Download May 2002 - GF Abela Junior College

UNIVERSITY OF MALTA
G.F.ABELA JUNIOR COLLEGE
FIRST YEAR
END-OF-YEAR TEST
June Session 2002
Subject: Physics
Date: 5th June 2002
Level: Advanced
Time: 09.00hrs – 12.00hrs
Directions to Candidates
You are requested to show your working and write the units where
necessary.
Answer ALL questions from Section A.
Answer any TWO questions from Section B.
Answer any TWO questions from Section C.
Wherever necessary assume g = 10ms-2.
Section A
Attempt ALL eight questions in this section. Each question carries 5 marks. This
section carries 40% of the total mark for this paper.
1. Two cars, travelling in the same direction, skid on a patch of smooth, level ice. Car
A, of mass 1400kg, skids straight into the back of car B, of mass 1000kg. The two
cars become entangled after impact and continue to move in the same straight line.
Car A
Car B 8m/s
Smooth ice
Immediately before impact, car B is moving with a velocity of 8m/s. Immediately
after impact, both cars move with a velocity of 15m/s.
(a)Calculate the velocity of car A just before the collision takes place.
(2)
(b)After the collision, the cars leave the patch of ice and continue skidding along the
road. They come to rest in a distance of 20m after leaving the ice. Calculate the
average frictional force acting on the cars as they come to rest.
(3)
2. The two graphs in figure are load-extension graphs of two different materials X and
Y. Each strand is of length 2m and cross-sectional area 1.0mm2.
(a) State which material is ductile and which is brittle. Explain.
(b) Calculate the Young’s modulus of material X.
(c) Deduce the strain energy stored in the strand of material Y for an
extension of 2mm.
(1)
(2)
(2)
3. A helicopter with supplies hanging from a rope, circles a lighthouse to deliver
them. The load of 80kg is moving in a circular path of radius 20m at 3.3m/s.
(a) Explain why the rope cannot be vertical.
(2)
(b) By considering the tension in the rope and the centripetal force needed,
establish the angle of the rope to the horizontal.
(3)
4. A tennis player hits a ball at a height of 2.4m. The ball has an initial horizontal
velocity. The ball just passes over the net that is 0.6m high and 6m away from her.
(Neglect air resistance)
2.4m
0.6m
6.0m
(a) Calculate the time required for the ball to reach the net.
(b) What was the speed of the ball as it left the racquet?
(2)
(3)
5. Light enters a layer of glue at the end of an optical fibre as shown in the figure. The
refractive index of the glue, ηglue is 1.36 and of the core glass ηcore is 1.58. A ray is
incident on the end of the fibre at 10°.
layer of glue
cladding
core glass
10°
cladding
(a) Determine at what angle does it hit the core-cladding boundary?
(2)
(b) Draw the diagram on your booklet and show, with calculations, what happens
to the light once it is incident on the core-cladding boundary. The refractive
index of cladding is 1.48.
(3)
6. The wavelength of monochromatic light from a lamp is to be determined by means
of a double slit experiment.
(a) Draw on your booklet a set up of the arrangement that will enable you to
determine λ.
(1)
(b) State what measurements are taken and explain how these measurements are
used to calculate the wavelength.
(3)
(c) Describe the screen pattern that results.
(1)
7. Bending and lifting incorrectly often cause back injury. The diagram below shows
a man about to lift a box.
(a) What is the vertical component Tv of the tension in the back muscles in the
situation shown in figure.
(1)
(b) Calculate the tension in the back muscles.
(2)
(c) Suggest a better way of lifting the box. Explain.
(2)
8. The graph below shows the gravitational field strength at various heights above the
earth’s surface.
Gravitational
field
strength
in
N/kg
Height above the Earth’s surface in km
(a) Given that the radius of the earth is 6400km show with the aid of the graph that
the gravitational field strength varies with distance according to an inverse square
law.
(2)
(b)What is the speed of orbit of a satellite that is 5000km above the earth’s surface.(3)
Section B
Attempt TWO questions in this section. Each question carries 15marks. This section
carries 30% of the total mark of this paper.
9a.State and explain the equation defining simple harmonic motion.
(2)
b. The graph in figure shows how the acceleration of a mass-spring system
undergoing simple harmonic motion varies with time.
Deduce from the numerical values given on the graph, the values for this simple
harmonic motion of :
(i)
the period
(ii)
the frequency
(iii) the angular frequency
(iv)
the amplitude of the oscillation
(6)
c. Sketch on your booklet a graph which shows how the
(i)
the displacement varies with time.
(ii)
the velocity changes with time
(4)
d. The experiment is repeated using a mass of four times the original mass. Determine
the new period and frequency of this mass-spring system.
(3)
10a. Distinguish between transverse and longitudinal waves and state an example of
each.
(4)
b. Using diagrams explain what is meant by:
(i)
an unpolarised wave
(ii)
a plane-polarised wave.
