PHYC10003
Physics 1
Semester 1, 2017 Assessment
Question 1 [(3 + 3) + (2 + 3 + 3 + 1) = 15 marks]
a) Briefly explain the sensation of weightless felt during free-fall even though gravity is present? (you may ignore air resistance when answering).
b) Consider the force(s) felt by a passenger in a car making a sharp left hand turn. Use this example to explain the difference between centripetal and centrifugal force.
Two sailors, Jex and Beatrice are meant to be competing in a race across an large rectangular lake. The race begins with both sailors effectively crossing the starting (0,0) line together.
Jex finds it hard to sail in a straight line, and moves with a displacement from the start at (0,0) given by r(t) = ti(^)+0.2t2j(^).
c) What is the magnitude of Jex’s displacement from the start after 10 s?
d) Jex’s displacement after 10 s is not equal to the magnitude of the distance covered in that time. Which is greater? Give reasons for your answer.
e) What is Jex’s speed at t = 10 s?
The other competitor Beatrice, starts at the same time. Her displacement is given by:
r(t) = ti(^) -0.3t2j(^)
f) Write down Jex’s displacement relative to Beatrice in (i,j) notation.
Question 2 [7 + 3 = 10 marks]
The diagram below depicts the geometry of an inelastic collision of a moving white-striped billiard ball and a grey billiard ball which is initially at rest. The white-striped ball is played in the positive-x direction such that it collides with the grey ball. The collision causes the grey ball to move off towards the lower-right pocket at an angle of 30° from the x-axis.
The mass of the grey ball is 0.15 kg and the white-striped ball is 0.18 kg. A sound recording reveals that the collision happens 0.25 s after the player has struck the white-striped ball and that the grey ball falls into the pocket 0.35 s after the collision.
a. Calculate the velocity of the white ball after the collision?
b. Calculate the energy lost to the environment in this collision?
Question 3 [ (2 + 5 + 2 + 3) + (5 + 3) = 20 marks]
Steve is going on holiday and has carefully packed some physics demos into a suitcase. The mass of the suitcase is m = 7.0 kg, and he intends to place it on the roof of the car without any restraints. In preparation, he has measured the coefficient of kinetic friction between the roof of the car and the suitcase as μk = 0.2 and the coefficient of static friction is μs = 0.5. He is also aware the he cannot ignore air resistance. However, Steve is confident that his driving skills and friction will ensure that the suitcase remains on the roof of the car. Steve gently accelerates from rest to 40 km/hr, striving to ensure that the suitcase remains where he has placed it.
a) If you wish to analyse the motion of the suitcase using Newton’s laws, which frame of reference, that of the car or that of an observer on the footpath, should you use? Explain why.
b) The car increases in speed as it travels in a straight line on a flat road. Draw a diagram in your exam booklet clearly showing all forces acting on the suitcase. Define all symbols introduced.
c) Considering only the friction between the suitcase and the roof (of the car), calculate the maximum acceleration of the car to ensure that the suitcase does not slide off the roof.
Steve decides to increase his speed to 60 km/hr, ensuring that he never exceeds the maximum acceleration calculated in part c) above. Despite all of this, Steve observes the suitcase begins to slide off.
d) Considering all of the forces acting on the suitcase, justify why the suitcase begins to slide off at this greater speed.
Jean is riding her bike quickly along a raised pathway at constant velocity as shown in the diagram below. As she reaches position “P” she accidentally drops her drink container and, remarkably, it lands directly into a recycling bin 3.0 m directly below, just as she passes point “Q” 10 m away. You may ignore air resistance.
e) How fast was Jean travelling when the drink container was dropped?
f) What is the speed of the drink container as it reaches the top of the bin directly below Q?
A small firework of mass 1.5kg.is attached to the base of the hot air balloon which is stationary and floating 100m above the ground as shown (not to scale). As the firework is lit, there is an explosion which causes the firework to split into two unequal fragments, which are emitted horizontally back-to- back as a result of the explosion. One fragment, A, has a mass of 0.5 kg, while the other, B, has a mass of 1.0 kg.
