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Rocket Propulsion

Rocket Propulsion

Edited By Vishal kumar | Updated on Jul 02, 2025 05:33 PM IST

The propulsion of a rocket is an example of momentum conservation. In a rocket, gases at high temperatures and pressure, are produced by the combustion of fuel. They escape with a large constant velocity through a nozzle. The large backward momentum of the gases imparts an equal forward momentum to the rocket. However, due to the decrease in the mass of the rocket fuel system, the acceleration of the rocket keeps on increasing.

Rocket Propulsion
Rocket Propulsion

This concept belongs to the laws of motion which is an important chapter in Class 11 physics. It is not only essential for board exams but also for competitive exams like the Joint Entrance Examination (JEE Main), National Eligibility Entrance Test (NEET), and other entrance exams such as SRMJEE, BITSAT, WBJEE, BCECE and more. Over the last ten years of the JEE Main exam (from 2013 to 2023), two questions have been asked on this concept. And for NEET no direct questions were asked from this concept.

What is Rocket Propulsion?

Let us assume a rocket of total initial mass (rocket + fuel) m0, starts moving upward due to the thrust force of the fuel jet. Assuming the velocity of the fuel jet with respect to the rocket to be u (assumed to be constant for this discussion) in a vertically downward direction and the mass of jet fuel emerging out of the rocket per unit time to be dmdt. Let the velocity of rocket after t time of motion be v and the acceleration of the rocket be a in vertically upward direction.

Thrust on the Rocket


F=−udmdt

Where F= Thrust
dmdt= rate of ejection of the fuel

u=velocity of exhaust gas with respect to rocket

m=mass of the rocket at time t

The net force on rocket-


Fnet =−udmdt−mg∗F=−udmdt[ if gravity neglected ]

Acceleration of Rocket (a)

a=−umdmdt−g

If g is neglected then
a=−umdmdt

Instantaneous Velocity of Rocket (v)

If g is neglected then-

a=−umdmdtdvdt=−umdmdt∫0vdv=−u∫m0m1mdm⇒v=uloge⁡(m0m)v=u∗loge⁡(m0m)=2.303u∗log10⁡(m0m)

Burnt Speed of Rocket

  • It is the speed attained by the rocket when complete fuel gets burnt.

  • It is the maximum speed attained by the rocket

  • Formula

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Vb=Vmax=uloge⁡(m0mr)
Vb→ burnt speed
mr→ residual mass of empty container

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Solved Example Based On Rocket Propulsion

Example 1: A rocket with a lift-off mass 3.5×104 kgis blasted upwards with an initial acceleration of 10 m/s2. Then the initial thrust of the blast is:

1) 3.5×105 N
2) 7.0×105 N
3) 14.0×105 N
4) 1.75×105 N

Solution:

Rocket Propulsion

dmdt= rate of ejection of the fuel
* Thrust on the rocket
F=−udmdt−mg
F= Thrust
∗F=−udmdt[ if gravity neglected ]

wherein

The negative sign indicates the direction of thrust is opposite to the direction of the gases.

Initial thrust = (Lift-off mass) $\times$ (a + g)

=(3.5×104)×(20)=7×105 N

Hence, the answer is option (2).

Example 2: A rocket of mass 1000 Kg set for vertical firing the exhaust speed is 200 m/s to give on initial acceleration of 15 m/s^2 what will be the amount of gas ejected per second (in Kg/s ) to supply the needed thrust (g = 10 m/s )

1) 125

2) 100

3) 150

4) 75

Solution:

Acceleration of Rocket

a=umdmdt−ga=umdmdt [If g is neglected]

wherein

Instantaneous Velocity of Rocket

v=uloge⁡(m0m)−gt
m∘→ Initial mass of Rocket

Force applied by the gases on the rocket =vdmdt

vdmdt−mg=madmdt=m(g+a)v=1000(10+15)200=125Kg/s

Hence, the answer is option (1).

Example 3: If the maximum possible exhaust velocity of a rocket is 2 Km/s, calculate the ratio m0mr for it to require the escape velocity of 11.2 km/s after starting from rest (approx) [ m0→ initial velocity, mr→ mass of emptied rocket]

1) 270

2) 300

3) 350

4) 200

Solution:

Given

Maximum relative velocity of fuel, u=2000m/s,

Escape velocity of rocket vb=11.2km/hr=11200m/s,

Neglecting the effect of gravity, the expression for the speed of rocket-

Vb=Vmax =uloge⁡(m0mr)mr→ residual mass of empty container Vb=2.303ulog⁡(m0mr)11.2=2.303×2×log10⁡(m0mr)log10⁡(m0mr)=11.22.303×2=2.432(m0m)=antilog(2.432)=270.4

Hence, the answer is the option (1).