(2)
c. Describe the effect of two crossed polaroids (i.e. two polaroids with axis at right
angles to each other) on unpolarised light.
(2)
d. A biologist is studying the effect of different colours of light on a sample of
chlorophyll. He sets up the apparatus shown below, using a diffraction grating with
6.0 x 105 lines per metre to produce a first order spectrum of sunlight.
θ
A
ray of
sunlight
X
diffraction
grating
1st order
spectrum
a sample
of chlorophyll
Y
(i) The wavelength of the light at the end X of the spectrum is 410nm. Calculate the
value of the angle θ.
(2)
(ii) The angle A in the diagram is 9°. Calculate the wavelength at end Y of the
spectrum.
(3)
(iii) The biologist now uses a triangular prism to produce a continuous spectrum from
a ray of sunlight. State two differences between this spectrum and the spectrum
produced by the grating.
(2)
11. A photocell has a cathode coated with a material, which emits electrons when
visible light shines on it.
a. When light of wavelength 550nm shines on the cathode, electrons are just emitted.
(i)
What is the threshold frequency of this material?
(ii)
What is the work function, φ, of the metal in joules?
(5)
b. The wavelength of the light is changed to 400nm at the same intensity.
(i)
What is the maximum possible K.E. of an ejected electron?
(ii)
How does this change of frequency affect the number of electrons emitted
each second?
(5)
c. The intensity is then increased. What is the effect on:
(i)
the KE of the ejected electrons
(ii)
the number of electrons emitted per second?
(c = 3.0 x 108m/s, h = 6.6 x 10-34 Js)
(5)
Section C
Attempt TWO questions in this section. Each question carries 15marks. This section
carries 30% of the total mark of this paper.
12. The figure shows a Ferris wheel, at a fun fair, which rotates in a vertical plane
about a horizontal axis.
Below is data on the Ferris wheel.
Moment of inertia of the wheel empty = 8.8 x 105 kgm2
Maximum passenger mass per chair = 200kg
Number of chairs = 16
Radius of the wheel = 10m
With each chair carrying its maximum load, the Ferris wheel is found to rotate 7 times
in 30s, when rotating at its maximum angular speed.
(a)
(b)
(c)
(d)
Determine the moment of inertia of the loaded wheel
(2)
Find the angular velocity of the wheel
(2)
Calculate the rotational KE of the loaded wheel at this speed.
(2)
With the driver motor switched off and with no application of the
brakes, the system decelerates uniformly to rest from its maximum
speed in 20 revolutions. Calculate the frictional torque that causes this
deceleration.
(3)
(e) The wheel takes 50s, from rest to reach its maximum angular speed.
Calculate its angular acceleration.
(2)
(f) Calculate the torque of the driver motor which would produce this
acceleration of the loaded Ferris wheel.
(4)
13. An electron is projected into an evacuated space between two charged plates of
length 5cm as shown in figure. The electric field strength E is 3.5 x 104 NC-1. The
velocity of the electron, v, is 3.2 x 107m/s. Neglect any gravitational effects.
(a) State whether the quantity ‘electric field strength’ is a vector or a
scalar quantity ?
(1)
(b) What is the size and direction of the electric force on the electron? (3)
(c) What is the horizontal velocity of the electron as it leaves the uniform
field?
(1)
(d) How long does it take to pass between the plates?
(2)
(e) What is the vertical acceleration of the electron?
(2)
(f) What is the vertical velocity on leaving the plates?
(4)
(g) What is the size and direction of the final velocity?
(3)
(electronic charge e = 1.6 x 10-19C, mass of electron me = 9.1 x 10-31kg)
14. a. Define the capacitance of a capacitor.
(1)
b. The figure shows a circuit diagram of three capacitors, of capacitance 10µF, 5µF
and 25µF respectively, connected in a network with a battery of e.m.f. 12V.
(i)
(ii)
(iii)
Which capacitors are in parallel?
(1)
Calculate the capacitance of the single capacitor, connected across the
battery, which is equivalent to the network of three capacitors.
(3)
Calculate the energy stored in the network of capacitors.
(3)
c. The figure is a diagram of a circuit containing a resistor R and a capacitor C,
together with a two-way switch S and a battery of e.m.f. 10V. When the switch is in
position A the capacitor and resistor are connected in series with the battery; when
the switch is in position B the capacitor discharges through the resistor.
(i) With switch S in position A, what is the maximum possible potential difference
across the capacitor C?
(1)
When the capacitor C is fully charged, the switch S is moved from position A to
position B at t=0s. The graph in figure shows the potential difference V across the
capacitor C as a function of time t in the range from 0 to 12s.
(ii) Estimate the time constant of the circuit from the graph.
(iii) If the capacitance of C is 20µF, what is the value of the resistance R?
(iv) Calculate the current flowing in the circuit, 1s after switching on.
(2)
(2)
(2)