9231 · 3.6
Momentum flashcards
Revision flashcards for Cambridge 9231 Momentum (syllabus 3.6). Flip, recall, then mark a real past-paper question.
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What is linear momentum?
A vector quantity defined as the product of an object's mass and its velocity. Formula: $\vec{p} = m\vec{v}$. The standard unit is kg m s⁻¹.
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State the Principle of Conservation of Linear Momentum.
For a system of interacting bodies, the total linear momentum in any direction is constant, provided no external force acts on the system in that direction.
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What is impulse?
The change in momentum of an object. It is a vector quantity. Formula: $\vec{I} = \Delta \vec{p} = m\vec{v} - m\vec{u}$. Its unit is the newton-second (Ns), which is equivalent to kg m s⁻¹.
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How is impulse related to force?
Impulse is the product of a constant force and the time it acts for ($I = F \Delta t$). For a variable force, impulse is the integral of force with respect to time, which is the area under a force-time graph.
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State Newton's Law of Restitution for direct collisions.
The speed of separation of two colliding bodies is directly proportional to their speed of approach. Formula: Speed of Separation = $e \times$ Speed of Approach.
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What does the coefficient of restitution, $e$, represent?
A dimensionless scalar value ($0 \le e \le 1$) that measures the elasticity of a collision. It quantifies the ratio of relative speed after to relative speed before impact.
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What is a perfectly elastic collision?
A collision in which total kinetic energy is conserved. The coefficient of restitution for such a collision is $e=1$.
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What is a perfectly inelastic collision?
A collision in which the particles coalesce (stick together) and move with a common velocity after impact. This corresponds to the maximum possible loss of kinetic energy. The coefficient of restitution is $e=0$.
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What is a common trap when applying momentum and restitution formulae?
Incorrectly handling signs and directions. Always define a positive direction at the start of the problem and apply it consistently to all velocities. A negative velocity simply means motion in the opposite direction.
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When is momentum conserved but kinetic energy is not?
In any inelastic collision ($0 \le e < 1$). Momentum is conserved as long as the system is closed (no external forces), but kinetic energy is converted into other forms like heat, sound, or deformation.
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How do you apply Newton's Law of Restitution for a collision with a fixed surface (e.g., a wall)?
Treat the fixed surface as a particle of infinite mass with zero velocity before and after the collision. The law simplifies to: Speed of rebound = $e \times$ Speed of approach.
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What is the formula for 'Speed of Approach' for two particles A and B?
If particles A and B are moving towards each other with speeds $u_A$ and $u_B$, the speed of approach is $u_A + u_B$. If they are moving in the same direction with $u_A > u_B$, it is $u_A - u_B$. A general formula is $|u_A - u_B|$.