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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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Questions & Answers

the meaning of phrase in physics
Chovwe Reply
is the meaning of phrase in physics
write an expression for a plane progressive wave moving from left to right along x axis and having amplitude 0.02m, frequency of 650Hz and speed if 680ms-¹
Gabriel Reply
how does a model differ from a theory
Friday Reply
To use the vocabulary of model theory and meta-logic, a theory is a set of sentences which can be derived from a formal model using some rule of inference (usually just modus ponens). So, for example, Number Theory is the set of sentences true about numbers. But the model is a structure together wit
with an iterpretation.
what is vector quantity
Ridwan Reply
Vector quality have both direction and magnitude, such as Force, displacement, acceleration and etc.
Is the force attractive or repulsive between the hot and neutral lines hung from power poles? Why?
Jack Reply
what's electromagnetic induction
Chinaza Reply
electromagnetic induction is a process in which conductor is put in a particular position and magnetic field keeps varying.
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what is mutual induction?
mutual induction can be define as the current flowing in one coil that induces a voltage in an adjacent coil.
how to undergo polarization
Ajayi Reply
show that a particle moving under the influence of an attractive force mu/y³ towards the axis x. show that if it be projected from the point (0,k) with the component velocities U and V parallel to the axis of x and y, it will not strike the axis of x unless u>v²k² and distance uk²/√u-vk as origin
Gabriel Reply
show that a particle moving under the influence of an attractive force mu/y^3 towards the axis x. show that if it be projected from the point (0,k) with the component velocities U and V parallel to the axis of x and y, it will not strike the axis of x unless u>v^2k^2 and distance uk^2/√u-k as origin
Gabriel Reply
No idea.... Are you even sure this question exist?
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yes it was an assignment question "^"represent raise to power pls
mu/y³ u>v²k² uk²/√u-vk please help me out
An engineer builds two simple pendula. Both are suspended from small wires secured to the ceiling of a room. Each pendulum hovers 2 cm above the floor. Pendulum 1 has a bob with a mass of 10kg . Pendulum 2 has a bob with a mass of 100 kg . Describe how the motion of the pendula will differ if the bobs are both displaced by 12º .
Imtiaz Reply
no ideas
if u at an angle of 12 degrees their period will be same so as their velocity, that means they both move simultaneously since both both hovers at same length meaning they have the same length
Modern cars are made of materials that make them collapsible upon collision. Explain using physics concept (Force and impulse), how these car designs help with the safety of passengers.
Isaac Reply
calculate the force due to surface tension required to support a column liquid in a capillary tube 5mm. If the capillary tube is dipped into a beaker of water
Mildred Reply
find the time required for a train Half a Kilometre long to cross a bridge almost kilometre long racing at 100km/h
method of polarization
What is atomic number?
Makperr Reply
The number of protons in the nucleus of an atom
type of thermodynamics
Yinka Reply
oxygen gas contained in a ccylinder of volume has a temp of 300k and pressure 2.5×10Nm
Taheer Reply

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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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