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CCEA GCE Physics (1210) · Unit AS 1: Forces, Energy and Electricity
Mini-Lesson

Forces, Energy & Electricity

This mini-lesson covers the whole of CCEA Unit AS 1: physical quantities and units, scalars & vectors, the principle of moments, linear motion and projectiles, Newton's laws, momentum & impulse, work, energy & power, and electricity — current, p.d., e.m.f., resistance, resistivity, internal resistance and potential dividers.

forces & motion energy & power electricity every quantity = a number AND a unit

Work through each screen, answer the questions (several are full A-level calculations) and collect ⭐ stars. Press Start when you are ready.

1.1 Physical quantities

Quantities, base units and prefixes

Every physical quantity is a numerical magnitude together with a unit. All units can be built from six SI base units:

  • kilogram (kg) — mass · metre (m) — length · second (s) — time
  • ampere (A) — current · kelvin (K) — temperature · mole (mol) — amount of substance

Derived units are combinations. For example the newton: since F = ma, 1 N = 1 kg m s−2. The joule: W = Fs, so 1 J = 1 kg m2 s−2.

1 N = 1 kg m s⁻²Checking that both sides of an equation have the same base units is a fast way to spot an error (homogeneity).

Prefixes you must recall: T (1012), G (109), M (106), k (103), c (10−2), m (10−3), µ (10−6), n (10−9), p (10−12), f (10−15). Convert to standard form before substituting: 4.7 kΩ = 4.7 × 103 Ω; 220 µF = 2.20 × 10−4 F.

1.2 Scalars and vectors

Vectors: resolving and adding

A scalar has magnitude only (mass, speed, energy, time). A vector has magnitude and direction (displacement, velocity, acceleration, force, momentum).

A vector F at angle θ to the horizontal splits into two perpendicular components:

Fx = F cos θ  ·  Fy = F sin θResultant of two perpendicular vectors: R = √(Fx² + Fy²), direction tan θ = Fy / Fx
θ F F cos θ (horizontal) F sin θ (vertical)
Components are perpendicular, so they are independent of each other.

Equilibrium: for two or three coplanar forces acting at a point, equilibrium means the vector sum is zero — the force arrows form a closed triangle. Resolve in two perpendicular directions and set each total to zero.

Calculate

Your turn — resolving a force

1A sledge is pulled by a rope with a force of 50 N at 30° above the horizontal. Calculate the horizontal component of the force.
N
Hint: Fx = F cos θ = 50 × cos 30°.
1.3 Principle of moments

Moments, centre of gravity, equilibrium

The moment of a force about a point is the force multiplied by the perpendicular distance from the point to the line of action of the force.

moment = F × d⊥   (N m)Principle of moments: for a body in equilibrium, total clockwise moment about any point = total anticlockwise moment about the same point.

The centre of gravity is the single point where the whole weight of the body appears to act. For a uniform beam it is at the geometric centre — so the beam's weight acts there in your moments equation.

Two conditions for equilibrium: (1) the resultant force is zero (so it does not accelerate); (2) the resultant moment about any point is zero (so it does not rotate). You need both.

Quick check

Is it in equilibrium?

?A rigid body is acted on by three coplanar forces and stays at rest. Which statement must be true?
1.4–1.5 Linear motion & projectiles

Equations of motion and projectile motion

For uniform acceleration in a straight line (u = initial velocity, v = final velocity, a = acceleration, s = displacement, t = time):

v = u + at  ·  s = ut + ½at² v² = u² + 2as  ·  s = ½(u + v)t

On a velocity–time graph the gradient is the acceleration and the area under the graph is the displacement. On a displacement–time graph the gradient is the velocity.

Projectiles. Motion under gravity (ignoring air resistance) is a uniform velocity horizontally combined with a uniform acceleration (g downwards) vertically. The two are independent — the only quantity they share is the time.

Method that always works

Horizontal: a = 0, so x = uxt.

Vertical: a = g = 9.81 m s−2 down, so use the suvat equations with uy.

Find t from the vertical motion, then feed that t into the horizontal equation.