(a) If the total energy of the explosion is 2.5 kJ and 75% of this energy is converted into the kinetic energy of the fragments, what are the speeds with which the fragments are ejected? Clearly specify which fragment corresponds to which speed.
The fragments then fall under the influence of gravity (but air resistance can be ignored) and land on the same horizontal surface
(b) What is the difference in times for each fragment to strike the ground?
(c) Calculate the distance between where the fragments land.
Question 5 [1 + 1 + 1 + 1 = 4 marks]
A rocket closely resembling Thunderbird 3 is drifting sideways in outer space along the line p-q as shown. The rocket is not subject to any outside forces. Starting at position q, the rocket's engine is turned on and produces a constant thrust (force on the rocket) at right angles to the line p-q. The constant thrust is maintained until the rocket reaches a point r (not shown).
(a) Which path A to E below best represents the path of the rocket between points q and r ?
(b) As the rocket moves from position q to position r, its speed is:
(A) constant.
(B) continuously increasing.
(C) continuously decreasing.
(D) increasing for a while and constant thereafter.
(E) constant for a while and decreasing thereafter.
(c) At point r the rocket's engine is turned off and the thrust immediately drops to zero. Which of the paths A to E below will the rocket follow beyond point r?
(d) Beyond position r the speed of the rocket is:
(A) constant.
(B) continuously increasing.
(C) continuously decreasing.
(D) increasing for a while and constant thereafter.
(E) constant for a while and decreasing thereafter.
Question 6 [ (2 + 3 + 2 + 3) + (2 + 1 + 3) = 16 marks]
Two objects, m1 of mass 2.0 kg and m2 of mass 1.0 kg, are confined to move in a circular path along a frictionless track of radius 1.5 m. As shown in the diagram, m1 is initially moving in a counter(anti)-clockwise direction with an angular velocity of +0.5 rad.s-1 whilst m2 moves in the opposite direction, with an angular velocity equal in magnitude to that of m1. In answering the questions below, you may consider each object to be point like.
a) Show that the moment of inertia of m1 is 4.5 kg.m2.
b) Calculate the total angular momentum, of the system before the collision.
At an arbitrary point, the objects collide and remain stuck together. In answering the questions that follow, you may consider each object to be a point-like particle.
c) What is the total angular momentum, of the system after the collision?
d) Calculate the angular velocity (magnitude and direction) of the ‘combined’ object (m1+m2) after the collision.
A figure skater with arms extended and moment of inertia Ii is spinning on ice (assumed frictionless) at an angular speed of ωi. As the skater retracts (pulls in) his arms as shown, his moment of inertia changes to If and his angular speed increases to ωf.
e) Briefly explain why the skater’s angular speed increased as he retracted his arms.
Now consider the rotational kinetic energy, Kf, of the skater after his arms have been retracted.
f) Which one of the following statements is correct?
A. Kf is equal to Ki .
B. Kf is greater than Ki
C. Kf is less than Ki .
where Ki is the skater’s initial rotational kinetic energy.
g) Justify you answer to the previous question. Include a reference to conservation of energy or work done in your answer.
Question 7 [2 + 2 + 2 + 2 + 3 + 2 + 3 + 3 = 19 marks]
One of the closest stars to Earth is Alpha Centauri, which is 4.3 light-years away. A rocket carrying Sid Meier leaves Earth for Alpha Centauri at a speed of 0.9c. You may assume that the Earth and Alpha Centauri are at rest relative to each other.
(a) Define an inertial reference frame.
(b) State Einstein’s Principle of Special Relativity.
(c) Define proper distance.
(d) Sketch a graph of the Lorentz boost factor y versus velocity, v, in units ofc.
(e) What is the distance in km to Alpha Centauri as measured by an observer on Earth?
(f) Is the distance in part (e) the proper distance from Earth to Alpha Centauri? Justify your answer.
(g) According to Sid Meier, how much did he age in years during the journey?
(h) According to Sid Meier, how far did he travel to Alpha Centauri?
