PHYC10003
Physics 1
Semester 1, 2016 Assessment
Question 1 [ (2+2+1) + (2+2+1) + (2+3+3+2) = 20 marks]
(a) Newton’s 2nd law can be written F = ma or F= dp/dt.
i. Show that both of these equations are equivalent. Outline your reasoning and assumptions.
ii. State the name and explain the meaning of the type of frame in which Newton’s laws are directly applicable.
iii. How much work is done by the net force on (or by) an object moving in uniform circular motion?
(b) An Airbus A380 jet of mass 3 × 108 kg is cruising at a constant speed of 200 m/s, heading due east. A bird is also flying due east at 1.0 m/s directly in the path of the jet. The bird is 30 cm long, and has a mass of 1.0 kg.
After the collision, the pilot notices that the bird appears to be squashed flat and stuck to the front of the airplane.
(i) Show that it takes less than 2 ms for the airplane to squash the bird.
(ii) Calculate the average force exerted by the airplane on the bird during this time period.
(iii) State the average force exerted by the bird on the airplane during this time period.
(c) A student, Benedict, is competing in a race across an open rectangular field. He finds it hard to run in a straight line, and his displacement from the start at (0,0) is subsequently given by
where t denotes time.
i. What is the magnitude of his displacement from the start after 10 s?
ii. The magnitude of his displacement after 10 s is not equal to the magnitude of the distance
he covers in that time. Which is greater? Give reasons for your answer.
iii. What is his speed at t = 10 s?
Another student, Beatrice, starts at the same time. Her displacement is given by:
iv. Write down Benedict’s displacement relative to Beatrice in (i, j) notation.
Question 2 [3+ 3 + 1 + 2 + 3 + 3 = 15 marks]
Shown below is a graph of potential energy versus Δx, the separation of two atoms which could be brought together to form. a molecule. As the atoms are brought closer together, the potential between the atoms can lead to bonding.
a) Sketch the force F between the atoms as a function of the separation Δx. Clearly label your axes and
also include a label stating the relationship between F, the potential energy and the separation.
b) Indicate the region(s) of Δx which represent where the force between the atoms is
i) repulsive and
ii) attractive.
c) Estimate the value Δx for maximum bonding to occur in this molecule.
Alexandra is conducting a gravity experiment in the lift (elevator) of a tall building with her partner Lee. She asks Lee to stand on a weight measuring scale which has been calibrated in newton, not kilogram. They travel between several floors non-stop and the journey takes about 20 seconds. Graphed below are the readings obtained from the scale during this journey.
When the lift begins to move, the reading on scales changes significantly and then settles down to a steady value, until they approach the destination floor where once again it changes.
d) From the graph, determine Lee’s mass.
e) What is the maximum magnitude acceleration of the lift in the first 6 seconds ofthe journey ?
f) In which direction is the lift travelling (up or down)? Explain the reasoning behind your answer.
Question 3 [ (2 + 3 + 2) + (1 + 2 + 3 + 3) = 16 marks]
a) Consider the pulley which is attached to the roof by a bar as shown in the diagram. Two masses m1 and m2 are suspended by rope from this pulley.
Note: There is no friction preventing the pulley from turning and that the pulley, bar and connecting ropes may be considered massless.
DATA: m1 = 3.0 kg, m2 = 6.0 kg
i. Draw a free body force diagram for each of the masses. Use T for the tension in the rope between the two masses.
ii. Calculate the tension T in the rope and the accelerations a1 and a2 of the masses m1 and
m2 respectively. Show your working.
iii. Calculate the tension the bar connecting the pulley to the roof beam. Show your reasoning.
b) A box of mass m is being pulled along a flat surface by a constant force, F, as shown. The force
makes an angle θ to the horizontal. Assume that the force is not sufficient to ever lift the box off the surface and that the surface is frictionless.
i. Write an algebraic equation for the acceleration of the block.
ii. Write an algebraic equation for the normal reaction between the box and the flat surface, N.