Example 4: A spaceship in space sweeps stationary interplanetary dust. As a result, its mass increases at a rate dM(t)dt=bv2(t) where v(t) is its instantaneous velocity. The instantaneous acceleration of the satellite is:

1) −2bv3M(t)
2) −bv3M(t)
3) −bv3(t)
4) −bv32M(t)

Solution:

As given,

dM(t)dt=bv2(t)

As we know,

F=d(Mv)dt

So,
F=Mdvdt+vdMdtF=M(dvdt)+v(bv2)

We know that the net force is zero. F=0
dvdt=a=(−bv3M(t))

Where M(t) represents Mass as a function of times.

Hence, the answer is the option (2).

Example 5: The initial mass of the rocket is 1000 kg. Calculate at what rate the fuel should be burnt so that the rocket is given an acceleration of 20 ms-2. The gases come out at a relative speed of [Useg=10 m/s2]

1) 10Kgs−1
2) 60Kgs−1
3) 500Kgs−1
4) 6⋅0×102Kgs−1

Solution:

Minitial =1000 kga=20ms2Vrel =500ms

F−mg=maVrel dmdt−mg=ma(500)dmdt−1000×10=1000500(dmdt)=1000(30)⇒(dmdt)=60(kgs)

Hence, the answer is the option (2).

Summary

Rocket propulsion is the application of Newton's third law. It works on the principle of momentum conservation. In a rocket, gases at high temperatures and pressure, are produced by the combustion of fuel. They escape with a large constant velocity through a nozzle.

Frequently Asked Questions (FAQs)

