Collisions

Learn the models, terms, and applications of collisions.

Lesson 3 of 32 parts Practice Flashcards

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Concepts and Models

Objective: Explain the concepts and assumptions used in collisions.

Analyze a collision by defining a system and checking external impulse. A perfectly inelastic collision leaves objects moving together; conserve momentum but generally not kinetic energy. An ideal elastic collision conserves both momentum and kinetic energy. For a one-dimensional elastic collision between equal masses with one initially stationary, velocities exchange. Real collisions can involve rotation, deformation, sound, and heating; a sticking-cart calculation is a stated idealization rather than a universal rule.

Formulas

$v_stick=(m1v1+m2v2)/(m1+m2)$
elastic collision: K and p conserved under the model

Worked examples

Try itA 3 kg cart at 6 m/s sticks to a stationary 2 kg cart. Neglect external impulse. Find final velocity.Show answer

1. Conserve momentum, not kinetic energy for a sticking collision. 2. v_f=3×6/(3+2)=3.6 m/s.

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Concepts and Models

Objective: Explain the concepts and assumptions used in collisions.

Formulas

$v_stick=(m1v1+m2v2)/(m1+m2)$
elastic collision: K and p conserved under the model

Worked examples

Try itA 3 kg cart at 6 m/s sticks to a stationary 2 kg cart. Neglect external impulse. Find final velocity.Show answer

1. Conserve momentum, not kinetic energy for a sticking collision. 2. v_f=3×6/(3+2)=3.6 m/s.

Applications and Worked Problems

Objective: Apply collisions to calculations, evidence, and specified situations.

For the application problems, define the system and list the quantities supplied before choosing a relation. Use v_stick=(m1v1+m2v2)/(m1+m2); elastic collision: K and p conserved under the model. The relation must match the stated conditions. Convert to compatible units before substitution, preserve intermediate precision, and report the requested quantity with its unit or sign. When comparing alternatives, check the defining condition rather than a superficial word match. The worked examples below show the setup and calculation separately.

Formulas

$v_stick=(m1v1+m2v2)/(m1+m2)$
elastic collision: K and p conserved under the model

Worked examples

Try itA 3 kg cart at 6 m/s sticks to a stationary 2 kg cart. Neglect external impulse. Find final velocity.Show answer

1. Conserve momentum, not kinetic energy for a sticking collision. 2. v_f=3×6/(3+2)=3.6 m/s.

Try itCarts of 3 kg at +1 m/s and 2 kg at −6 m/s stick. Find final velocity.Show answer

1. Add signed initial momenta. 2. v_f=(3×1−2×6)/(3+2)=-1.8 m/s.

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