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Flashcards · AP® Physics 1: Algebra-Based · Unit 4

Unit 4: Linear Momentum flashcards

25 cards on topics 4.1 to 4.4. Pick a topic or study the whole unit.

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4.1 Linear Momentum

What is linear momentum?
p = mv, a vector in the direction of the velocity, measured in kg·m/s. In one dimension give p_x the sign of v_x for the stated axis.
How do you find the momentum of a system?
Take the vector sum of the parts' momenta (signed sum in 1D). Parts moving in opposite directions can cancel, so zero system momentum does not mean nothing moves.
An object's mass and speed both double. How do its momentum and kinetic energy change?
Momentum × 4 (p = mv). Kinetic energy × 8 (K = ½mv²). Doubling speed alone doubles p but quadruples K.
How are kinetic energy and momentum related?
K = p² ÷ (2m).
Does momentum change when a ball bounces back at the same speed?
Yes. Its direction reverses, so p changes even though the speed and kinetic energy are the same.
When does the collision model apply?
When forces between the objects are much larger than the net external force during the brief interaction. Then only the states just before and just after are analysed, treating each object as a point.

4.2 Change in Momentum and Impulse

What is impulse?
J = F_avg Δt, a vector in the direction of the net force, measured in N·s (= kg·m/s). For a varying force it is the area under the force–time graph.
What is the impulse–momentum theorem?
The impulse of the net external force equals the change in momentum: J = Δp = m(v − v₀). For constant mass it is equivalent to F_net = ma.
Take +x towards a wall. A 0.10 kg ball arrives at +5.0 m/s and leaves at −3.0 m/s. What is Δp?
Δp = 0.10 × (−3.0 − 5.0) = −0.80 kg·m/s. Unsigned velocities would wrongly give a change of only 2.0 m/s.
Why do soft landings, airbags and padding reduce injury?
They lengthen the stopping time. The impulse (equal to Δp) stays the same, so the average force F = Δp / Δt is smaller.
What does the slope of a momentum–time graph give?
The net external force. A flat p–t graph means constant momentum, not necessarily at rest.
How do you find the force from the floor during a landing, not the net force?
Find the net force from Δp / Δt, then add the weight: for an upward net force, floor force = net force + mg.

4.3 Conservation of Linear Momentum

When is a system's momentum conserved?
When no net external impulse acts on it. Internal forces have equal and opposite impulses (third law), so they cannot change the total. State which objects form the system.
How do you find the center-of-mass velocity of a system?
v_cm = p_sys / M_total = (m₁v₁ + m₂v₂ + …) / (m₁ + m₂ + …). Weight each velocity by its mass; it is not a plain mean.
A 4.0 kg trolley at rest fires a 0.20 kg beanbag backwards at 6.0 m/s. How fast does the trolley move?
Total momentum stays zero: 4.0 v = 0.20 × 6.0, so v = 0.30 m/s forwards.
Is momentum "lost" to friction?
No. Friction is an external force that transfers momentum to Earth. Your system's momentum changes by the external impulse, but none is destroyed.
How do you apply momentum conservation in two dimensions?
Conserve the x and y components separately: Σp_x and Σp_y are each constant. Set up the equations and reason with them.
Two objects interact only with each other. How are their momentum changes related?
Δp_A = −Δp_B: equal in size, opposite in direction. The lighter object's velocity changes more.

4.4 Elastic and Inelastic Collisions

What is the difference between elastic and inelastic collisions?
Both conserve momentum. Elastic: total kinetic energy is unchanged. Inelastic: total kinetic energy decreases, transformed into thermal energy, sound and deformation.
What is a perfectly inelastic collision?
The objects stick together and move with one velocity: m₁v₁ + m₂v₂ = (m₁ + m₂)v_f. It leaves the least kinetic energy that momentum conservation allows.
A 1.0 kg cart at 4.0 m/s sticks to a 3.0 kg cart at rest. What are the final speed and kinetic energies?
v_f = 4.0 / 4.0 = 1.0 m/s. K before = ½ × 1.0 × 4.0² = 8.0 J; K after = ½ × 4.0 × 1.0² = 2.0 J.
How do you classify a collision as elastic or inelastic?
Compare the system's total kinetic energy, Σ½mv², before and after. Judge the system total, not individual objects; bouncing apart does not by itself mean elastic.
What happens to kinetic energy in an explosion?
It increases, using stored energy such as spring or chemical energy. Momentum is still conserved.
Why can't you use kinetic energy conservation across a sticky collision?
Kinetic energy is not conserved in it. Use momentum conservation for the collision itself, and energy methods only for motion before or after.
A moving cart sticks to an identical cart at rest. What fraction of kinetic energy is transformed?
One half. In general, when m₁ sticks to m₂ at rest, the fraction transformed is m₂ / (m₁ + m₂).

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