The box is now sliding on surface with a coefficient of kinetic friction, μ between the box and the surface.
iii. Show that the acceleration a“ is now given by the expression
iv. Show that the maximum value of a“ , for a constant value ofF occurs when tanθ = μ . (Hint: use calculus
Question 4 [3 + 2 + 2 + 3 + 4 = 14 marks]
A young student is swinging in a circle around a vertical pole on the end of a 10 m rope, as shown in the diagram. The motion of the student traces a circle in the horizontal plane.
a) Sketch and label the physical forces acting on the student (use a free-body diagram).
b) Assuming the student has a mass of 50 kg, calculate the tension in the rope.
c) Calculate the centripetal force acting on the student.
d) Calculate the student’s speed.
Consider now the more general case, where the angle of the rope with the vertical is θ, the student has a mass of m kg and the length of the rope is l .
e) Show that the speed is given by
Question 5 [5 + 2 + 3 = 10 marks]
A thin rod of mass Mrod = 50 g and length L = 20 cm is attached to a small motor and rotated about one end as shown in the diagram below. Each complete revolution takes 6 seconds.
a) Show using calculus that the moment of inertia of the rotating rod described above is MrodL2 /3.
b) Calculate the angular momentum of this rotating rod.
Now consider the case when the rod is rotated about an axis, a distance %L from then end ofthe rod, as shown below.
c) Find or derive, in terms of Mrod & L, an expression for the moment of inertia of the rotating rod.
Note: The moment of inertia of a thin-rod rotated about its centre-of-mass is MrodL2 /12. (You may use the parallel axis theorem in your answer.)
Question 6 [ 2+ (1 + 1 + 1) + 2 + (3 + 2) + 2 + 1 + 2 + 2 = 19 marks]
Mirrors are placed 35,000 m apart on either side of Lake Eyre. A light source/detector combination is placed at the mid-point between the two mirrors at the origin of the stationary reference frame. as illustrated in the accompanying figure. At time t = 0 in the stationary reference frame a light pulse is emitted from the light source.
(a) State the principle of simultaneity.
(b) In the stationary reference frame find the space-time coordinates of the events:
(i) Light pulse arrives at Mirror R,
(ii) Light pulse arrives at Mirror L.
(iii) Light pulses arrive back at Detector (after having reflected from mirrors).
(c) Are the two events, light pulse arrives at mirror R and light pulse arrives at mirror L simultaneous in the stationary reference frame? Explain briefly.
At time t = 0 in the stationary reference frame Speedy Duck happens to be flying past from left to right at a speed of 6.00 × 107 m.s-1 . Speedy Duck is at the origin of her reference frame and at time t, = 0 the light source/detector is passing her position. (Lake Eyre, the mirrors and the light source/detector are moving from right to left at 6.00 × 107 m.s-1 in Speedy Duck’s reference frame.)
(d) In Speedy Duck’s reference frame what are the space-time coordinates of the events:
(i) Light pulse arrives at Mirror R,
(ii) Light pulse arrives at Mirror L.
(e) Conceptually, why do you expect the event light pulse arrives at mirror R to occur before the event light pulse arrives at mirror L in Speedy Duck’s reference frame? Explain briefly.
(f) In Speedy Duck’s reference frame, after reflecting from the mirrors the two light pulses arrive back at the light source/detector simultaneously even though the events described in part (e) are not simultaneous. Briefly explain how this is possible.
In the Stanford Linear Accelerator electrons are accelerated to a final energy of 4.0 × 10-9 J .
(g) Find the value for and the corresponding momentum of the electrons?
Astronomical Data:
|
Body
|
Mean radius of orbit (m)
|
Period
|
Mass(kg)
|
Mean Radius (m)
|
|
Moon
|
3.84×108 (from Earth)
|
27.3 days
|
7.36×1022
|
1.74×106
|
|
Earth
|
1.50×1011
|
1.00 y
|
5.98×1024
|
6.37×106
|
(a) By equating the weight force at the surface of the moon to the corresponding gravitational force show that the gravitational acceleration at the surface of the moon is !m""n = 1.62 !. s -z .
