Download Achievement - Waimea Physics

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Waimea College
Ni
PHYSICS
Mechanics Homework Assignment 1
Level 3
90521 Demonstrate understanding of mechanical systems
Credits: Six
Answer ALL the questions in the spaces provided.
If you need more space for any answer, use the pages provided at the back of this booklet and clearly
number the question.
For all numerical answers, full working should 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.
YOU MUST HAND THIS BOOKLET TO THE SUPERVISOR AT THE END OF THE ASSESSMENT.
For Assessor’s use only
Achievement Criteria
Achievement
Achievement
with Merit
Achievement
With Excellence
Identify or describe aspects of
phenomena, concepts or principles.
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)
90521 Demonstrate understanding of mechanical systems • NZIP 2008, 2007, 2006, 2005
2
You may find the following formulae useful
Fnet  ma
W  Fd
d  r


t
v  r
f  i  t
  
Fg 
GMm
r2
E  ky
1
2
p  mv
EK (LIN )  12 mv 2
2
  2f
  f  t
 i
2
  Fr
Fc 
mv
r
p  Ft

a  r
1
f 
T

t
EK (ROT )  12 2
f  i  2 
L  mvr
2
E p  mgh
2
  i t  12 t 2
L  
2
F   ky
y  A sin t
v  A cos t
y  A cos t
v   A sin t
T  2
l
g
a   A2 sin t
a   A2 cos t
m
k
2
a   y
T  2
g = 9.81 m s-2.
90521 Demonstrate understanding of mechanical systems • NZIP 2008, 2007, 2006, 2005
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NZIP 2008
QUESTION THREE: THE CORNER
Regan has a motorcycle which he sometimes races. He asks his physics teacher about
why motorcycles lean over while going around corners and she draws for him a free body
force diagram showing the forces acting on the motorcycle as it corners. She says that the
angle  is equal to the angle at which the bike is leaning over.
(a)
The force, F, is the total reaction force and is the sum of two other forces. What
forces are they?
F

Fg
_______________________________________________________________
_______________________________________________________________
(b)
Explain why the size of the vertical component of the force, F , acting on Regan and
the motorcycle is 2410 N. The combined mass of Regan and his bike is 246 kg.
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
90521 Demonstrate understanding of mechanical systems • NZIP 2008, 2007, 2006, 2005
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(c)
On one occasion Regan’s speed as he rounds a corner is 17.8 m s1.
(i) The corner has a radius of 22.5 m. Show that the size of the centripetal force acting
on Regan and his motorcycle as he travels round the corner is 3460 N.
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
(ii) Calculate the angle at which Regan and his motorcycle are leaning.
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
angle = _________________________________
(d)
On another occasion, on a very wet racetrack, Regan collides with another motorcycle.
The two motorcycles lock together and slide along the wet track for a while. A
representation of this collision is shown on the next page.
(i) Define the Centre of Mass of a two or more body system.
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
90521 Demonstrate understanding of mechanical systems • NZIP 2008, 2007, 2006, 2005
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(ii) Find and show on the diagram below the position of the centre of mass of the
system of both the motorcycles and their riders when they are at positions A1
and B1, A2 and B2, A3 and B3, A4 and B4 respectively. Label these positions
CM1, CM2, CM3 and CM4 respectively.
(iii) The momentum of the two locked together motorcycles is 10 100 kg m s1. If
Regan’s motorcycle is A, show that Regan was travelling at 22.3 m s1 when the
collision occurred.
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
90521 Demonstrate understanding of mechanical systems • NZIP 2008, 2007, 2006, 2005
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(iv) By first calculating Regan’s momentum, calculate the momentum of the other
rider and his motorcycle.
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
momentum = _________________________________
(e)
After sliding together for a while the motorcycles collide with a barrier that has been
fixed at the side of the track. Explain whether momentum is conserved in this
collision.
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
90521 Demonstrate understanding of mechanical systems • NZIP 2008, 2007, 2006, 2005
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NZIP 2006
QUESTION THREE: PLAYING HOCKEY
Linda
7.00m
Kelly
Two hockey players, Linda and Kelly, are running towards each other. The combined mass
of Linda and her hockey stick is 74.0 kg. The combined mass of Kelly and her hockey stick
is 69.0 kg. At a given instant as shown in the above diagram the distance between their
centres of mass is 7.00 m.
(a)
Calculate the position of the combined centre of mass of Linda and Kelly at the
instant shown in the above diagram.
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
Position of centre of mass =_________________
Linda hits the ball towards the goal. The ball collides with the goalkeeper’s boot at
8.50 ms1. Its momentum is 1.49 kgms-1. After colliding with the goalkeeper’s boot the ball
bounces off her boot at 8.50 ms-1 again, as shown in the diagram below
(b)
In the space given on the right of the diagram sketch a labelled vector diagram to
show the change in velocity of the ball.
8.50ms1
45O
45O
8.50ms1
90521 Demonstrate understanding of mechanical systems • NZIP 2008, 2007, 2006, 2005
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During the collision the ball was in contact with the boot for 0.45 s. The mass of the ball
is 0.175kg
(c)
Use your vector diagram to calculate the average force exerted by the ball during
the collision. Give your answer to the correct number of significant figure.
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
Average force = __________________________
(d)
State the direction of the force in (c).
_______________________________________________________________
_______________________________________________________________
90521 Demonstrate understanding of mechanical systems • NZIP 2008, 2007, 2006, 2005
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TROUBLE IN PICTON
Aratere, the new Inter-Island ferry, had a difficult first year, including a collision with the dock in
Picton. Collisions involving large ships moving at even low speeds can be quite damaging
because of the enormous amount of momentum such a large object possesses when moving.
N
Dock
The Aratere has a mass of approximately 2.04 x 10 8kg. The ship moves south towards the dock
at 0.752 kilometres per hour (see diagram).
(a) Show that 0.752kmh-1 is 0.209ms-1.
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
(b) Determine the magnitude and direction of the ship’s linear momentum.
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
90521 Demonstrate understanding of mechanical systems • NZIP 2008, 2007, 2006, 2005
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(c) The ship’s engines are put into reverse and apply an average force of
F = 1.23 x 106N for 25.8 seconds. Determine the magnitude and direction of the
ship’s change in momentum.
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
(d) Determine the magnitude and direction of the ship’s momentum after the engines are
switched off.
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
(e) Show that the speed of the ship after the engines have been switched off
is 0.0534ms-1.
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
90521 Demonstrate understanding of mechanical systems • NZIP 2008, 2007, 2006, 2005
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(f) The ship then collides with the Picton dock. It takes 1.34 seconds for the ship to
come to a complete stop. Determine the magnitude and direction of the average force
that the dock exerts on the ship to bring it to a stop.
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
(i) A 60kg passenger is seated aboard the ship as it collides with the dock. Determine the
amount of frictional force that the seat must apply to the passenger to keep him
stationary with respect to the seat when the collision occurs.
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
(j) Comment on the size of this frictional force by making a reference to other forces
that are commonly experienced.
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
90521 Demonstrate understanding of mechanical systems • NZIP 2008, 2007, 2006, 2005