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m 0 m r = e 4 . 48 = 88 . size 12{ { {m rSub { size 8{0} } } over {m rSub { size 8{r} } } } =e rSup { size 8{4 "." "48"} } ="88" "." } {}

Thus, the mass of the rocket is

m r = m 0 88 . size 12{m rSub { size 8{r} } = { {m rSub { size 8{0} } } over {"88"} } "." } {}

This result means that only 1 / 88 size 12{1/"88"} {} of the mass is left when the fuel is burnt, and 87 / 88 size 12{"87"/"88"} {} of the initial mass was fuel. Expressed as percentages, 98.9% of the rocket is fuel, while payload, engines, fuel tanks, and other components make up only 1.10%. Taking air resistance and gravitational force into account, the mass m r size 12{m rSub { size 8{r} } } {} remaining can only be about m 0 / 180 size 12{ size 11{m rSub { size 8{0} } /"180"}} {} . It is difficult to build a rocket in which the fuel has a mass 180 times everything else. The solution is multistage rockets. Each stage only needs to achieve part of the final velocity and is discarded after it burns its fuel. The result is that each successive stage can have smaller engines and more payload relative to its fuel. Once out of the atmosphere, the ratio of payload to fuel becomes more favorable, too.

The space shuttle was an attempt at an economical vehicle with some reusable parts, such as the solid fuel boosters and the craft itself. (See [link] ) The shuttle’s need to be operated by humans, however, made it at least as costly for launching satellites as expendable, unmanned rockets. Ideally, the shuttle would only have been used when human activities were required for the success of a mission, such as the repair of the Hubble space telescope. Rockets with satellites can also be launched from airplanes. Using airplanes has the double advantage that the initial velocity is significantly above zero and a rocket can avoid most of the atmosphere’s resistance.

The space shuttle is launched. It consists of the shuttle orbiter, two solid rocket boosters, and an expendable external tank. It takes off leaving much smoke and fire.
The space shuttle had a number of reusable parts. Solid fuel boosters on either side were recovered and refueled after each flight, and the entire orbiter returned to Earth for use in subsequent flights. The large liquid fuel tank was expended. The space shuttle was a complex assemblage of technologies, employing both solid and liquid fuel and pioneering ceramic tiles as reentry heat shields. As a result, it permitted multiple launches as opposed to single-use rockets. (credit: NASA)

Phet explorations: lunar lander

Can you avoid the boulder field and land safely, just before your fuel runs out, as Neil Armstrong did in 1969? Our version of this classic video game accurately simulates the real motion of the lunar lander with the correct mass, thrust, fuel consumption rate, and lunar gravity. The real lunar lander is very hard to control.

Lunar Lander

Section summary

  • Newton’s third law of motion states that to every action, there is an equal and opposite reaction.
  • Acceleration of a rocket is a = v e m Δ m Δ t g size 12{a= { {v"" lSub { size 8{e} } } over {m} } { {Δm} over {Δt} } - g} {} .
  • A rocket’s acceleration depends on three main factors. They are
    1. The greater the exhaust velocity of the gases, the greater the acceleration.
    2. The faster the rocket burns its fuel, the greater its acceleration.
    3. The smaller the rocket's mass, the greater the acceleration.

Conceptual questions

Professional Application

Suppose a fireworks shell explodes, breaking into three large pieces for which air resistance is negligible. How is the motion of the center of mass affected by the explosion? How would it be affected if the pieces experienced significantly more air resistance than the intact shell?

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mass × acceleration OR Work done ÷ distance
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the difference between virtual work and virtual displacement
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study of matter and energy and an inter-relation between them.
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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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