Grade 11 Science: Physics

In this unit, 'Units, measurement and motion in a straight line', you learn to use dimensions and kinematic equations. You work with exam-style questions and written reasoning. You see it, say it, then do it alone.

• Observe: see, touch, measure or watch a safe demonstration linked to 'Units, measurement and motion in a straight line' and write what you notice.
• Explain: use the key words of the unit to say what is happening and why, in a few lines.
• Use it: use dimensions and kinematic equations. Use a diagram, table or short calculation where it fits.
• Test and conclude: say what evidence supports your answer and what you would change.

Step by step.

1. Step 1, Write dimensions using M for mass, L for length and T for time. Velocity is [L T^-1], acceleration is [L T^-2], and force is [M L T^-2], since force is mass times acceleration. Their SI units are m/s, m/s^2 and newton (kg m/s^2).
2. Step 2, Check a formula by dimensions. In s = ut + (1/2)at^2 the term ut has [L T^-1][T] = [L], and at^2 has [L T^-2][T^2] = [L]. Both match the dimension of s, so the formula is consistent. Dimensions cannot fix pure numbers like 1/2.
3. Step 3, Use the kinematic equations for constant acceleration: v = u + at, s = ut + (1/2)at^2 and v^2 = u^2 + 2as. A car starts from rest with a = 2 m/s^2 for 5 s. Then v = 0 + 2 x 5 = 10 m/s and s = 0.5 x 2 x 25 = 25 m.
4. Step 4, Solve a braking problem. A car at u = 20 m/s decelerates at a = -5 m/s^2 until v = 0. Time t = (0 - 20)/(-5) = 4 s. Distance s = (0 - 400)/(2 x -5) = 40 m. Use v^2 = u^2 + 2as when time is not given.
5. Step 5, Practical: roll a trolley from rest down a 2.0 m ramp and time it with a stopwatch, getting 2.0 s. Then a = 2s/t^2 = 2 x 2.0/4.0 = 1.0 m/s^2. Safety: clamp the ramp, place a stop block at the bottom and keep feet clear. Repeat three times and average.
6. Step 6, Your turn: a stone is dropped from rest from an 80 m height with g = 10 m/s^2. Find the fall time and landing speed. Answer: t = square root of (2 x 80/10) = 4 s, and v = gt = 40 m/s.

Activity. About 40 to 50 minutes of class work, then one short practice task for home. Keep evidence: a timed paper and an error log.

Standard to meet. Use dimensions and kinematic equations: at least 70 percent on an exam-style task, with the method shown.

In this unit, 'Motion in a plane and laws of motion', you learn to use vectors, projectile motion and Newton's laws. You work with exam-style questions and written reasoning. You see it, say it, then do it alone.

• Observe: see, touch, measure or watch a safe demonstration linked to 'Motion in a plane and laws of motion' and write what you notice.
• Explain: use the key words of the unit to say what is happening and why, in a few lines.
• Use it: use vectors, projectile motion and Newton's laws. Use a diagram, table or short calculation where it fits.
• Test and conclude: say what evidence supports your answer and what you would change.

Step by step.

1. Step 1, Resolve a vector into components. A velocity of 10 m/s at 30 degrees above horizontal has v_x = 10 cos 30 = 8.66 m/s and v_y = 10 sin 30 = 5.0 m/s. Two perpendicular vectors of 3 and 4 units add to a resultant of 5 units, by Pythagoras.
2. Step 2, Treat projectile motion as two independent motions. Horizontal speed stays constant and vertical motion has acceleration g = 10 m/s^2 downward. A ball leaves a 45 m high cliff horizontally at 20 m/s. Fall time t = square root of (2 x 45/10) = 3 s.
3. Step 3, Find the range for that cliff ball: x = 20 x 3 = 60 m. For a launch at 20 m/s at 30 degrees from level ground, the flight time is 2u sin 30/g = 2 s, the maximum height is u^2 sin^2 30/(2g) = 5 m, and the range is u^2 sin 60/g = 34.6 m.
4. Step 4, Apply Newton's second law, F = ma. A 1200 kg car with a net force of 3000 N has a = 3000/1200 = 2.5 m/s^2. By the first law, if the net force is zero the velocity stays constant, as when thrust equals drag at steady speed.
5. Step 5, Use free-body thinking. A 5 kg block is pulled by 20 N against 5 N of friction, so the net force is 15 N and a = 15/5 = 3 m/s^2. By the third law, the block pulls back on the rope with 20 N, a force on a different body.
6. Step 6, Your turn: a stone is thrown horizontally at 10 m/s from a 20 m cliff, g = 10 m/s^2. Find the time of fall, the horizontal range and the vertical speed on landing. Answer: t = 2 s, range = 20 m, v_y = 20 m/s.

