Elastic and Inelastic Collisions · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Checking momentum and energy in collisions

Science · Forces & Motion · ages 17-18
Name ______________________   Date ____________

  1. What defines an elastic collision?

    • Both objects leave at the same final speed
    • Total kinetic energy is unchanged
    • Total momentum increases

  2. For two colliding objects, net external impulse during impact is negligible. Which total is approximately unchanged in both elastic and inelastic collisions?

    • Total momentum
    • Total kinetic energy
    • Sum of speeds

  3. Objects must stick together for a collision to be inelastic.

    Circle one:   True   False

  4. A 2 kg trolley at +3 m/s hits a stationary 1 kg trolley. After impact, their velocities are +1 and +4 m/s, respectively. Net external impulse is zero. Treat the data as exact. Calculate total KE before and after. How is the collision classified?

    • Inelastic, with a gain in total KE
    • Elastic, with no change in total KE
    • Inelastic, with a decrease in total KE

  5. Right is positive. A 2 kg trolley at +5 m/s collides with a 1 kg trolley at -2 m/s. Net external impulse is zero. The 2 kg trolley leaves at +1 m/s. What is the signed final velocity of the 1 kg trolley, in m/s?

    Answer: ______________

  6. Total kinetic energy decreases during an inelastic collision. Which statement describes a possible transfer of that energy?

    • It may heat or deform objects, or become sound
    • It is destroyed during impact
    • It becomes momentum without any other energy change

  7. Right is positive. Two 2 kg trolleys move at +2 and -2 m/s. Tom says zero total momentum means zero total kinetic energy. Which calculation checks his claim?

    • Each trolley has -4 J, giving a total of -8 J
    • Each trolley has 4 J, giving a total of 0 J
    • Each trolley has 4 J, giving a total of 8 J

  8. A 2 kg trolley moving right at 6 m/s hits a stationary 4 kg trolley and sticks. Net external impulse is zero. Use momentum to find their shared speed, then calculate the decrease in total kinetic energy. Enter only the decrease, in J.

    Answer: ______________

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Answer key

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Checking momentum and energy in collisions W1-mt_JMwUuh1YUq-s1

  1. Total kinetic energy is unchanged · An elastic collision conserves the sum of the objects' kinetic energies. Their individual speeds can change.
  2. Total momentum · Negligible net external impulse leaves total momentum approximately unchanged. Kinetic energy need not stay the same.
  3. False · Objects can bounce apart in an inelastic collision. Sticking together is the special case called perfectly inelastic.
  4. Elastic, with no change in total KE · KE before is 0.5 × 2 × 3² = 9 J. Afterward it is 0.5 × 2 × 1² + 0.5 × 1 × 4² = 1 + 8 = 9 J. Equal totals mean elastic.
  5. 6 · Initial momentum is +10 - 2 = +8 kg m/s. The 2 kg trolley carries +2 afterward, leaving +6 kg m/s for the 1 kg trolley: +6 m/s.
  6. It may heat or deform objects, or become sound · The decrease can increase internal energy through heating or deformation, or transfer energy away as sound. Energy is not destroyed.
  7. Each trolley has 4 J, giving a total of 8 J · The momenta +4 and -4 kg m/s cancel. Both squared velocities equal 4, so each trolley has 4 J of kinetic energy. Their total is 8 J.
  8. 24 · Momentum is 12 kg m/s and joined mass is 6 kg, giving 2 m/s. KE decreases from 36 J to 12 J. The decrease is 24 J.
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