Question 8 [ 2 + 2 + 5 = 9 marks]
a) Define the concept of escape velocity.
b) The mass and radius of the Moon are 7.4 × 1022 kg and 1.73 × 106 m, respectively. What is the escape velocity from the surface of the moon?
c) If the mass of the earth is 6.0 × 1024kg and the distance between the Earth and the Moon is
384,400 km, at what distance from the Earth would an object experience zero net gravitational force from these two masses?
Question 9 [2 + 4 + 2 + 2 = 10 marks]
A box of mass m, attached to a spring, oscillates horizontally in simple harmonic motion on a frictionless surface. When it reaches its point of maximum displacement a student places a quantity of sand, also of mass m into the box.
a) How does adding the sand change the frequency and amplitude of oscillation of the system?
b) Given that position of the oscillator obeys the equation x(t) = Acos(wt) show that the total energy of the oscillator is constant.
c) A damping term proportional to the velocity of the box is now switched on. Is the energy of the oscillator still a constant with time? If not, what happens to the oscillator energy?
d) Finally, a time-dependent periodic driving force is applied to the box. If the mass of the box is
100 g and the spring constant is 0.5 N/m, what period should the driving force have in order to make the system resonate?
Question 10 [1 + 1 + 3 + 3 = 8 marks]
A transverse sinusoidal wave is travelling along a string in the positive x-direction i.e. toward the right. The accompanying figure shows a plot of the displacement as a function of position at time t = 0.
Determine:
(a) the amplitude,
(b) the wavelength,
(c) the phase constant, φ 0 .
If the wave speed is v = 12 m/s
(d) find the angular frequency, w
Question 11 [ (1 + 1) + (1 + 1) + (4 + 4) + 4 = 16 marks]
(a) A string of mass per unit length 7.0 × 10一4 kg/m is clamped at both ends and stretched to a tension such that the velocity of waves along it is 320 m/s. If the string is vibrating at a frequency of 240 Hz:
(i) Find a value for the wavelength of this vibration.
(ii) Find a value for the tension in the string.
(b) A train whistle has a power of 250 W and emits sound waves that travel out uniformly in all directions. Assume that the whistle is a point source:
(i) What is the equation for the intensity of the sound as a function of radial distance, R, from the whistle?
(ii) At a distance of 1.5 km from the whistle, what is the intensity of the sound from the whistle?
Potentially Useful Information:
Parts (c) and (d) of this question refer to the following diagram:
(Speed of sound in air = 343 m/s)
(c) Taking the tunnel to be a pipe of length L that is open at both ends:
(i) Sketch the standing wave patterns (for displacement) for the first three harmonics in the tunnel and find a formula for all resonant wavelengths that can be excited in the tunnel.
(ii) If the tunnel has length L = 25.0 m, show that the frequency of the 10th harmonic is f = 68.6 Hz.
(d) A fast train continuously sounds its whistle as it approaches the tunnel. The train driver hears a frequency fs = 55.0 Hz from the whistle. The whistle excites the 10th harmonic in the tunnel,f = 68.6 Hz. Find the speed, v, of the train. (Assume that there is no wind blowing.)
Question 12 [ 3 + 2 + (3 + 3 + 2) = 13 marks]
(a) An electron microscopy study of Carabid beetles (H. E. Hinton and D. F. Gibbs, Journal of
Insect Physiology, vol 15, p 959, 1969) revealed the presence of ridge structures that act as diffraction gratings, giving rise to iridescence. When green light of wavelength 532 nm shines vertically onto the ridge structures the first order diffraction angle is θ = 22。. Find a value for the ridge spacing, d.
(b) In the centre of the shadow of a disk or sphere there is a small bright spot, called the Poisson or
Fresnel bright spot, as shown in the figure below. Briefly explain how this bright spot arises.
(c) An object is located 520 cm from a thin converging lens of focal length f = 50cm as shown in the accompanying figure.
(i) With the aid ofa diagram, show where the image will form.
(ii) Calculate the distance from the lens at which the image is formed
(iii) Calculate the transverse magnification of this image.