HSC Physics Blackbody Radiation

A tutorial sheet of questions on the blackbody radiation follows.

1. An iron bar is heated in a flame. Describe the energy released by the bar at a certain temperature.
2. Does a heated iron bar produce a continuous, line emission spectrum, absorption spectrum or a combination of these?
3. When a hydrogen discharge tube releases light a series of characteristic wavelengths can be observed. Does the gas produce a continuous spectrum as well?
4. What is a black body? Is a blackbody a perfect absorber, a perfect emitter of radiation or both?
5. What actually is the black body? Is it the high temperature walls of a container, the gas inside the container or a small hole in the wall of the container?
6. A blackbody has its kelvin temperature doubled. Is more energy released at each wavelength?

IB Physics Circular Aperture Diffraction

Tutorial questions on HL Topic 9.4 are given below.

1. In the equation 𝜽=1.22⋋/b, what does 𝜽 represent? ( The Rayleigh resolution criterion states that two point sources of equal intensity can just be resolved with a diffraction-limited optical device with a circular aperture if they are separated in angle by 1.22⋋/b radians, where b is the diameter of the aperture collecting light and ⋋ is the wavelength of the light. The central image of a point source is of angular radius 𝜽 and is called the Airy disc containing 84% of the energy in the image.)
2. The images of two stars seen through a telescope are just resolved when yellow light is used. Will the images of these stars be seen as distinct when red light is used? (No. Red light increases the diameter of the Airy disc in an image so the Airy discs of each star will overlap more and the images are not resolved. The angle subtended by the stars at the telescope is the same. To obtain greater image resolution the wavelength must be reduced to produce narrower non-overlapping Airy discs in each image.)
3. Two stars in a binary star system subtend an angle of 2.0 x 10^-4 ° at the Earth. The stars are observed through a telescope in yellow light of wavelength 580 nm. Find the minimum diameter of the telescope that allows the star images to be resolved. (20.0 cm)
4. Two star images are just resolved when the wavelength of light is ⋋ and the diameter of the telescope is b. Find the diameter of the telescope that can just resolve the star images in light of wavelength 1.5⋋. (1.5b)
5. Two star images are just resolved when the wavelength of light is ⋋ and the diameter of the telescope is b. Find the wavelength of the light that can just resolve the images of these stars if a telescope of diameter b/4 is used. (⋋/4)
6. Remember. Angular separation of stars = 𝜽, for resolution 𝜽 ≧ 1.22 ⋋/b

IB Physics Air Resistance is Small (but not negligible)

Most textbook problems state that air resistance, the drag force on a projectile due to friction as it moves through a fluid medium, is to be neglected. A tutorial sheet of “show that” questions for the case where the drag force is small compared to the weight are given below. All questions give approximate solutions, correct to the first order in k/m, where k is a small positive number called the drag constant and m is the mass of the particle.

1. A particle of mass m falls vertically from rest through air. If the drag force is given by f_d = -k v, where v is the speed of the object, show that the distance fallen at time t is given by s = 1/2 gt²( 1 - kt/(3m) ).
2. A particle of mass m falls vertically from rest through air. If the drag force is given by f_d = -k v², where v is the speed of the object, show that the distance fallen at time t is given by s = 1/2 gt²( 1 - gkt²/(6m) ).
3. A particle of mass m is projected at a speed u at an angle 𝛼 to the horizontal in air where the drag force is proportional to the velocity vector of the particle, f_d = -k v⃗, where k is a small positive constant. Show that the time taken to reach the highest point is given by t = u sin𝛼/g - k u²sin²𝛼/(2mg²).
4. A particle of mass m is projected at a speed u at an angle 𝛼 to the horizontal in air where the drag force is proportional to the velocity vector of the particle, f_d = -k v⃗, where k is a small positive constant. Show that the path of the projectile is y = x tan𝛼 - g x²sec²𝛼/(2u²) + k/m( x²sin𝛼/(2ucos²𝛼) - 2/3x³/(ucos𝛼)³ )

IB Physics Projectile Thrown from a Cliff

The maximum range of a projectile on the horizontal level of its projection (neglecting air resistance) occurs when the angle of projection to the horizontal is 45°. A more difficult problem is when the point of projection is above the horizontal plane on which the object lands. A tutorial sheet of difficult “show that” problems is given below.