Free-fall experiment (1.4.3): drop a ball through two light gates connected to a computer; software records the time between gates and the gate separation, giving g from the velocities. Repeat and average to reduce random error.

Calculate

Your turn — projectile

2A ball is thrown horizontally at 15 m s⁻¹ from the top of a cliff 20 m high. Take g = 9.81 m s⁻². How far from the base of the cliff does it land?
m
Hint: Vertical: 20 = ½ × 9.81 × t², so t = √(40/9.81) = 2.02 s. Horizontal: x = 15 × t.
1.6 Newton's laws

Newton's three laws

  • First law: a body stays at rest, or moves with constant velocity, unless a resultant force acts on it.
  • Second law: the resultant force is proportional to the rate of change of momentum; for constant mass this gives F = ma.
  • Third law: if body A exerts a force on body B, then B exerts an equal and opposite force on A — same type of force, acting on different bodies.
Fresultant = maF in newtons, m in kilograms, a in m s⁻². Friction and drag are forces that oppose motion, so they subtract from the driving force.

Classic trap: the weight of a book on a table and the normal contact force on the book are not a Newton's third law pair — they act on the same body and are different types of force. The third-law partner of the book's weight is the gravitational pull of the book on the Earth.

Quick check

Spot the third-law pair

?A book rests on a table. Which pair of forces is a genuine Newton's third law pair?
1.7 Momentum & impulse

Momentum, impulse and collisions

Momentum p = mv (kg m s−1) — a vector, so direction and sign matter.

Ft = mv − muImpulse (Ft, in N s) = change of momentum. Newton's second law in momentum form: F = Δp / Δt.

Conservation of linear momentum: in the absence of external forces, the total momentum before a collision equals the total momentum after. This is true for all collisions.

  • Elastic collision — kinetic energy is also conserved.
  • Inelastic collision — kinetic energy is not conserved (some becomes internal energy/sound). Momentum still is.

Confirm it by calculation: work out total ½mv² before and after. If they are equal, the collision was elastic; if the total KE has fallen, it was inelastic. Momentum should balance either way — if it does not, you have a sign error.

Calculate

Your turn — impulse

3A tennis ball of mass 58 g hits a racket at 25 m s⁻¹ and rebounds along the same line at 20 m s⁻¹. The contact lasts 5.0 ms. Calculate the average force on the ball.
N
Hint: Take the rebound direction as positive: Δp = 0.058 × (20 − (−25)) = 0.058 × 45 = 2.61 N s. F = Δp / t = 2.61 / 0.0050.
Sort it

Scalar, vector or base unit?

Tap an item, then tap the box it belongs in.

📏 Scalar quantity

➡️ Vector quantity

🔢 SI base unit

1.8 Work, energy and power

Work, energy, power and efficiency

Work done = force × distance moved in the direction of the force. If the force is at an angle θ to the motion, only the component along the motion does work:

W = Fs cos θΔp.e. = mgΔh  ·  k.e. = ½mv²  ·  work–energy: ½mv² − ½mu² = Fs

Power is the rate of energy transfer:

P = W / t   and   P = Fvefficiency = useful energy (or power) output ÷ total energy (or power) input

Conservation of energy in practice: for an object falling freely, the loss of gravitational p.e. equals the gain in k.e.: mgΔh = ½mv², so v = √(2gΔh) — the mass cancels. Where friction or drag act, some energy is dissipated as internal energy, so efficiency is below 100%.

Quick check

How efficient?

?An electric winch is supplied with 500 J of electrical energy and raises a load, increasing its gravitational potential energy by 150 J. What is the efficiency of the winch?
1.9 Current, charge, p.d. and e.m.f.

Charge, current, potential difference, e.m.f.

Current is the rate of flow of charge:

I = Q / t1 A = 1 C s⁻¹. The charge on an electron is 1.60 × 10⁻¹⁹ C.

Potential difference (p.d.) is the energy transferred from the charge per unit charge as it passes through a component:

V = W / Q   and   V = P / IThe volt is one joule per coulomb: 1 V = 1 J C⁻¹.

E.m.f. (E) is the energy given to each coulomb of charge by the source. It is also measured in volts.