Activity. About 40 to 50 minutes of class work, then one short practice task for home. Keep evidence: a timed paper and an error log.

Standard to meet. Use vectors, projectile motion and Newton's laws: at least 70 percent on an exam-style task, with the method shown.

In this unit, 'Work, energy, power and systems of particles', you learn to apply conservation of energy and momentum. You work with exam-style questions and written reasoning. You see it, say it, then do it alone.

• Observe: see, touch, measure or watch a safe demonstration linked to 'Work, energy, power and systems of particles' and write what you notice.
• Explain: use the key words of the unit to say what is happening and why, in a few lines.
• Use it: apply conservation of energy and momentum. Use a diagram, table or short calculation where it fits.
• Test and conclude: say what evidence supports your answer and what you would change.

Step by step.

1. Step 1, Calculate work with a force at an angle. A 50 N force at 60 degrees pulls a cart 4 m. W = F d cos 60 = 50 x 4 x 0.5 = 100 J.
2. Step 2, Use the work-energy theorem. A 2 kg block starts at 3 m/s and the net force of 4 N acts for 5 m. Work = 20 J. Initial KE = 0.5 x 2 x 9 = 9 J. Final KE = 29 J, so v = sqrt(2 x 29 / 2) = 5.39 m/s.
3. Step 3, Conserve mechanical energy. A pendulum bob of 0.5 kg is released from a height 0.8 m above its lowest point. mgh = 0.5 x 10 x 0.8 = 4 J. At the bottom v = sqrt(2 x 10 x 0.8) = 4 m/s.
4. Step 4, Conserve momentum in a collision. A 2 kg trolley at 3 m/s hits a stationary 1 kg trolley and they stick. Momentum 6 kg m/s. v = 6 / 3 = 2 m/s. KE before 9 J, after 6 J, so 3 J is lost: inelastic.
5. Step 5, Compute power and centre of mass. A motor lifts 100 kg through 10 m in 20 s: P = mgh/t = 100 x 10 x 10 / 20 = 500 W. The centre of mass of masses 2 kg at x = 0 and 4 kg at x = 3 m is 12 / 6 = 2 m.
6. Step 6, Your turn: a 1 kg ball moving at 4 m/s hits and sticks to a 3 kg stationary ball. Find the final speed and KE lost. Answer: v = 4 / 4 = 1 m/s; KE lost = 8 - 2 = 6 J.

Activity. About 40 to 50 minutes of class work, then one short practice task for home. Keep evidence: a timed paper and an error log.

Standard to meet. Apply conservation of energy and momentum: at least 70 percent on an exam-style task, with the method shown.

In this unit, 'Rotational motion and gravitation', you learn to use torque, angular momentum and Kepler's laws. You work with exam-style questions and written reasoning. You see it, say it, then do it alone.

• Observe: see, touch, measure or watch a safe demonstration linked to 'Rotational motion and gravitation' and write what you notice.
• Explain: use the key words of the unit to say what is happening and why, in a few lines.
• Use it: use torque, angular momentum and Kepler's laws. Use a diagram, table or short calculation where it fits.
• Test and conclude: say what evidence supports your answer and what you would change.

Step by step.

1. Step 1, Define torque: tau = r F sin(theta). A spanner of length 0.25 m is pulled with 40 N at right angles, so tau = 0.25 x 40 = 10 N m. If the pull makes 30 degrees with the spanner, sin 30 = 0.5 and the torque is 5 N m. Longer handles give more turning effect.
2. Step 2, Apply rotational equilibrium: clockwise torques equal anticlockwise torques. A 30 kg child sits 2 m from the pivot of a seesaw, and a 20 kg child balances it at distance x. Then 30 x 2 = 20 x x, so x = 3 m. The weight units cancel on both sides.
3. Step 3, Use conservation of angular momentum, L = I omega. A skater spins at 2 rad/s with I = 3 kg m^2, then pulls in her arms so I = 1.5 kg m^2. With no external torque, omega = 3 x 2/1.5 = 4 rad/s. Smaller I gives faster spin.
4. Step 4, Use Kepler's laws. The second says the line to a planet sweeps equal areas in equal times, so it moves fastest when closest to the Sun. The third says T^2 is proportional to a^3. For a = 4 AU, T^2 = 64 so T = 8 years.
5. Step 5, Apply gravitation: F = GMm/r^2 and g = GM/R^2, so g falls with the square of distance. At the surface g = 9.8 m/s^2. At a height of one Earth radius, r = 2R, so g = 9.8/4 = 2.45 m/s^2.
6. Step 6, Your turn: find the orbital period of a planet at 9 AU from the Sun, and the torque of a 60 N perpendicular force at 0.5 m. Answer: T^2 = 729 so T = 27 years, and tau = 0.5 x 60 = 30 N m.