1. A projectile is thrown at an angle 𝜽 to the horizontal at a speed u from a vertical height h. Show that the horizontal range of the projectile is u²/(2g)( sin2𝜽 +√(sin²2𝜽 +8ghcos²𝜽/u²) ).
2. A projectile is thrown at a speed u from a height h above horizontal ground. Show that the angle of projection to the horizontal for maximum range on the ground is tan^-1√ (u²/(u²+2gh) ).
3. A projectile is thrown at a speed u from a height h above horizontal ground. Show that the maximum range of the projectile is u/g√(u²+2gh).
4. A projectile is thrown from a vertical height above the ground and maximum range occurs when the angle of projection to the horizontal is 𝜽. Show that the angle (in the maximum range case only) at which the projectile strkes the horizontal is 90° - 𝜽.

Mathematical Tripos Dynamics and Relativity 2021

Below are my answers to the 2021 MT Part 1A Dynamics and Relativity questions.

1. 3C, t = m₀( 1 - e^-V₀/U)/α
2. 4C, I_zz = M( a² + b² )/3
3. 9C, V_e² = 2λF₀/m, escapes if V_e ≥V₀, T = 8λ/( V_e√(1 - V₀²/V_e²) ) sin^-1(V₀/V_e)
4. 10C, (c) (i) C=2 (ii) √( k/r₁) √ ( Cr₂/(r₁ r₂) - 1 ), √( k/r₂) √ ( Cr₁/(r₁ r₂) - 1 ) (iii) Use dA/dt = h/2, t = πab/h, t² = π²a b²/(k(1-e²)) = π²a³/k = π² (r₁ + r₂)³/(8k)
5. 11C (ii) 𝜽 = 0, 𝜽 = cos^-1(g/⍵²R), 𝜽 = 𝜋 provided g < ⍵²R. In this case 𝜽 = 0 and 𝜽 = 𝜋 are unstable and the period of small oscillations about 𝜽 = cos^-1(g/⍵²R) is 2𝜋/⍵ ✕ 1/√(1 - g²/(⍵⁴R²)). If g > ⍵²R there is equilibrium when 𝜽 = 0 and 𝜽 = 𝜋. In this case 𝜽 = 0 is stable with a period of small oscillations 2𝜋/⍵ ✕ 1/√( g/(⍵²R) -1) )and 𝜽 = 𝜋 is unstable. If g = ⍵²R there is equilibrium when 𝜽 = 0 and 𝜽 = 𝜋. In this case the period of oscillations about 𝜽 = 0 is expressible in terms of a complete elliptic integral of the first kind and 𝜽 = 𝜋 is unstable. (iii)Force has perpendicular components N (towards the center of the circle) and Q (into the page). N = m(gcos𝜽 + ⍵²Rsin²𝜽 + R𝜽̇²), Q = 2mR⍵𝜽̇. F=√(N² + Q²).
6. 12C a = 1/(ɣm)( F - F·v v/c² ), v = cqEt/√( c²m² + q²E²t² ). As t → ∞ , v → c.

IB Physics Two Masses and a String

A tutorial sheet with problems involving two masses connected by a string is given below.

A 2.0 kg block and a 3.0 kg block are tied to the ends of a light inextensible string. Find the tension in the string in each case.

