Key Concepts: Momentum $p = mv$ (kg m/s). Conservation of momentum: total momentum before = total momentum after (in a closed system). Hooke's law: $F = ke$; extension is proportional to force in the linear region. Elastic limit is where this proportionality breaks down.
Section A — Scalars and Vectors
1. State the difference between a scalar quantity and a vector quantity. Give one example of each. [4]
2. Classify each of the following as scalar or vector: speed, velocity, mass, force, distance, acceleration. [3]
Section B — Momentum
3. Write the equation for momentum and state the units. [2]
4. Calculate the momentum of a 1200 kg car travelling at $15\,\text{m/s}$. [2]
5. State the principle of conservation of momentum. [2]
6. A 2 kg ball moving at $5\,\text{m/s}$ collides with a stationary 3 kg ball. After the collision the balls stick together. Calculate the velocity of the combined mass after the collision. [3]
7. A 4 kg trolley moving at $6\,\text{m/s}$ collides with a stationary 2 kg trolley. After the collision the 4 kg trolley moves at $2\,\text{m/s}$ in the same direction. Find the velocity of the 2 kg trolley after the collision. [3]
Section C — Hooke's Law and Elasticity
8. State Hooke's law and write the equation, defining all symbols. [3]
9. A spring extends by 6 cm when a force of 3 N is applied. Calculate the spring constant $k$ in N/m. [3]
10. Using the spring from question 9, predict the extension when a force of 7 N is applied (assuming the elastic limit has not been reached). [2]
11. Describe how a force-extension graph would look for a spring: [3]
a) Below the elastic limit
b) Beyond the elastic limit
c) What happens to the spring when the force is removed if it has not exceeded the elastic limit?
12. Describe a practical to investigate Hooke's law. Include the independent and dependent variables, one control variable, and what graph you would plot. [4]
Total marks: 34
Mark Scheme
1. Scalar: magnitude only, e.g. speed or mass [2]; Vector: magnitude and direction, e.g. velocity or force [2] [4]
2. Scalar: speed, mass, distance [1.5]; Vector: velocity, force, acceleration [1.5] (award 1 mark per correct pair) [3]
3. $p = mv$ [1]; units: kg m/s [1] [2]
4. $p = mv = 1200 \times 15 = 18\,000\,\text{kg m/s}$ [2]
5. The total momentum of a system remains constant [1] provided no external forces act (closed/isolated system) [1] [2]
6. Momentum before = $2 \times 5 + 0 = 10\,\text{kg m/s}$ [1]; total mass after = 5 kg [1]; $v = 10/5 = 2\,\text{m/s}$ [1] [3]
7. Momentum before = $4 \times 6 = 24\,\text{kg m/s}$ [1]; momentum after = $4 \times 2 + 2v = 8 + 2v$ [1]; $8 + 2v = 24$; $v = 8\,\text{m/s}$ [1] [3]
8. Force is proportional to extension (in the linear region) [1]; $F = ke$ [1]; $k$ = spring constant (N/m), $e$ = extension (m) [1] [3]
9. $k = F/e = 3/(0.06) = 50\,\text{N/m}$ [3] (mark for converting cm to m, substituting, correct answer)
10. $e = F/k = 7/50 = 0.14\,\text{m}$ (14 cm) [2]
11. a) Straight line through origin (extension proportional to force) [1]; b) Line curves/becomes non-linear (extension increases faster than force) [1]; c) Spring returns to original length (elastic behaviour) [1] [3]
12. Independent variable: force applied (masses added) [1]; dependent variable: extension [1]; control variable: same spring / temperature [1]; plot force (y-axis) vs extension (x-axis) — straight line through origin shows Hooke's law obeyed [1] [4]