PHYC10003

PHYSICS 1

SESSION 2

TUESDAY 12 JUNE 2018

Question 1 [3 + 5 + 4 + 2 = 14 marks]

The starship Enterprise has a mass of 3.0×106 kg. It captures an abandoned vessel belonging to the Romulan Star Empire that has a mass of 1.0×104  kg. The Enterprise uses a “tractor beam” that applies a constant attractive force of 2.0×104 N to the alien vessel to bring it inside its cargo bay.  Both the Enterprise and the alien vessel are initially at rest in deep space and separated by 10 km.

a) What are the accelerations ofthe Enterprise and the alien vessel?

b) How far has the Enterprise moved relative to its initial position when the alien vessel has been brought into the cargo bay?

c) How fast is the alien vessel moving relative to the Enterprise when it enters the cargo bay?

d) Does the alien vessel safely enter the cargo bay of the Enterprise? Explain why, using at least one physics concept.

Question 2                [6 + 3 + 3 + 2 = 13 marks]

The planet Tralfamadore is populated by autonomous machines that enjoy playing ball games. One of these machines throws a ball that follows a parabolic trajectory. At time t = 0 s, the vertical position of the ball is given by y = 0 and the horizontal position by x = 0. At time t = 1 s, the ball reaches a height of y = 4 m and the ball’s velocity, v, is given by

v = (2.0 i + 2.0j) ms-1

where i andj are unit vectors in the x- and y-direction, respectively.

a)   What is the value of the gravitational constant, g, near the surface ofTralfamadore?

b)   What was the magnitude of the initial velocity of the ball?

c)   At what angle, θ, to the horizontal was the ball launched?

d)   What is the mass ofTralfamadore ifits equatorial radius is 5234 km?

Question 3          [(2 + 2 + 3 + 5) + (3 + 2) = 17 marks]

a)  Suppose that the co-efficient of kinetic friction of the hard rubber of an automobile tyre sliding on the road surface is 0.80 and that the co-efficient of static friction is 0.90.

(i)  What is the deceleration of the automobile on a flat surface if the driver brakes suddenly locking the wheels?

(ii) What is the maximum deceleration possible if the driver avoids locking the wheels?

(iii) The driver now wishes to park the car on a street with a steep slope. What is the steepest slope of the street on which the car can be parked (with wheels locked) without slipping? Give your  answer in degrees with zero degrees being a flat surface.

(iv) Many cars are now fitted with antilock braking systems. Describe, in no more than 200 words (approx. 1 page), how these systems work. Why do they make driving safer?

b) In February 1955, a paratrooper fell 370 m from an airplane without being able to open his parachute, but happened to land in snow, suffering only minor injuries. Assume that his speed upon impact was 56 m/s, that his mass including gear was 85 kg, and that the magnitude of the force on him from the snow was at the survivable 1.2 ×  105 N.

(i)  What is the minimum depth of snow that would have stopped him safely?

(ii) Calculate the magnitude of the impulse from the snow.

Flywheels are large wheels, usually very heavy, that are used to store energy. They can be brought to   their maximum rotational speed quite slowly, but the energy that is stored in them can be accessed and used very quickly in applications that require high power delivered over a short time.

A particular industrial flywheel has a diameter of 1.5 m and a mass of 250 kg. Assume that all of the mass is located near the outside circumference of the wheel. Its maximum angular velocity is 1200 rpm (revolutions per minute).

a)   A small motor spins the flywheel by exerting a constant torque of 50 Nm. How long does it take to reach its maximum angular velocity?

b)   How much energy is stored in the flywheel?

c)   The motor is disconnected and the spinning flywheel is connected to a machine that will utilise the energy stored in the flywheel. Half of the energy is delivered in 2.0 s. What is the average power delivered by the flywheel to the machine?

d)   What is the torque exerted by the flywheel on the machine?

Question 5              [5 + (4 + 2) = 11 marks]

a) The ballistic pendulum was used to measure the speeds of bullets before electronic timing devices were developed. In one version, a large block of wood of mass M = 0.54 kg was suspended from two long cords. A bullet of mass m = 9.5 g is fired into the block coming quickly to rest. The block of wood (with the embedded bullet) swings upward to a height of h = 6.3 cm.

Calculate the initial speed of the bullet just before it hits the block.

b) The figure below shows the potential energy of a diatomic molecule (a two-atom system like H2 or O2), which is given by the equation;

where r is the separation of the two atoms of the molecule and A and B are positive constants. This potential energy is associated with the force that binds the two atoms together.

(i)  Find the equilibrium separation—that is, the distance between the atoms at which the force on each atom is zero.

(ii)  Is the force repulsive (the atoms are pushed apart) or attractive (they are pulled together) if their separation is (1) smaller and (2) larger than the equilibrium separation?

Question 6            [4 + 3 + 1 + 1 = 9 marks]

Discuss, in about one page, the process of precession. Your answer should include:

(i) The conditions under which precession occurs,

(ii) The physical factors that determine the rate of precession of a body,

(iii) An example in which the phenomenon of precession is observed and

(iv) A practical application of precession.

