Answer Key

Test Your Understanding

Momentum & Impulse

  1. A small model rocket has a mass of 120g (0.120kg). What is its momentum if its speed is 22m/s?
    ANS: M = mv therefore M = 22 x 0.120 = 2.64kg m/s (kilogram metres per second)

  2. A small rocket has a fixed mass m and it is acted upon by a force for a time interval . At the end of the time interval its change in velocity is . (Assume all motion lies in a straight line). Consider the following cases.

    1. ) If everything stays the same, except that the time internal is doubled, then the change in velocity is

      1. unchanged, i.e. .
      2. ANS: doubled (two fold), i.e. 2
      3. tripled (three fold), i.e. 3
      4. quadrupled (four-fold), i.e. 4
      5. one half, i.e. /2

    2. ) If everything stays the same, except that the mass of the rocket is doubled, then the change in speed will be

      1. unchanged, i.e. .
      2. doubled (two fold), i.e. 2
      3. tripled (three fold), i.e. 3
      4. quadrupled (four-fold), i.e. 4
      5. ANS: one half, i.e. /2

    3. ) If everything stays the same, except that the force is doubled, then the change in velocity will be

      1. unchanged, i.e. .
      2. ANS: doubled (two fold), i.e. 2
      3. tripled (three fold), i.e. 3
      4. quadrupled (four-fold), i.e. 4
      5. one half, i.e. /2

    4. ) If everthing stays the same, but the rocket is taken to Mars where its weight is only one third that of its Earth weight, then its change in velocity is

      1. ANS: unchanged, i.e. .
      2. doubled (two fold), i.e. 2
      3. tripled (three fold), i.e. 3
      4. quadrupled (four-fold), i.e. 4
      5. one third, i.e. /3.

  3. Fuel and oxidizer, whose total mass is 875 grams (0.875kg) is ejected downward from a small rocket with a net downward momentum of 3.3kg· m/s. What is the upward velocity attained by the rocket if its mass is 150 grams (0.150kg)?
    ANS: from Mup(rocket) + Mdown(fuel) =0
    we get vr = -Mdown(fuel) /mr = 3.3/0.150 = 22.0m/s

  4. The combusion products of a rocket engine have a total mass of 900 grams (0.900kg) and is ejected downward from a rocket nozzle with a net downward impulse of 5.0Ns. What is the upward velocity attained by the rocket if its mass is 150 grams (0.150kg)? ANS: from Mup(rocket) + Mdown(fuel) =0
    we get vr = -Mdown(fuel) /mr = 5.0/0.150 = 33.3m/s

  5. The combusion products of a rocket engine having a total mass of 1300 grams (1.300kg) is ejected downward from a small rocket with a net downward momentum of 12.0 kg· m/s. What is the upward velocity attained by the rocket if its mass is 220 grams (0.150kg)?
    ANS: from Mup(rocket) + Mdown(fuel) =0
    we get vr = -Mdown(fuel) /mr = 12.0/0.220 = 54.5m/s

  6. Show, by dimensional analysis, that Momentum ( M=mv) has the same units as Impulse ( I=Ft).

  7. A 150 gram rocket experiences an average force of 330N for 35ms. What speed is achieved by the rocket?
    ANS: From mv = Ft, we get v = (Ft)/m.
    therefore v = ( 330 x 35 x10-3)/(150 x10-3) = 77.0m/s.

  8. A 120 gram rocket experiences an average force of 330N for 15ms. What speed is achieved by the rocket?
    ANS: From mv = Ft, we get v = (Ft)/m.
    therefore v = ( 330 x 15 x10-3)/(120 x10-3) = 41.3m/s.

  9. A 240 gram rocket experiences an average force of 330N for 15ms. What speed is achieved by the rocket?
    ANS: From mv = Ft, we get v = (Ft)/m.
    therefore v = ( 330 x 15 x10-3)/(240 x10-3) = 20.6m/s.

  10. A 150 gram rocket experiences an average force of 165N for 35ms. What speed is achieved by the rocket?
    ANS: From mv = Ft, we get v = (Ft)/m.
    therefore v = ( 165 x 35 x10-3)/(150 x10-3) = 38.5m/s.