Conservation of Linear Momentum - AP Physics C: Mechanics
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Identify the SI unit for linear momentum.
Identify the SI unit for linear momentum.
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Kilogram meter per second (kg·m/s). Derived from mass (kg) times velocity (m/s).
Kilogram meter per second (kg·m/s). Derived from mass (kg) times velocity (m/s).
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Determine the impulse for a 3 kg object accelerating from 2 m/s to 5 m/s.
Determine the impulse for a 3 kg object accelerating from 2 m/s to 5 m/s.
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$J = 9 , \text{N·s}$. $J = m\Delta v = 3(5-2) = 9 , \text{N·s}$
$J = 9 , \text{N·s}$. $J = m\Delta v = 3(5-2) = 9 , \text{N·s}$
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Calculate the momentum of a 2 kg object moving at 3 m/s.
Calculate the momentum of a 2 kg object moving at 3 m/s.
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$p = 6 , \text{kg·m/s}$. Using $p = mv$: $2 \times 3 = 6$ kg·m/s.
$p = 6 , \text{kg·m/s}$. Using $p = mv$: $2 \times 3 = 6$ kg·m/s.
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What is the effect of longer collision time on force experienced?
What is the effect of longer collision time on force experienced?
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Force decreases as collision time increases. Impulse $J = F\Delta t$ remains constant.
Force decreases as collision time increases. Impulse $J = F\Delta t$ remains constant.
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What is the relationship between force and time in changing momentum?
What is the relationship between force and time in changing momentum?
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Impulse equals force times time. Impulse-momentum theorem: $J = F\Delta t$.
Impulse equals force times time. Impulse-momentum theorem: $J = F\Delta t$.
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Find the final momentum of a 5 kg object initially 10 kg·m/s with 2 m/s velocity change.
Find the final momentum of a 5 kg object initially 10 kg·m/s with 2 m/s velocity change.
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$p_f = 20 , \text{kg·m/s}$. $p_f = p_i + m\Delta v = 10 + 5(2) = 20 , \text{kg·m/s}$
$p_f = 20 , \text{kg·m/s}$. $p_f = p_i + m\Delta v = 10 + 5(2) = 20 , \text{kg·m/s}$
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Calculate the momentum of a 2 kg object moving at 3 m/s.
Calculate the momentum of a 2 kg object moving at 3 m/s.
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$p = 6 , \text{kg·m/s}$. Using $p = mv$: $2 \times 3 = 6 , \text{kg·m/s}$
$p = 6 , \text{kg·m/s}$. Using $p = mv$: $2 \times 3 = 6 , \text{kg·m/s}$
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Calculate the average force if a 5 kg object changes speed by 4 m/s in 2 s.
Calculate the average force if a 5 kg object changes speed by 4 m/s in 2 s.
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$F = 10 , \text{N}$. From $F = \frac{m\Delta v}{\Delta t} = \frac{5 \times 4}{2} = 10$ N.
$F = 10 , \text{N}$. From $F = \frac{m\Delta v}{\Delta t} = \frac{5 \times 4}{2} = 10$ N.
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What determines the change in momentum in a system?
What determines the change in momentum in a system?
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Impulse, or force applied over time. Impulse creates the momentum change.
Impulse, or force applied over time. Impulse creates the momentum change.
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What condition is necessary for momentum conservation in a collision?
What condition is necessary for momentum conservation in a collision?
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No external net forces. Essential requirement for momentum conservation.
No external net forces. Essential requirement for momentum conservation.
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What is the principle of conservation of momentum in a closed system?
What is the principle of conservation of momentum in a closed system?
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Momentum is conserved in a closed system with no external forces. External forces must be absent for conservation.
Momentum is conserved in a closed system with no external forces. External forces must be absent for conservation.
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How does conservation of momentum apply to rocket propulsion?
How does conservation of momentum apply to rocket propulsion?
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Momentum of expelled gas equals momentum change of rocket. Action-reaction pairs conserve total momentum.
Momentum of expelled gas equals momentum change of rocket. Action-reaction pairs conserve total momentum.
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What is the effect of an external net force on a system's momentum?
What is the effect of an external net force on a system's momentum?
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Changes the system's momentum. External net force creates momentum change.
Changes the system's momentum. External net force creates momentum change.
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Calculate the momentum of a 3 kg object at rest.
Calculate the momentum of a 3 kg object at rest.
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$p = 0 , \text{kg·m/s}$. Zero velocity means zero momentum.
