Physics • Year 11 • Module 2 • Lesson 12
Conservation of Momentum
Build HSC Band 5–6 extended-response technique on applying conservation of momentum, evaluating kinetic energy changes, and assessing whether proposed outcomes are physically possible.
1. Data analysis: bullet–block experiment (Band 5–6)
8 marks Band 5–6
Scenario. A physics student fires a 0.020 kg bullet horizontally into a 4.980 kg wooden block suspended from a string (a “ballistic pendulum”). The bullet embeds in the block and the block–bullet system swings upward. The student measures the height risen by the block–bullet system as h = 0.45 m. Use g = 9.8 m/s².
| Quantity | Symbol | Value |
|---|---|---|
| Mass of bullet | mb | 0.020 kg |
| Mass of block | mB | 4.980 kg |
| Total mass (block + bullet) | M | 5.000 kg |
| Height risen after embedding | h | 0.45 m |
| Initial velocity of bullet | vb | ? |
| Combined velocity immediately after embedding | vf | ? |
Q1. Analyse the ballistic pendulum to determine the bullet’s initial speed. In your response you must:
- Use energy conservation after embedding to find vf (the combined velocity immediately after the bullet embeds).
- Use conservation of momentum during the collision to find the bullet’s initial velocity vb.
- Calculate the kinetic energy of the bullet before the collision and the combined KE immediately after.
- Calculate the kinetic energy lost during the collision and express it as a percentage of the bullet’s initial KE.
- Classify the collision type and explain why the KE loss is especially large in this scenario.
- State one source of experimental error and explain how it would affect the calculated vb.
2. Experimental design — testing conservation of momentum (Band 5–6)
7 marks Band 5–6
Research question. A student claims that “momentum is always conserved in any collision, even when friction is present.” Design a scientific investigation using the equipment available in a Year 11 physics laboratory to test this claim. Equipment available: two dynamics trolleys with Velcro coupling pads, a 2 m air track (frictionless) and a standard laboratory table surface, spring-loaded plunger for launching, ticker-tape timer with power supply, metre ruler, balance.
Constraints: Your investigation must include a comparison between a frictionless surface and a surface with friction (i.e. no air track). You must measure momentum before and after at least one collision on each surface.
Q2. Design the investigation and present it in the format below:
- State a testable hypothesis naming the independent and dependent variables.
- Identify at least two controlled variables and explain why they must be controlled.
- Describe the procedure in at least five numbered steps, including how you will measure trolley velocities using the ticker tape.
- State what result would falsify the claim (and your hypothesis).
- Identify two limitations of the design and one specific improvement.
Q1 — Sample Band 6 response (8 marks), annotated
Step 1 — Find vf using energy conservation after the collision:
At the highest point KE = 0. Energy conservation: ½Mvf² = Mgh → vf = √(2gh) = √(2 × 9.8 × 0.45) = √(8.82) = 2.97 m/s [1 mark].
Step 2 — Find vb using conservation of momentum during the collision:
mbvb + mB × 0 = (mb + mB)vf. 0.020 × vb = 5.000 × 2.97. vb = 14.85/0.020 = 742.5 m/s [1 mark].
Step 3 — KE of bullet before; KE after:
KEbullet = ½ × 0.020 × 742.5² = ½ × 0.020 × 551 306 = 5513 J [1 mark].
KEafter = ½ × 5.000 × 2.97² = ½ × 5.000 × 8.82 = 22.1 J [1 mark].
Step 4 — KE lost and percentage:
KE lost = 5513 − 22.1 = 5491 J.
Percentage = (5491/5513) × 100 = 99.6% of initial bullet KE is lost [1 mark].
Step 5 — Collision classification and explanation:
This is a perfectly inelastic collision — the bullet embeds in the block and they move together with a single final velocity [1 mark]. The KE loss is exceptionally large because the bullet’s mass (0.020 kg) is tiny compared with the block’s mass (4.980 kg). Almost all the bullet’s KE must go into deforming the wood, generating heat, and accelerating the huge combined mass. The combined system requires only 22.1 J to swing to height h, which is a very small fraction of the bullet’s original KE [1 mark].
Step 6 — Experimental error:
One source: air resistance and string mass are ignored; the string exerts a backward component of force as the pendulum swings, meaning some KE is lost to the string, not just the collision. This would cause the measured h to be slightly less than it would be in an ideal pendulum, so vf from the energy equation would be slightly underestimated, and therefore vb from the momentum equation would also be underestimated [1 mark].
Marking criteria summary (8 marks): 1 = vf correctly calculated using ½Mvf² = Mgh; 1 = vb correctly calculated using momentum conservation; 1 = KEbullet correct; 1 = KEafter correct; 1 = KE lost as percentage correctly calculated; 1 = collision classified as perfectly inelastic with justification; 1 = explanation of why KE loss is large (mass ratio argument); 1 = valid experimental error with correct direction of effect on vb.
Q2 — Sample Band 6 response (7 marks), annotated
Hypothesis: If friction acts as an external force during a collision, then total momentum will not be conserved on a rough surface (momentum decreases), whereas total momentum will be conserved on a frictionless air track. IV = surface type (frictionless / rough). DV = total momentum before and after the collision (N s). [1 mark]
Controlled variables: (1) Masses of trolleys — same trolleys in both trials, measured with balance; changes in mass would change momentum even without friction. (2) Initial speed of trolley A — use same plunger compression setting to give the same launch speed for each trial; different speeds would give different initial momenta, confounding comparisons. [1 mark]
Procedure: (1) Measure and record the mass of each trolley using the balance. (2) Air-track trial (frictionless): set up trolley A on the air track with a ticker-tape attached; trolley B stationary at the far end with Velcro coupling facing A. Fire trolley A using the spring plunger and record the tape. Measure the dot spacing before the collision to find vA, and the dot spacing after (combined tape from both trolleys if tape is long enough, or use a second ticker tape on trolley B) to find vf. (3) Calculate pbefore = mAvA and pafter = (mA + mB)vf. Compare. (4) Rough-surface trial: repeat exactly but on the laboratory bench top (no air track), with Velcro coupling. Record both tapes. (5) Calculate pbefore and pafter for the rough surface. Compare with air-track result. Repeat each trial three times and average. [1 mark — 5 clear steps including ticker-tape velocity method]
Falsification: If pbefore = pafter (within measurement uncertainty) on the rough surface, the claim that friction does not prevent conservation of momentum would be supported (not falsified). The hypothesis would be falsified only if there is no statistically meaningful difference in momentum conservation between the two surfaces. [1 mark]
Limitations: (1) Ticker-tape friction: the ticker-tape itself creates additional friction on the bench surface, reducing the trolley’s speed independently of the surface friction — this contaminates the friction comparison. (2) The Velcro coupling may not create a perfectly inelastic collision on the rough surface if the trolleys bounce slightly; this introduces uncertainty in whether vf truly represents a single combined velocity. [1 mark for each limitation = 2 marks]
Improvement: Use a motion sensor (data logger) instead of ticker tape to measure velocities, eliminating tape friction entirely and providing higher precision velocity data at the moment of impact. [1 mark]
Marking criteria summary (7 marks): 1 = testable hypothesis naming IV and DV; 1 = two controlled variables with reasons; 1 = five steps including ticker-tape velocity measurement method; 1 = states what would falsify the claim/hypothesis; 1 = first valid limitation; 1 = second valid limitation; 1 = specific improvement addressing one of the limitations.