Question 7                     [ 3 + 2 + 2 + 2 + 2 + 2 + 4 = 17 marks]

(a)     Briefly explain the term “relativity of simultaneity” .

(b)     State Einstein’s Principle of Special Relativity.

(c)     Define proper time.

(d)     On a plot of linear momentum, p, versus speed, u, compare the relationship between p and u in a classical Newtonian viewpoint to that in Special Relativity.

The following figure shows a moon/planet system. In the reference frame of the moon/planet system the moon and planet are 4.00×108  m apart. At time tp   = 0 s a microwave pulse is emitted from the surface of the moon just as a starship travelling from left to right at a speed of 0.6c passes the moon. At time te   =  1.5 s in the moon/planet reference frame an explosion occurs on the planet. The moon is at the origin of the moon/planet reference frame and the starship is at the origin of its reference frame. In the starship’s reference frame t/  = 0 s as the moon passes the starship.

In moon/planet reference frame.

(i)  At time tp = 0 s microwave pulseemitted from moon

(e)     Is it possible that the arrival of the microwave pulse at the planet triggered the explosion? Explain briefly.

(f)      In the moon/planet reference frame. what are the space-time coordinates of the explosion? (Assume that the y and Z coordinates of the explosion are 0.)

(g)     In the reference frame of the starship what are the space-time coordinates of the explosion? (Assume that the y /  and Z /  coordinates of the explosion are 0.)

Question 8               [ 5 + 3 + 3 = 11 marks]

Astronomical Data:

(a)  A particular insect called the Spittle Bug is reported to be able to jump to a height of 60 cm. If   the Spittle Bug can do this on Earth find a value for how high the Spittle Bug could jump on the Moon?

(b) The Sun rotates on its axis approximately every 26 days. Calculate the radius ofa

“heliosynchronous” orbit; that is, an orbit that stays over the same spot on the Sun’s surface.

(c)  Find a value for the radial distance from the centre of the Earth where the magnitude of the gravitational potential is 1/8 th of its value at the surface?

Question 9              [ 3 + (6 + 2) = 11 marks]

(a)     A sand pendulum consists ofa funnel shaped object filled with sand and  suspended from a long string (not shown) as depicted in the diagram. As the pendulum swings back and forth in simple harmonic motion the sand gradually falls from the base of the funnel through a small hole in the bottom. Predict what will happen to the period of oscillation of the pendulum as mass is gradually lost. Explain briefly. You may assume that the mass of the string is negligible and ignore the effects of air resistance.

(b)   A pan containing beads is mounted on a spring and oscillates vertically in simple harmonic motion as shown in the following figure.

(i)      If the frequency of oscillation of the pan is 60 Hz find

the amplitude of the motion at which the beads will start to lift-off the pan. Show your reasoning and working.

(ii)     At what point in the motion will this occur? Explain your reasons for your answer.

Question 10             [ (1 + 2 + 2 + 2 + 3) + (1 + 4 + 2) = 17 marks]

(a)     A transverse wave on a string, of mass per unit length 11 g m-1, has a displacement given by:

Find values for the following:

(i)      the wave amplitude,

(ii)     the wavelength,

(iii)    the period,

(iv)    the wavespeed,

(v)     the string tension.

(b)     Polly the parrot is being held captive in a cage with a door made of crystal. By tapping on the

crystal door with her beak Polly has been able to determine that the natural resonant frequency of the crystal is 800 Hz. The highest frequency squawk Polly can achieve is 793 Hz but at one time   she belonged to a Physics professor so Polly knows about the Doppler effect.

(i)      Will Polly have to fly toward or away from the cage door to Doppler shift her squawk to match the resonant frequency of the crystal?

(ii)    Find a value for how fast Polly will have to fly so that her Doppler-shifted squawk matches

the resonant frequency of the crystal. Assume that the speed of sound is 343 ms-1.

(iii)   If the sound intensity level needed to break the crystal door is 110 dB and Polly wants to be able to break the door from a distance of 1.2 m, find a value for the power in Watts of her squawk that will be required to achieve this. You may assume that Polly is a point source of sound.

Question 11 [ 2 + (3 + 3) + (3 + 3 + 3 + 2) =19 marks]

(a)      In the centre of the shadow of a disk or sphere there is a small bright spot, called the Arago or Poisson spot, as shown in the figure below. Briefly explain how this spot arises.

(b)

(i)      Describe with reference to Huygens’ principle why light incident on a single slit will show a diffraction pattern.

(ii)     A laser of wavelength 600 nm is incident on a circular aperture of radius 100 micrometres and is then projected onto a screen a distance of 1 metre away. What is the width of the central brightness maximum?

(c)        A converging lens has a focal length of 10 cm. An object is placed at a distance of 3 cm from the lens

(i)      Define the distinction between a real and a virtual image

(ii)     Use ray tracing to find the location of the image.

(iii)    Calculate the distance to the image. Is it real or virtual?

(iv)    Calculate the transverse magnification of the image.