negligible. Use the formula
I = mr2 to calculate the new rotational inertia of the system.
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____________________________ rotational inertia = ______________________
Physics 3.4: Mechanical Systems - Question and Answer Booklet 2005
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QUESTION FOUR: SPACE STATION
The diagram below shows a design for a space station. It consists of a hollow tube with
circular shape, like a large wheel. There are four tunnels connecting outer tube to the
central section of the space station. The radius of the wheel is 11.2m. An artificial gravity
(gravity like effect) is created by rotating the space station about the centre.
(a)
State the direction of the artificial gravity experienced by an astronaut who is in the
outer rim.
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(b)
Using the idea of forces explain why the astronaut experiences an artificial gravity
when the space station is rotated.
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(c)
Calculate the linear speed of the outer rim needed to produce an artificial gravity of
9.81 Nkg-1.
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_______________________________ Linear speed = ______________________
Physics 3.4: Mechanical Systems - Question and Answer Booklet 2005
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(d)
While the space station is rotating the astronaut moves through the connecting
tunnel to the centre. Explain how her experience of the sensation of weight changes
as she moves towards the centre.
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(e)
The four rockets on the rim are fired simultaneously to rotate the space station.
Each rocket exerts a force of 65.5 N. The space station’s angular velocity is
increased at a constant angular acceleration of 3.63 x 10-3 rads-2. Each rocket is
11.2 m away from the centre (You may ignore the change in mass of the rockets
caused by burning fuel). Calculate the rotational inertia of the system.
__________________________________________________________________
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____________________________ Rotational inertia = ______________________
(f)
When the rockets are fired the space station starts from rest and rotates with a
constant angular acceleration of 3.63 x 10-3 rads-2. The rockets are fired until the rim
rotates with a linear speed of 10.8 ms-1. Calculate the time taken for the rim to
reach a linear speed of 10.8 ms-1.
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__________________________________________________________________
__________________________________________________________________
__________________________________________________________________
_____________________________________ Time = ______________________
Physics 3.4: Mechanical Systems - Question and Answer Booklet 2005
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Question
Number
If you need more space for any answer, continue here. Clearly number the question.
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Physics 3.4: Mechanical Systems - Question and Answer Booklet 2005
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