$p = 0 , \text{kg·m/s}$. Zero velocity means zero momentum.
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What factor does not affect total momentum in a closed system?
What factor does not affect total momentum in a closed system?
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Internal forces. Internal forces cancel by Newton's third law.
Internal forces. Internal forces cancel by Newton's third law.
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Which type of collision conserves only momentum?
Which type of collision conserves only momentum?
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Inelastic collision. Kinetic energy is lost but momentum conserved.
Inelastic collision. Kinetic energy is lost but momentum conserved.
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Which type of collision conserves both momentum and kinetic energy?
Which type of collision conserves both momentum and kinetic energy?
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Elastic collision. Kinetic energy is also conserved in elastic collisions.
Elastic collision. Kinetic energy is also conserved in elastic collisions.
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What is the relationship between force and time in changing momentum?
What is the relationship between force and time in changing momentum?
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Impulse equals force times time. Impulse-momentum theorem: $J = F\Delta t$.
Impulse equals force times time. Impulse-momentum theorem: $J = F\Delta t$.
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Determine the impulse for a force of 10 N over 2 seconds.
Determine the impulse for a force of 10 N over 2 seconds.
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$J = 20 , \text{N·s}$. Using $J = F\Delta t = 10 \times 2 = 20$ N·s.
$J = 20 , \text{N·s}$. Using $J = F\Delta t = 10 \times 2 = 20$ N·s.
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What is conserved in an isolated system of colliding objects?
What is conserved in an isolated system of colliding objects?
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Momentum. Fundamental conservation law for isolated systems.
Momentum. Fundamental conservation law for isolated systems.
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If two objects have equal but opposite momenta, what is their total momentum?
If two objects have equal but opposite momenta, what is their total momentum?
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Zero. Equal magnitudes cancel each other out.
Zero. Equal magnitudes cancel each other out.
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What is the momentum of a 10 kg mass moving with 0 m/s velocity?
What is the momentum of a 10 kg mass moving with 0 m/s velocity?
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Zero, since velocity is zero. Zero velocity results in zero momentum.
Zero, since velocity is zero. Zero velocity results in zero momentum.
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How is momentum affected by external forces?
How is momentum affected by external forces?
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Momentum changes due to external forces. External forces create momentum change.
Momentum changes due to external forces. External forces create momentum change.
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Calculate the velocity of two 5 kg objects sticking together post-collision, $v_1=3$ m/s, $v_2=0$ m/s.
Calculate the velocity of two 5 kg objects sticking together post-collision, $v_1=3$ m/s, $v_2=0$ m/s.
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$v_f = 1.5 , \text{m/s}$. Perfectly inelastic: $(5)(3) + (5)(0) = (10)v_f$.
$v_f = 1.5 , \text{m/s}$. Perfectly inelastic: $(5)(3) + (5)(0) = (10)v_f$.
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In a two-object system, how does momentum transfer during collision?
In a two-object system, how does momentum transfer during collision?
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Momentum lost by one is gained by the other. Newton's third law applied to momentum.
Momentum lost by one is gained by the other. Newton's third law applied to momentum.
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What is the effect of longer collision time on force experienced?
What is the effect of longer collision time on force experienced?
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Force decreases as collision time increases. Impulse $J = F\Delta t$ remains constant.
Force decreases as collision time increases. Impulse $J = F\Delta t$ remains constant.
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State the formula relating impulse and momentum.
State the formula relating impulse and momentum.
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$J = \triangle p = F \triangle t$. Impulse-momentum theorem relating force and time.
$J = \triangle p = F \triangle t$. Impulse-momentum theorem relating force and time.
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What is impulse in relation to momentum?
What is impulse in relation to momentum?
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Impulse is change in momentum. Impulse equals the change in momentum.
Impulse is change in momentum. Impulse equals the change in momentum.
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Calculate final speed of two 3 kg objects colliding with $v_1=2$ m/s, $v_2=0$ m/s.
Calculate final speed of two 3 kg objects colliding with $v_1=2$ m/s, $v_2=0$ m/s.
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$v_f = 1 , \text{m/s}$. Perfectly inelastic: $(3)(2) + (3)(0) = (6)v_f$.
$v_f = 1 , \text{m/s}$. Perfectly inelastic: $(3)(2) + (3)(0) = (6)v_f$.
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What happens to total momentum when two objects collide in isolation?
What happens to total momentum when two objects collide in isolation?
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Total momentum remains constant. No external forces means momentum is conserved.
Total momentum remains constant. No external forces means momentum is conserved.
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