1. The blocks are released from rest with the 3.0 kg hanging below the 2.0 kg.
2. The blocks are released from rest with the 2.0 kg hanging below the 3.0 kg.
3. The blocks are pulled along a smooth horizontal surface by a force of 1.0 N applied parallel to the surface acting on the 2.0 kg block.
4. The blocks are at rest on a rough horizontal surface of coefficient of static friction 0.4. A force of 1.0 N parallel to the surface is applied to the 2.0 kg block.
5. The blocks are at rest on a rough horizontal surface of coefficient of static friction 0.4. A force of 3.0 N parallel to the surface is applied to the 2.0 kg block.
6. A smooth pulley is at rest in the laboratory. The string is passed over the pulley and the blocks are released from rest.
7. In question 6 the axle of the pulley accelerates upwards uniformly at 2.0 m s^-2.
8. In question 7 what must be the acceleration of the pulley if the blocks stay at rest relative to each other?

IB Physics Omega in Simple Harmonic Motion

Many good Physics students are confused when ⍵ is used in simple harmonic motion (SHM) questions. How can something moving in a straight line have an angular velocity ⍵? In SHM it is best to call ⍵ the angular frequency of the motion. SHM is the projection of uniform circular motion (UCM) onto a diameter of the circle.

1. In Physics what is the name of the quantity that has the symbol ⍵?
2. What is the SI unit for ⍵?
3. Imagine that an object is moving in uniform circular motion (UCM) of radius 1.0 m and period 2.0 s. You are watching the object from the side and the object appears to be moving in simple harmonic motion. (a) what is the amplitude of the SHM? (b) what is the period of the SHM? (c) what is the angular velocity of the UCM? (d) what is the angular frequency of the SHM? (1.0 m, 2.0 s, 𝜋 rad s^-1, 𝜋 rad s^-1).
4. The radius r of the circular path of a particle moving in UCM is the amplitude x₀ of the image of the particle moving in SHM in a straight line along a diameter of the circle.
5. The angle turned through in a time t by a particle moving in UCM is 𝜽 = ⍵t.
6. The displacement of a particle from the equilibrium position in SHM is the component of the radius vector in UCM along the direction of the SHM. If at t=0, x=x₀ then x = x₀ cos(⍵t). If at t=0, x=0 and the particle is moving in the positive direction then x = x₀ sin(⍵t). If at t=0, x=0 and the object is going in the negative direction then x = -x₀ sin(⍵t).
7. The speed of a particle moving in UCM is given by v = ⍵r. In SHM the velocity is the component of the UCM velocity vector along the direction of the SHM. If at t=0, x=x₀ then v = -⍵x₀ sin(⍵t). If at t=0, x=0 and the object is moving in the positive direction then v = ⍵x₀ cos(⍵t). If at t=0, x=0 and the object is moving in the negative direction then v = - ⍵x₀ cos(⍵t).

IB SL Physics Poorly Answered Questions 3

The third sheet of SL Physics questions on areas that are not well answered is given below.

1. In a longitudinal wave what are the ray directions and direction of the wavefront? What are these directions for a transverse wave?
2. A string of length 40 cm is fixed at each end and set oscillating in its fundamental mode. What is the phase difference between two points on the string that are 25 cm part?
3. A particle is moving in simple harmonic motion. Sketch a graph showing the momentum of the particle versus its speed.
4. When two waves interfere constructively what is the ratio of the intensity produced by the two waves interfering constructively to the intensity due to one of the waves only?
5. An ammeter and a voltmeter are connected in series with a cell of emf 12 V connected to a 2 Ω resistor. What is the reading on each meter?
6. An electron is accelerated from rest between two electrodes a distance d apart and the final kinetic energy of the electron is X eV. If the electodes are now placed a distance 2d apart the final kinetic energy of the electron is (a) X/√2, (b) X/2 (c) X (d) 2X
7. A mass is placed on the end of a light rod of length L and is made to revolve in a vertical plane at a constant speed. At what point in the path is the force exerted by the rod on the mass maximum?
8. Two resistors P and Q are made of the same material and are at the same temperature. P has twice the length of Q and one half the diameter of Q. If the resistance of Q is 2 Ω, find the resistance of P and Q when they are connected in parallel.

IB SL Physics Poorly Answered Questions 2

A sheet with SL questions that are not well answered is given below.