(b) A Cuban professional volleyball player named Leonel Marshall is reported to have a vertical leap of 1.27m from a standing start. How high could he leap on the Moon? (In answering, you may neglect the effects of air resistance on Earth (and on the Moon too!))
More Astronomical Data:
|
Body
|
Mass(kg)
|
|
Mars
|
6.39×1023
|
|
Phobos
|
1.07×1016
|
(c) Phobos is one of the moons of Mars. It is closer to its primary (the planet around which it orbits) than any other planetary moon in the solar system. The radius of its orbit is r = 9.38× 106 m (6000 km above the surface of Mars). Find a value of the orbital period of this fast moving little moon. Express your answer in hours.
Question 8 [(3 + 2) + (2 + 3) = 10 marks]
(a) A simple pendulum hangs from the ceiling of a lift (elevator). For each of the following situations state whether the period of oscillation will increase, decrease or remain the same compared to the lift being stationary. Briefly justify each of your answers.
(i) The lift accelerates downward at 5.0 !. s -z .
(ii) The lift moves downward at a steady speed of 5.0 !. s -: ..
(b) A pan containing beads is mounted on a spring and oscillates vertically in simple harmonic motion as shown in the following figure.
(i) Starting with the equation for the displacement versus time, x (!) = ! cos‘ut + !,, show
that the magnitude of the maximum acceleration of the pan is given by !m"x = “z!.
(ii) If the frequency of oscillation of the pan is 25 Hz find the amplitude of the motion at which the beads will start to lift-off from the pan.
Question 9 [ 1 + 1 + 2 + 3 + 2 = 9 marks]
The figure shows a position versus time graph for a particle of mass 80 g, suspended from a spring, oscillating in simple harmonic motion. Find values for the following quantities:
(a) The amplitude,
(b) The period,
(c) The angular frequency,
(d) The phase constant,
(e) The spring constant.
Question 10 [ (3 + 4) + (3 + 3) + (2 + 3) = 18 marks]
(a) Fi is an opera singer and a bit of a dare devil. He likes to base jump (jump off buildings, cliffs etc with a parachute). He jumps from the top of a building and free-falls vertically away from his dog Do. While he is in free-fall Fi constantly sings a note of B-flat (466.16 Hz).
(i) Briefly explain in the context of the Doppler effect what Do will hear while Fi is in free-fall.
(ii) How fast will Fi be falling when Do hears a note ofA= 440 Hz? Assume that the air temperature is 20。c.
(b) The African Cicada, Brevisana Brevis, has been measured to produce a sound level of 106.7dB at a distance of 50cm from the source.
(i) What intensity does this sound level correspond to?
(ii) What is the power at the source (assuming the cicada is a point source of sound)?
Potentially Useful Information:
(c) Opposite walls of a shower cubicle are parallel and 1.3 m apart. With the aid of diagrams find:
(i) the wavelengths ofthe 1st (fundamental) and 2nd harmonics for standing sound waves in the cubicle, and
(ii) a general formula for the frequencies of the standing waves.
(a) A scientist wants to design a reflection diffraction grating so that for normal incidence of red laser light, λ = 632.8nm , the first order, m = 1 , maximum occurs at an angle of 33。. Find the required groove spacing, d .
(b) A fibre optic cable has a core with a refractive index of 1.44 and a cladding with a refractive index of 1.43. For light incident on the end of the fibre as illustrated in the figure what is the maximum value of θ1 for the light to be guided in the fibre?
(c) A camera is equipped with a convex lens of focal length 10.0 cm.
(i) If a person is 3.0 m from the lens, what will the image distance be?
(ii) If the person is 1.5 m tall, what is the image height?