Activity. About 40 to 50 minutes of class work, then one short practice task for home. Keep evidence: a timed paper and an error log.

Standard to meet. Use torque, angular momentum and Kepler's laws: at least 70 percent on an exam-style task, with the method shown.

In this unit, 'Properties of solids and fluids', you learn to use stress, strain and Bernoulli's principle. You work with exam-style questions and written reasoning. You see it, say it, then do it alone.

• Observe: see, touch, measure or watch a safe demonstration linked to 'Properties of solids and fluids' and write what you notice.
• Explain: use the key words of the unit to say what is happening and why, in a few lines.
• Use it: use stress, strain and Bernoulli's principle. Use a diagram, table or short calculation where it fits.
• Test and conclude: say what evidence supports your answer and what you would change.

Step by step.

1. Step 1, Calculate stress and strain. A steel wire of length 2 m and cross-section 1 mm2 (1e-6 m2) carries a load of 100 N. Stress = 100 / 1e-6 = 1 x 10^8 Pa. Taking Young's modulus of steel as about 2 x 10^11 Pa, strain = 5 x 10^-4. Extension = 5e-4 x 2 = 1 mm.
2. Step 2, Compute pressure in a fluid. In water at depth 5 m, gauge pressure = rho g h = 1000 x 10 x 5 = 5 x 10^4 Pa. With atmosphere 1.0 x 10^5 Pa, absolute pressure is 1.5 x 10^5 Pa.
3. Step 3, Use the continuity equation A1 v1 = A2 v2. Water in a pipe of 4 cm2 at 2 m/s narrows to 1 cm2. v2 = 4 x 2 / 1 = 8 m/s.
4. Step 4, Use Bernoulli's principle P + 0.5 rho v^2 + rho g h = constant. Horizontal pipe: v1 = 2 m/s, v2 = 8 m/s. Pressure drop = 0.5 x 1000 x (64 - 4) = 30000 Pa. Higher speed means lower pressure, as in an aerofoil.
5. Step 5, Surface tension and viscosity: capillary rise h = 2 T cos(theta) / (rho g r). With T = 0.072 N/m, r = 0.5 mm: h = 2 x 0.072 / (1000 x 10 x 0.0005) = 0.0288 m, about 2.9 cm.
6. Step 6, Your turn: find the speed in a 2 cm2 section if a 6 cm2 section has 1 m/s flow. Answer: v = 6 x 1 / 2 = 3 m/s.

Activity. About 40 to 50 minutes of class work, then one short practice task for home. Keep evidence: a timed paper and an error log.

Standard to meet. Use stress, strain and Bernoulli's principle: at least 70 percent on an exam-style task, with the method shown.

In this unit, 'Thermodynamics and kinetic theory', you learn to apply the laws of thermodynamics. You work with exam-style questions and written reasoning. You see it, say it, then do it alone.

• Observe: see, touch, measure or watch a safe demonstration linked to 'Thermodynamics and kinetic theory' and write what you notice.
• Explain: use the key words of the unit to say what is happening and why, in a few lines.
• Use it: apply the laws of thermodynamics. Use a diagram, table or short calculation where it fits.
• Test and conclude: say what evidence supports your answer and what you would change.

Step by step.

1. Step 1, Apply the first law Q = delta U + W. A gas in a cylinder gets 800 J of heat and expands doing 300 J of work. delta U = 800 - 300 = 500 J, so its internal energy increases.
2. Step 2, Do an isothermal process. For 1 mol of ideal gas at 300 K, expanding from 2 L to 4 L, W = nRT ln(V2/V1) = 1 x 8.314 x 300 x 0.693 = 1729 J. delta U = 0 so Q = 1729 J.
3. Step 3, Use the second law and the Carnot engine. An engine runs between 600 K and 300 K. Efficiency = 1 - 300/600 = 50 per cent. If it takes 1000 J from the source it rejects 500 J and does 500 J of work.
4. Step 4, Kinetic theory: average KE per molecule = 3/2 k T. At 300 K, with k = 1.38e-23 J/K: 6.21 x 10^-21 J. The rms speed of nitrogen (M = 0.028 kg/mol) is sqrt(3RT/M) = sqrt(3 x 8.314 x 300 / 0.028) = 517 m/s.
5. Step 5, Use specific heats. For a monatomic gas Cv = 3/2 R = 12.47 J per mol per K and Cp = 5/2 R, ratio gamma 1.67. Heat 2 mol by 20 K at constant volume: Q = 2 x 12.47 x 20 = 499 J.
6. Step 6, Your turn: find the efficiency of a Carnot engine between 500 K and 400 K. Answer: 1 - 400/500 = 20 per cent.

Activity. About 40 to 50 minutes of class work, then one short practice task for home. Keep evidence: a timed paper and an error log.

Standard to meet. Apply the laws of thermodynamics: at least 70 percent on an exam-style task, with the method shown.