1. The average speed of a hydrogen atom at -23 °C is v. Determine the average speed of a helium atom at -148 °C. (v/√8)
2. The increase in volume ∆V of a solid when it is heated is proportional to both its volume V and change in temperature ∆T. What is the SI unit for the constant of proportionality?
3. The energy stored in a stretched spring is E. What is the work done in doubling the extension of the spring? (3E)
4. A simple pendulum of mass m is oscillating through an angle of 40°. What is the magnitude of the resultant force acting on the mass at the top of its swing? (mgcos20)
5. A car starts from rest and moves in a straight line with uniform acceleration a. Draw a graph showing the distance travelled every second versus the total time taken.(straight line, gradient a, y-intercept -a/2)
6. On another planet a ball is released from rest and falls 2.0 m in the third second of its movement. What is the gravitational field strength of this planet? (0.8 N kg^-1)
7. A stationary firework of mass M explodes into pieces of mass 3M/4 and M/4. The kinetic energy of the smaller piece is E. What is the kinetic energy of the larger piece? (E/3)
8. A car moves at a constant speed v around a circular track. What is the magnitude of the change in velocity of the car after travelling through an angle of 60°? (v)

IB Physics Motion in a Vertical Circle

A sheet of vertical circle problems is given below.

1. A mass m is tied to a string of length L and hangs vertically at rest. The mass is given an initial horizontal speed u. What is the initial acceleration of the mass?
2. A mass on a string is released from rest swings as a simple pendulum. What is the speed of the mass when its vertical drop is ∆h?
3. A mass m is placed on the end of a light rigid rod of length r and made to move in a vertical circle at a constant speed v. Is the magnitude of the acceleration of the mass a constant value of v²/r? (no, this is the radial component of the acceleration only)
4. In the previous question draw a free-body diagram if the radius to the mass makes an angle 𝜽 with the vertical when 𝜽 < 90°. Show that the force exerted on the mass by the rod has a component mgsin𝜽 perpendicular to the rod and a component mv²/r - mgcos𝜽 parallel to the rod.
5. In the previous question at what angle to the vertical is the force exerted by the rod maximum? (180°)

IB Physics Spring Problems

A sheet testing Physics concepts involving a mass on a spring is given below.

1. At a certain instant a mass on a spring has zero velocity. Must it have zero acceleration?
2. An object on a spring has zero acceleration at a certain instant. Must it have zero velocity?
3. A mass on a spring is at rest. Is there no force acting on the mass?
4. Is the tension in a spring equal to the resultant force acting on the mass?
5. State Hooke's law (be careful).
6. A mass moves in SHM on a spring. Is the speed of the mass at the instant it passes through the equilibrium position the same as the average speed during one oscillation?
7. A mass M is placed on a spring of constant k that hangs vertically. If the mass is released from rest does the mass fall a distance Mg/k before coming to rest?
8. A block of mass M rests on a smooth horizontal surface. A spring of force constant k connects the block to a wall on the left. On the right a constant horizontal force F pulls on the block. Is the extension of the spring F/k when the block comes to rest?
9. A mass M is on a smooth horzontal table. Two identical springs, one on the left and one on the right, are connected to the mass. The other end of each spring is held at rest. If the mass is displaced a small amount in the line of the springs and released, what is the period of the oscillations? Each spring has a spring constant k.
10. A spring has a spring constant k. The spring is cut in half. What is the spring constant of each section?
11. A 2.0 kg mass slides from rest down an inclined plane of angle of elevation 30°. After travelling 4.0 m the mass encounters a spring of spring constant 100 Nm^-1. Find the maximum compression of the spring if (a) the incline is smooth, (b) the coefficient of friction between the mass and the plane is 0.20. ((a) 0.989 m, not 0.885 m (b)0.783 m)
12. In question 11 (b) determine the compression of the spring when the mass eventually comes to rest. (8.6 cm, from Tipler Physics 2nd edition page 220)

IB Physics Pulling Apart a Hydrogen Atom

1. When a hydrogen atom is ionised does the mass decrease, stay the same or increase?

2. When an electron “jumps down” to its ground state does the mass of the hydrogen atom decrease, stay the same or increase?