The distinction CCEA wants: e.m.f. = energy converted from another form into electrical energy per coulomb (in the source). P.d. = electrical energy converted out of the circuit per coulomb (in a component). Same unit, opposite direction of energy conversion.

1.10 Resistance and resistivity

Resistance, resistivity and I–V characteristics

R = V / I  ·  P = I²R  ·  R = ρL / ASeries: R = R₁ + R₂ + …   Parallel: 1/R = 1/R₁ + 1/R₂ + …

Resistivity ρ (unit: Ω m) is a property of the material, not the sample: a wire's resistance rises with length and falls with cross-sectional area. To measure it, plot R against L for a wire of known diameter — gradient = ρ / A, with A = πd²/4 from a micrometer reading.

Ohm's law: the current through a metallic conductor is directly proportional to the p.d. across it, provided the temperature is constant.

metal wire (constant T) filament lamp diode IV IV IV
Straight through the origin = ohmic. The lamp curves over (R rises as it heats). The diode conducts one way only, above ~0.6 V.

Thermistor (ntc): as temperature rises, more charge carriers are released, so its resistance falls. A metal does the opposite — hotter ions vibrate more, scattering electrons, so resistance rises. A superconductor below its critical temperature has zero resistivity.

Calculate

Your turn — resistivity

4A wire of length 1.5 m and diameter 0.40 mm is made of a metal of resistivity 1.7 × 10⁻⁸ Ω m. Calculate its resistance.
Ω
Hint: r = 0.20 mm = 2.0 × 10⁻⁴ m, so A = πr² = 1.26 × 10⁻⁷ m². R = ρL/A = (1.7 × 10⁻⁸ × 1.5) / 1.26 × 10⁻⁷.
Quick check

Reading the lamp curve

?The I–V graph for a filament lamp bends towards the V axis as V increases. What does this tell you?
1.11–1.12 Internal resistance & potential dividers

Internal resistance and the potential divider

A real cell has internal resistance r. Some of the e.m.f. is 'lost' driving current through the cell itself (the lost volts, Ir), so the terminal p.d. you actually measure is:

V = E − IrComparing with y = mx + c: plot V (y) against I (x) — the intercept is E and the gradient is −r.

A potential divider uses two resistors in series to tap off a fraction of the supply. Because the same current flows through both, the p.d. splits in the ratio of the resistances:

Vout = Vin × R₂ / (R₁ + R₂)Swap R₁ for an LDR or a thermistor and Vout changes with light level or temperature — the basis of lighting and heating control circuits.

Watch out: connecting a load across R₂ puts it in parallel with R₂, lowering the combined resistance and therefore lowering Vout below the unloaded value. Always combine the parallel pair first, then apply the divider formula.

Calculate

Your turn — internal resistance

5A battery of e.m.f. 12.0 V and internal resistance 0.50 Ω is connected to an external resistor of 5.5 Ω. Calculate the terminal potential difference.
V
Hint: I = E / (R + r) = 12.0 / 6.0 = 2.0 A. Then V = E − Ir = 12.0 − (2.0 × 0.50).
Quick check

Tapping off a voltage

?A 12 V supply is connected across a 4.0 kΩ resistor in series with an 8.0 kΩ resistor. What is the p.d. across the 8.0 kΩ resistor (with no load connected)?
Match it

Match each equation to what it gives you

Tap an item on the left, then its partner on the right.

Equation
What it gives
Recap

Unit AS 1 — the big ideas

Quantities: magnitude + unit; six base units; prefixes T→f; check homogeneity

Vectors: F cos θ and F sin θ; equilibrium = zero resultant force AND zero resultant moment

Motion: suvat; v–t gradient = a, area = s; projectiles = independent horizontal and vertical motion

Newton: F = ma; third-law pairs act on different bodies

Momentum: p = mv; Ft = mv − mu; momentum always conserved, KE only in elastic collisions

Energy: W = Fs cos θ; ½mv²; mgΔh; P = W/t = Fv; efficiency = useful ÷ total

Electricity: I = Q/t; V = W/Q; R = V/I; R = ρL/A; V = E − Ir; potential divider VinR₂/(R₁+R₂)

Press Finish to see your score.

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