In this unit, 'Oscillations and waves', you learn to describe simple harmonic motion and wave speed. You work with exam-style questions and written reasoning. You see it, say it, then do it alone.

• Observe: see, touch, measure or watch a safe demonstration linked to 'Oscillations and waves' and write what you notice.
• Explain: use the key words of the unit to say what is happening and why, in a few lines.
• Use it: describe simple harmonic motion and wave speed. Use a diagram, table or short calculation where it fits.
• Test and conclude: say what evidence supports your answer and what you would change.

Step by step.

1. Step 1, Describe SHM x = A sin(omega t) with A = 0.05 m and period T = 2 s. omega = 2 pi / T = 3.14 rad/s. Maximum speed = A omega = 0.157 m/s and maximum acceleration = A omega^2 = 0.49 m/s2.
2. Step 2, Spring-mass system. m = 0.5 kg and k = 200 N/m. T = 2 pi sqrt(m/k) = 2 pi sqrt(0.0025) = 2 pi x 0.05 = 0.314 s, so f = 3.18 Hz.
3. Step 3, Simple pendulum. L = 1 m gives T = 2 pi sqrt(L/g) = 2 pi sqrt(1/9.8) = 2.01 s. Quadrupling L to 4 m doubles T to 4.01 s.
4. Step 4, Energy in SHM. For the spring system with A = 0.1 m: total energy = 0.5 k A^2 = 0.5 x 200 x 0.01 = 1 J. At x = 0.05 m, PE = 0.5 x 200 x 0.0025 = 0.25 J, so KE = 0.75 J.
5. Step 5, Wave speed v = f lambda. A wave of f = 50 Hz and lambda = 6.8 m travels at 340 m/s. On a string, v = sqrt(T/mu): with T = 100 N and mu = 0.01 kg/m, v = 100 m/s. Fundamental on 1 m string: f = v / 2L = 50 Hz.
6. Step 6, Your turn: find the period of a 0.25 m pendulum (g = 9.8). Answer: 2 pi sqrt(0.25/9.8) = 1.00 s.

Activity. About 40 to 50 minutes of class work, then one short practice task for home. Keep evidence: a timed paper and an error log.

Standard to meet. Describe simple harmonic motion and wave speed: at least 70 percent on an exam-style task, with the method shown.

On the slide: L1 Basic · Pushes and pulls

Notes: Name forces as pushes or pulls and say how they change movement. Notes: roll a toy car down a ramp onto the floor and mark where it stops; learners push it again with a bigger start and compare. Keep the floor clear so nobody trips.

On the slide: L2 Awareness · Energy and simple circuits

Notes: Describe energy stores and build a simple circuit that lights a bulb. Notes: use one 1.5 V cell, one small bulb and two leads; learners draw the loop and say what happens when it is broken. Use only cells or batteries at low voltage, never mains sockets.

On the slide: L3 Foundation · Speed, distance and time

Notes: Calculate speed from distance and time and read a distance-time graph. Notes: practice case is 100 m in 12.5 s, so speed is 8 m/s. Learners time a walked 20 m with a phone stopwatch, repeat three times, find the mean, and then work out the speed.

On the slide: L4 Practitioner · Force, mass and acceleration

Notes: Apply F = ma to find an unknown force, mass or acceleration. Notes: a 1200 kg car with a net force of 3000 N has acceleration 2.5 m/s2. Learners then find the net force when the engine gives 3500 N and drag is 500 N, and check that the answer matches.

On the slide: L5 Specialist · Series and parallel circuits

Notes: Analyse resistor networks using Ohm law and the rules for current and voltage. Notes: 24 ohm and 12 ohm in parallel give 8 ohm, since 1/24 plus 1/12 is 1/8. On 6 V, current is 0.75 A. Check power ratings and keep currents low before building; use a meter to verify.

This course: Grade 11 Science Physics is at this level. Its units include Units, measurement and motion in a straight line; Motion in a plane and laws of motion; Work, energy, power and systems of particles; Rotational motion and gravitation and more.

On the slide: L6 Advanced · Oscillations and waves

Notes: Apply the simple harmonic motion model and solve for period, frequency and energy. Notes: a 0.50 kg mass on a spring of constant 200 N/m has period 2 pi times the square root of 0.0025, about 0.314 s. Learners measure ten swings with a stopwatch and compare, keeping the mass low so it cannot hurt a hand.

On the slide: L7 Super expert · Uncertainty and fitting

Notes: Evaluate measurements and models with uncertainty propagation, fitting and goodness of fit. Notes: a pendulum with L of 1.000 m and T of 2.007 s gives g equal to 4 pi squared L over T squared, 9.80 m/s2. Learners propagate a 0.002 s timing error, plan repeats, and decide if a model is supported. Check clamps and stand stability.