3. When an electron “jumps up” from its ground state to its first excited state does the mass of the hydrogen atom decrease, stay the same or increase?

4. Is the mass of a hydrogen atom equal to the mass of a proton plus the mass of an electron?

5. Imagine that a proton and an electron link to form a hydrogen atom. Is energy released or absorbed in the process? In what form is the energy change?

6. Is the proton in the hydrogen atom the same as a free proton?

7. In the Bohr theory of the hydrogen atom the speed of the electron in the ground state is v. What is the speed of the electron in the first excited state?

8. In the Bohr theory of the hydrogen atom the energy of the ground state is E. What is the energy of the first excited state?

9. How can the hydrogen atom have a negative energy?

10. The ground state energy of the hydrogen atom is -13.6 eV. A potential difference is applied to some hydrogen gas in a discharge tube. Will an applied voltage of 3.4 V cause the gas to emit light?

See Resnick and Halliday, Basic Concepts in Relativity and Early Quantum Theory , second edition, page 113

IB HL Physics Capacitors

1. Where does the charge “go” when a capacitor discharges?

2. Where does the energy “go” when a capacitor discharges?

3. Is there an electric field between its plates when a capacitor discharges?

4. Is there a magnetic field between its plates when a capacitor discharges?

5. Is I = dq/dt correct when a capacitor discharges?

6. Two charged capacitors are placed in series. Does the equation on page 11 of the Physics Data Booklet apply in this case?

IB HL Physics Misunderstood Concepts 2

Below are some HL questions on concepts that are not well understood.

1. A metallic surface is irradiated with infrared radiation and photoelectrons are emitted from the surface. This radiation is replaced by ultraviolet light of the same intensity. How does this affect the kinetic energy of the emitted photoelectrons and their rate of release?
2. A mass m is tied to a string and revolves in a circular path of radius R in a vertical plane. What is the least total energy of the mass if it is to maintain its circular motion?
3. A train has a whistle of frequency f. The train moves to the east at a constant speed v. Another train also has a whistle of the same frequency and this train moves to the west at a constant speed v. What is the frequency of the sound heard on the train moving to the west?
4. The diameter of a nuclide of mass number 2A is 3r. What is the radius of a nuclide of mass number 3A?
5. A mass m has a total energy E when it moves in simple harmonic motion of amplitude A on a spring. What is the total energy of the motion if a mass m is added and the amplitude is increased by 50%?
6. A wind farm consisting of 65 turbines, each of power 15 MW, would generate the same amount of energy as a typical nuclear plant of 975 MW. True or false? (reference, Physics World, March 2011)
7. Which is closest to the efficiency of commercial solar panels made of silicon that are used on rooftops, 20%, 50%, 75%, 100%? (reference, Physics World, April 2021)

IB Physics Relativity

A common examination response is that a rapidly moving object is observed to be contracted in length as it passes an observer. Is this correct? No. The observed overall length of a far away object is the same and it is seen to be rotated with the back of the object visible to the observer and is seen as red shifted. The below extract from Electromagnetic Fields and Waves by Lorrain, Corson and Lorrain (3rd edition, 1988) p254 summarises this.

"Suppose one looked through a telescope at a far-away cube moving at a velocity v≅c perpendicular to the line of sight. Then the face normal to the line of sight would appear to be foreshortened in the direction of motion by the factor 1/ɣ. Also one would see the trailing face for the following reason. At a given instant, the eye senses the photons that arrive at that instant. Photons originating from distant parts of the object have left earlier than others and the object has moved in the meantime. The net effect is that the cube would appear to be rotated through an angle arctan(v/c). If the cube were not far away, then it would appear distorted in peculiar ways, depending on its distance and velocity. This effect, which never has been observed, was discovered by James Terrell in 1959, 54 years after the publication of Einstein's first paper on relativity."

