(Perfectly elastic collisions / Nearly elastic collisions / Rocket Propulsions)
In this section, the three interesting points are perfectly elastic collisions, nearly elastic collisions, and rocket propulsions. As an alternative, this section could be slightly revised and titled as “three types of collisions” (elastic, inelastic, and super-elastic). Historically, Wallis investigated perfectly inelastic collisions, Wren and Huygens focused on perfectly elastic objects, whereas Newton included experiments that are in between perfectly elastic and perfectly inelastic (French, 1971).
1. Perfectly elastic collisions:
“…the speeds before and after an elastic collision are equal is not a matter of conservation of momentum, but a matter of conservation of kinetic energy (Feynman et al., 1963, section 10–4 Momentum and energy).”
Feynman explains that the speeds before and after an elastic collision are equal is a matter of conservation of kinetic energy. It is worth mentioning that the total momentum of two objects is conserved whether the collision is perfectly elastic or perfectly inelastic. Importantly, there is a loss of kinetic energy for a brief moment during the impact when the two objects are in contact and both are compressed. Furthermore, both objects have zero velocity (in an inertial frame) when their kinetic energies are converted into potential energies of the elastic bodies. One may add that the internal forces (electromagnetic) cause the objects to decelerate and accelerate during the impact.
Feynman simply mentions that there are various degrees of elasticity, but he did not provide further details. Mathematically, it refers to the coefficient of restitution (e) between colliding objects and it is related to the ratio of the relative velocities of the two colliding objects after and before the collision: e = (v2 – v1)/(u1 – u2) in which the subscripts 1 and 2 refer to the object 1 and object 2 respectively. Physicists may define a perfectly elastic collision (or in short, elastic collision) as one where there is no loss of total kinetic energy after the collision. However, it is possible that the kinetic energies of both objects are converted into elastic potential energy momentarily during the collision.
2. Nearly elastic collisions:
“…between very elementary objects, the collisions are always elastic or very nearly elastic (Feynman et al., 1963, section 10–4 Momentum and energy).”
It is potentially confusing to students that there are so many terms such as “perfectly elastic collisions,” “perfectly inelastic collisions,” “elastic collisions,” “inelastic collisions,” and “nearly elastic collisions.” In general, physics teachers may explain that there is always a conversion of kinetic energy of a ball into thermal energy, elastic potential energy, and sound energy after a collision. On the other hand, Feynman states that the collisions between very elementary objects are always elastic (as an approximation) or very nearly elastic. In the real world, the collisions between atoms or molecules in a gas are said to be not perfectly elastic. For instance, there is a loss of kinetic energy in a collision of gas molecules due to an emission of infrared ray (or light).
Feynman suggests that it is feasible to make colliding bodies from highly elastic materials, such as steel (with carefully designed spring bumpers) such that a collision generates very little heat and vibration. Additionally, nearly elastic collisions are possible for systems that have no internal “gears, wheels, or parts” in which kinetic energy can be transferred. In 1964 (two years after this lecture of Feynman), Norm Stingley invented a toy ball (or Superball) that is made from a type of synthetic rubber instead of steel. Interestingly, Stingley offered the toy ball to his employer, Bettis Rubber Company in California, but it was turned down because it did not seem to be a profitable product. The toy balls are nearly elastic to the extent that they can bounce to about 90% (or up to 92%) of the drop height.
3. Rocket propulsion:
“Rocket propulsion is essentially the same as the recoil of a gun: there is no need for any air to push against (Feynman et al., 1963, section 10–4 Momentum and energy).”
Feynman ends the section by discussing rocket propulsion. He simplifies the calculation by using the law of conservation of momentum to deduce the velocity (v) of a rocket of mass (M) as equal to mV/M in which m represents a small piece of ejected mass that is moving with a velocity V relative to the rocket. Due to the continuous ejection of material, a more accurate equation would be mdV/dt = -vdm/dt.
More important, Tymms (2015) explains that “[t]he rocket effectively works by super-elastic collisions… (p. 131).” Essentially, rocket propulsion is contributed by super-elastic collisions in which the rocket’s kinetic energy is being increased by “explosions” (or chemical energy).
Students may be confused by Feynman’s statement that “there is no need for any air to push against” in order to have rocket propulsion. For example, one may use Newton’s third law to explain that there is an action that pushes the rocket forward (due to air) and a reaction on air (due to the rocket). One need not emphasize that air molecules continuously push the rocket forward, but they mainly move backward. Note that the law of conservation of momentum is more fundamental than Newton’s third law in the sense that it also holds true in quantum mechanics. In Feynman’s tips on physics, Feynman (2006) explains photon propulsion rockets as follows: “the momentum per second thrown out is the force needed to hold the rocket in place, while the energy per second thrown out is the power of the engine generating the photons (p. 88).”
Questions for discussion:
1. How would you define a perfectly elastic collision?
2. How would you explain that collisions in the real world are nearly elastic instead of perfectly elastic?
3. Is the principle of rocket propulsion is related to collisions?
The moral of the lesson: between very elementary objects, the collisions are very nearly elastic because the energy in the form of light or heat radiation could come out of a gas.
References:
1. Feynman, R. P., Gottlieb, & M. A., Leighton, R. (2006). Feynman’s tips on physics: reflections, advice, insights, practice: a problem-solving supplement to the Feynman lectures on physics. San Francisco: Pearson Addison-Wesley.
2. Feynman, R. P., Leighton, R. B., & Sands, M. (1963). The Feynman Lectures on Physics, Vol I: Mainly mechanics, radiation, and heat. Reading, MA: Addison-Wesley.
3. French, A. (1971). Newtonian Mechanics. New York: W. W. Norton.
4. Tymms, V. (2015). Newtonian Mechanics for Undergraduates. London: World Scientific.
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