Cambridge International AS & A Level · 3 · structured
Inertia and two collision outcomes
Inertia and two collision outcomes · Original GioPhysics question with a detailed, mark-by-mark answer guide.
- Demand
- demanding
- Marks
- 11
- Topics
- 3
- Answer
- Complete
All motion is along a straight horizontal track and external impulse during each collision is negligible. Two 1.0 kg trolleys initially have velocities +4.0 and0 m s⁻¹. In trial E their final velocities are0 and+4.0 m s⁻¹. In trial S they stick and move at+2.0 m s⁻¹.
- (a)
Before the collisions, the same 3.0 N resultant force is applied separately to carts of masses 1.0 kg and3.0 kg. Compare their accelerations and explain the meaning of inertial mass.
3 marks - (b)
State the two characteristic conditions for a one-dimensional elastic collision, then use trial E's data to test whether both are satisfied.
4 marks - (c)
For trial S, compare initial/final momentum and kinetic energy. Explain why total energy is conserved although kinetic energy is not.
4 marks
Ready to self-mark?Reveal the detailed answer guide
(a)
Before the collisions, the same 3.0 N resultant force is applied separately to carts of masses 1.0 kg and3.0 kg. Compare their accelerations and explain the meaning of inertial mass.
List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.
- 1
Use a=F/m for each cart.
- 2
Identify the inverse response to mass for fixed force.
- 3
Define mass as the property resisting change in motion.
(b)
State the two characteristic conditions for a one-dimensional elastic collision, then use trial E's data to test whether both are satisfied.
List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.
- 1
State kinetic-energy conservation (1 mark).
- 2
Calculate 8.0 J before and after (1 mark).
- 3
State equal relative approach and separation speeds (1 mark).
- 4
Calculate both relative speeds as 4.0 m s⁻¹ (1 mark).
(c)
For trial S, compare initial/final momentum and kinetic energy. Explain why total energy is conserved although kinetic energy is not.
List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.
- 1
Initialmomentum=1×4=4; final=2×2=4.
- 2
FinalKE=½×2×2²=4 J.
- 3
Identify4 J decrease in kinetic energy.
- 4
Include non-kinetic energy transfers; momentum conservation does not require kinetic-energy conservation.
Complete marking guidance
Use these worked steps alongside the part-by-part answers. They explain the method and mark allocation; they do not add extra marks.
- (a) Use a=F/m for each cart.
- (a) Identify the inverse response to mass for fixed force.
- (a) Define mass as the property resisting change in motion.
- (b) State kinetic-energy conservation (1 mark).
- (b) Calculate 8.0 J before and after (1 mark).
- (b) State equal relative approach and separation speeds (1 mark).
- (b) Calculate both relative speeds as 4.0 m s⁻¹ (1 mark).
- (c) Initialmomentum=1×4=4; final=2×2=4.
- (c) FinalKE=½×2×2²=4 J.
- (c) Identify4 J decrease in kinetic energy.
- (c) Include non-kinetic energy transfers; momentum conservation does not require kinetic-energy conservation.
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