IB SL Physics Poorly Answered Questions 1

Below are 6 questions encountered in IB SL Physics that are poorly answered. Can you do them?

1. A motor is used to lift a load by a rope passing over a pulley. The output power of the battery supplying the motor is 60 W. If in a time interval of 2.0 min the load gains 3.0 kJ of energy and friction in the pulley releases 0.5 kJ of energy, determine the efficiency of the motor. Neglect air resistance.
2. A stationary closed vertical cylinder of mass M, cross sectional area A and length L contains N particles of an ideal gas at a kelvin temperature T and pressure P. The cylinder sits on an digital balance. Determine an expression for the reading on the balance.
3. A particle is moving in SHM on a spring with total energy E on a smooth horizontal table. The amplitude of the motion is x₀. Determine, in terms of E only, the work done by the spring when the extension of the spring changes from 3x₀/4 to x₀/2.
4. Sketch a graph showing the speed of a particle moving in SHM in terms of the displacement from the equilibrium point.
5. A buoy floating in the ocean moves in simple harmonic motion of period 20 s. Which of the following energy resources can cause this oscillation? tidal motion, wind energy, solar energy.
6. One ampere is now defined using which of the following natural constants? e, h, c, k_B, f_Cs, N_A, K_cd .

IB HL Physics Poorly Answered Questions 1

Below are 11 questions encountered in IB HL Physics that are poorly answered. Can you do them?

1. The current in the primary coil of an ideal transformer having 200 turns in the primary coil and 120 in the secondary coil is a sine function of period 2.0 s and phase angle 𝜋/2. Draw the current-time graph for the secondary coil from t=0 to t=2.0 s.
2. Photoelectrons are being emitted from a metal surface. Light of the same intensity but higher frequency now shines on the metal. Does the rate of photoelectron emission stay the same, decrease or increase?
3. The initial activity of a radioactive substance is known. The half-life is required to be found. Can the half-life be found if the mass remaining at a later time is measured?
4. A coil spins at a constant rate of 2.0 rads^-1 in a uniform magnetic field. The average electrical power due to ohmic heating in the coil is 40 W. Draw a graph showing the electrical power versus time for one complete rotation of the coil. Initially the plane of the coil is perpendicular to the magnetic field lines.
5. A stationary vertical cylinder of cross sectional area A and length L contains N particles of an ideal gas at a kelvin temperature T and pressure P. The mass of the gas is M. What is the force exerted by the gas on the base of the cylinder?
6. Two stars are observed through a telescope. The images are just resolved when a yellow filter is placed over the telescope. Are separate images seen when the yellow filter is replaced by a red filter? Why?
7. Two parallel wires of lengths 1.0 m and 2.0 m carry currents of 2.0 A and 1.0 A in opposite directions in a vacuum respectively. If the magnitude of the electromagnetic force acting on the shorter wire is 2.0 mN determine the magnitude and direction of the electromagnetic force acting on the longer wire.
8. The air column in a pipe is vibrating in its second harmonic. Are the nodes always at the centre of a compression?
9. A single electron atom has 4 energy levels. In terms of energy values, the lower two energy levels are close together and the top two levels are very close together. Draw the emission spectrum of this atom labelling the longest wavelength transition.
10. A weight W is suspended from the roof by two strings of equal length. When one of the strings is suddenly cut the initial tension in the remaining string (a) always increases (b) always decreases (c) always stays the same (d) can stay the same
11. One kilogram is now defined in terms of which of the following natural constants? e, c, h, k_B, f_Cs, N_A, K_Cd

IB Physics Where do Magnetic Fields Come From?

A tutorial sheet of questions, from SL, HL and the Relativity topic is given below.

S is a reference frame at rest relative to the laboratory. S' is another reference frame moving at a constant non-zero velocity relative to S.

