Quiz: Momentum and Collisions
Test your understanding of momentum and collisions with these 10 questions.
1. What is linear momentum?
- The rate of change of velocity
- The product of an object's mass and velocity
- The force acting on an object
- The energy of a moving object
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The correct answer is B. Linear momentum (p) is defined as the product of an object's mass and velocity: p = mv. It's a vector quantity pointing in the same direction as the velocity. Momentum measures the 'quantity of motion' an object possesses.
Concept Tested: Linear Momentum
2. How does impulse relate to momentum?
- Impulse equals the change in momentum
- Impulse is the same as kinetic energy
- Impulse is the mass times velocity squared
- There is no relationship between impulse and momentum
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The correct answer is A. The impulse-momentum theorem states that impulse (force applied over time) equals the change in momentum: J = FΔt = Δp. This is why airbags work—they increase the time over which the force is applied, reducing the force needed to stop the momentum of an occupant.
Concept Tested: Impulse-Momentum Theorem
3. In a closed system with no external forces, what is conserved?
- Velocity
- Kinetic energy
- Total momentum
- Acceleration
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The correct answer is C. In an isolated system (no external forces), total momentum is conserved and remains constant. This powerful principle allows us to analyze collisions and interactions without knowing all the details of the forces involved. Kinetic energy is not always conserved (only in elastic collisions).
Concept Tested: Conservation of Momentum
4. Two billiard balls collide head-on. Before collision, ball A (1 kg) moves at 4 m/s and ball B (2 kg) moves at 1 m/s toward A. What is the total momentum before collision?
- 1 kg·m/s
- 2 kg·m/s
- 6 kg·m/s
- 2 kg·m/s (considering opposite directions)
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The correct answer is D. Momentum is a vector. Taking the direction of A's motion as positive: p_A = 1 × 4 = 4 kg·m/s. Ball B moves toward A (opposite direction): p_B = 2 × (-1) = -2 kg·m/s. Total momentum = 4 + (-2) = 2 kg·m/s.
Concept Tested: Conservation of Momentum
5. What is the key difference between elastic and inelastic collisions?
- Elastic collisions occur only in space
- In elastic collisions, kinetic energy is conserved; in inelastic collisions, it is not
- Inelastic collisions have faster-moving objects
- Elastic collisions transfer more momentum
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The correct answer is B. In elastic collisions, both momentum and kinetic energy are conserved. Examples include billiard ball collisions and atomic scattering. In inelastic collisions, momentum is conserved but kinetic energy is not—some is converted to heat, sound, or deformation. Most real-world collisions are inelastic.
Concept Tested: Elastic Collisions
6. In a perfectly inelastic collision, what happens to the colliding objects?
- They bounce apart at high speed
- They stick together and move as one object
- They reverse direction completely
- They both come to rest
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The correct answer is B. In a perfectly inelastic collision, the objects stick together and move as a single unit after collision. Maximum kinetic energy is lost (converted to heat, deformation, sound). However, momentum is still conserved: m₁v₁ + m₂v₂ = (m₁ + m₂)v_final.
Concept Tested: Perfectly Inelastic Collisions
7. A 1000 kg car moving at 20 m/s collides with a stationary 1000 kg car in a perfectly inelastic collision. What is their combined velocity after collision?
- 5 m/s
- 10 m/s
- 20 m/s
- 40 m/s
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The correct answer is B. Using conservation of momentum: m₁v₁ + m₂v₂ = (m₁ + m₂)v_final. (1000)(20) + (1000)(0) = (2000)v_final. 20,000 = 2000v_final. v_final = 10 m/s.
Concept Tested: Perfectly Inelastic Collisions
8. What is the center of mass of a system?
- The heaviest point in the object
- The geometric center of an object
- The point where all mass can be considered concentrated for analyzing motion
- The point of maximum density
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The correct answer is C. The center of mass is the point where all the mass of a system can be considered concentrated for analyzing translational motion. For symmetric objects of uniform density, it's at the geometric center. For non-uniform objects or systems of separate masses, it's calculated as a weighted average position.
Concept Tested: Center of Mass
9. A 0.1 kg firework rocket with initial velocity 50 m/s explodes into two fragments of equal mass. One fragment has velocity 80 m/s forward. What is the velocity of the second fragment?
- 20 m/s forward
- 20 m/s backward
- 80 m/s backward
- 30 m/s backward
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The correct answer is A. Initial momentum: p_i = 0.1 × 50 = 5 kg·m/s. After explosion, two 0.05 kg fragments. Using conservation: 5 = (0.05)(80) + (0.05)v₂. 5 = 4 + 0.05v₂. v₂ = 20 m/s (same direction).
Concept Tested: Conservation of Momentum
10. Why does a rocket accelerate forward when it expels gases backward?
- The rocket pushes on the expelled gases
- Conservation of momentum: gases gain backward momentum, rocket gains forward momentum
- The exhaust pushes on the surrounding air
- Gravity provides the forward force
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The correct answer is B. Rocket propulsion is based on conservation of momentum. By Newton's Third Law, the rocket expels gases backward (chemical reaction), and the gases exert an equal and opposite force forward on the rocket. This is why rockets work in space where there's no air to push against.
Concept Tested: Rocket Propulsion