1. An electron is at rest in S. Is there an electric field in S? Is there a magnetic field in S?
2. An electron is at rest in S'. Is there an electric field in S'? Is there a magnetic field in S'?
3. An electron is at rest in S. Is there an electric field in S'? Is there a magnetic field in S'?
4. A uniform magnetic field B acts along the X axis in S. There is no electric field in S. S' moves parallel to the X axis of S. Is there an electric field in S'? Is there a magnetic field in S'?
5. A uniform magnetic field B acts along the X axis in S. There is no electric field in S. S' moves parallel to the Y axis of S. Is there an electric field in S'? Is there a magnetic field in S'?
6. A uniform electric field E acts along the X axis in S. There is no magnetic field in S. S' moves parallel to the X axis of S. Is there an electric field in S'? Is there a magnetic field in S'?
7. A uniform electric field E acts along the X axis in S. There is no magnetic field in S. S' moves parallel to the Y axis of S. Is there an electric field in S'? Is there a magnetic field in S'?
8. Two electrons each move at a constant velocity v along parallel paths. In S' the electrons are always on the Y axis at a distance d apart. (a) what are the forces between the electrons in S? (b) what are the forces between the electrons in S'? (c) is the magnitude of the force between the electrons the same in each reference frame?

What is an electron?

Particle or wave? Here is a quote from a textbook describing what an electron “is”.

1. Giancoli, Physics 5th edition page 837. We might ask ourselves: "What is an electron?" The early experiments of J. J. Thomson indicated a glow in a tube that moved when a magnetic field was applied. The results of these and other experiments were best interpreted as being caused by tiny negatively charged particles which we now call electrons. No one, however has actually seen an electron directly. The drawings we sometimes make of electrons as tiny spheres with a negative charge on them are merely convenient pictures (now recognized to be inaccurate). Again we must rely on experimental results, some of which are best interpreted using a particle model and others the wave model. These models are mere pictures that we use to extrapolate from the macroscopic world to the tiny microscopic world of the atom. And there is no reason to expect that these models somehow reflect the reality of an electron. We thus use a wave or a particle model (whichever works best in the situation) so that we can talk about what is happening. But we shouldn't be led to believe that an electron is a wave or a particle. Instead, we could say that an electron is the set of its properties that we can measure. Bertrand Russell said it well when he wrote that an electron is a "logical construction".

IB Physics Challenging Mechanics Questions

A tutorial sheet of difficult mechanics questions is given below.

1. A ball rolls horizontally from a table of height 2.0 m. On collision with the smooth horizontal floor the kinetic energy of the ball is reduced by one-half. At what speed does the ball leave the table if it strikes a vertical wall 1.0 m from the table at a height of 1/3 m above the floor? (0.75 m/s, 1.20 m/s, 1.92 m/s)
2. Adapted from the Moscow Physics Problems (MPP) 1986-2005, 1.15. A projectile moves horizontally at 10.0 ms^-1 at a height above the ground of 30.0 m. When it is 25.0 m from a vertical wall it explodes and disintegrates into many fragments flying in all directions and all having an initial speed of 20.0 ms^-1 relative to the projectile. Find the area on the surface of the wall that will be hit by the debris. Assume that fragments hitting the ground do not bounce and ignore air resistance. ( 4673.91 m² , x axis along initial direction of motion, max height on wall z = 50.19 m, hits wall at ground level at y = 61.75 m, g = 9.81 m s^-2 )
3. In the previous question the wall is not present. Determine the area on the ground that can be struck by debris from the explosion. (1.8007 ha, on x axis debris lands 104.14 m ahead and 28.73 m behind explosion point)
4. In question 3 determine the time interval during which debris is hitting the ground. ( 4.08 s )
5. In question 3 the explosion occurs at a vertical height of 30.0 m over an inclined plane of angle of elevation 20°. Determine the area on the incline on which debris lands. ( 1.1801 ha, debris lands a maximum 70.92 m ahead and 46.38 m behind, on the incline measured from the perpendicular to the plane through the explosion point )