1. How does a rocket move in space without anything to push against?
Rockets move in space using the principle of conservation of momentum. They expel high-speed gases in one direction, which pushes the rocket in the opposite direction. This is based on Newton's Third Law of Motion: for every action, there's an equal and opposite reaction. The rocket doesn't need air or ground to push against; it's the expulsion of mass (exhaust gases) that provides the thrust.
2. Why do rockets need multiple stages?
Rockets use multiple stages to increase efficiency and payload capacity. As fuel is consumed, the empty tanks become dead weight. By discarding these empty stages, the rocket becomes lighter, allowing the remaining fuel to accelerate the payload more effectively. Each stage is optimized for its specific part of the flight, from liftoff through atmospheric flight to space operations.
3. What's the difference between solid and liquid rocket propellants?
Solid propellants are pre-mixed fuel and oxidizer in a solid form, while liquid propellants keep fuel and oxidizer separate until combustion. Solid propellants are simpler and can be stored long-term, but can't be throttled or shut off once ignited. Liquid propellants are more complex but offer better control, higher efficiency, and the ability to restart engines.
4. How does changing the mass of a rocket affect its acceleration?
According to Newton's Second Law (F = ma), for a given force (thrust), acceleration is inversely proportional to mass. As a rocket burns fuel and becomes lighter, its acceleration increases even if the thrust remains constant. This is why rockets accelerate faster as they ascend, assuming constant thrust.
5. What role does Earth's gravity play in rocket launches?
Earth's gravity is a major factor in rocket launches. It creates the need for escape velocity (about 11.2 km/s) to leave Earth's gravitational field. Gravity also affects the trajectory of the rocket, requiring more fuel for vertical ascent. However, rockets often use gravity to their advantage through techniques like the gravity turn, which allows for more efficient ascent paths.
6. Why do some rockets ignite their engines before liftoff?
Some rockets ignite their engines before release to ensure all engines are functioning correctly before committing to launch. This "hold-down" technique allows for a safe abort if any issues are detected. It also allows the engines to reach full thrust, ensuring maximum performance from the moment of liftoff.
7. What is a gravity assist, and how does it help space missions?
A gravity assist, or gravitational slingshot, is a technique where a spacecraft uses the gravity of a planet or other celestial body to alter its path and speed. By approaching a planet in a specific way, the spacecraft can gain kinetic energy and change direction without using propellant. This technique is crucial for many interplanetary missions, allowing probes to reach distant targets with less fuel.
8. What is a rocket's payload, and how does it affect the design?
A rocket's payload is the cargo it carries, such as satellites, spacecraft, or scientific instruments. The payload mass directly impacts the rocket's design, as more massive payloads require more powerful engines, more fuel, and stronger structures. Maximizing the payload capacity while minimizing the rocket's overall mass is a key challenge in rocket design.
9. How do rockets deal with the extreme temperatures during launch and space flight?
Rockets use various methods to manage extreme temperatures:
10. What is the role of telemetry in rocket launches?
Telemetry is the collection and transmission of data from the rocket to ground control. It provides real-time information about the rocket's performance, position, velocity, and health of various systems. This data is crucial for monitoring the launch, making decisions about flight termination if necessary, and analyzing the rocket's performance for future improvements.
11. How do rockets navigate in space?
Space navigation involves several techniques:
12. What is the significance of rocket nozzle expansion ratio?
The nozzle expansion ratio is the ratio of the nozzle exit area to its throat area. It's significant because:
13. How do rockets minimize gravitational losses during ascent?
Rockets minimize gravitational losses through:
14. What is the role of turbopumps in liquid-fueled rockets?
Turbopumps in liquid-fueled rockets:
15. What is the purpose of a rocket fairing?
A rocket fairing serves several purposes:
16. How do rocket engines cool themselves to prevent melting?
Rocket engines employ various cooling methods:
17. What is the significance of the rocket's payload fairing separation?
Payload fairing separation is significant because:
18. How do ion thrusters work, and why aren't they used for launches?
Ion thrusters work by electrically charging particles and accelerating them using electric fields. They provide very low thrust but extremely high efficiency, making them ideal for long-duration space missions. They aren't used for launches because their low thrust can't overcome Earth's gravity and atmospheric drag quickly enough. They're most effective in the vacuum of space for long-term acceleration.
19. What is specific impulse, and why is it important for rocket propulsion?
Specific impulse is a measure of the efficiency of a rocket engine, expressed as the thrust produced per unit of propellant consumed per unit time. It's essentially the "fuel economy" of a rocket. Higher specific impulse means the engine can produce more thrust for a given amount of fuel, allowing for either longer burn times or reduced fuel mass, both crucial for space missions.
20. How does air resistance affect rocket launches?
Air resistance, or drag, opposes a rocket's motion through the atmosphere. It increases with velocity and air density, reaching a maximum at an altitude where the rocket's speed and air density combine for peak drag (often called "Max Q"). Rockets must be designed to withstand these forces and often throttle down engines during this phase to reduce stress on the vehicle.
21. How does the shape of a rocket nozzle affect its performance?
The rocket nozzle shape is crucial for performance. A converging-diverging (de Laval) nozzle is typically used to accelerate exhaust gases to supersonic speeds. The nozzle's shape is optimized for specific atmospheric pressures, with wider nozzles being more efficient in space but less effective at sea level. This is why some rockets have extendable nozzles for different flight phases.
22. What is thrust vectoring, and why is it important for rockets?
Thrust vectoring is the ability to change the direction of the rocket's thrust. It's achieved by gimbaling (pivoting) the engine nozzle or using auxiliary thrusters. This technique is crucial for steering the rocket, maintaining stability, and executing precise maneuvers, especially in the absence of aerodynamic control surfaces in space.
23. How does a rocket's mass change during flight affect its trajectory?
As a rocket burns fuel, its mass decreases significantly. This mass change affects the rocket's acceleration and, consequently, its trajectory. The rocket becomes more responsive to thrust as it gets lighter, which must be accounted for in guidance systems. This mass change is also why rockets often follow a curved path (gravity turn) rather than going straight up, to optimize fuel efficiency.
24. What is the rocket equation, and why is it considered the fundamental equation of spaceflight?
The rocket equation, also known as the Tsiolkovsky equation, relates the change in a rocket's velocity to its exhaust velocity and the ratio of initial to final mass. It's fundamental because it shows the exponential nature of the relationship between payload mass and propellant mass, highlighting the difficulty of achieving high velocities in space travel.
25. How do multi-stage rockets improve efficiency compared to single-stage rockets?
Multi-stage rockets improve efficiency by discarding empty fuel tanks and engines as they become unnecessary. This reduces the rocket's mass, allowing the remaining fuel to accelerate the payload more effectively. Each stage can also be optimized for its specific part of the flight (e.g., high thrust for liftoff, high efficiency for space operations), further improving overall performance.
26. What is the difference between thrust and impulse in rocket propulsion?
Thrust is the instantaneous force produced by the rocket engine, measured in Newtons. Impulse is the total change in momentum imparted by the engine over time, measured in Newton-seconds. While thrust determines the rocket's acceleration at any given moment, impulse is more indicative of the rocket's overall performance and ability to change velocity over its entire burn time.
27. How do rocket engines work in the vacuum of space?
Rocket engines work in space by expelling mass (exhaust gases) at high velocities. Unlike jet engines, they don't rely on atmospheric oxygen, carrying their own oxidizer. In vacuum, rocket engines actually become more efficient as there's no atmospheric pressure to overcome at the nozzle exit, allowing for greater exhaust velocity and thus more thrust per unit of propellant.
28. What is the role of oxidizers in rocket propulsion?
Oxidizers are substances that rockets carry to allow fuel combustion in the absence of atmospheric oxygen. They provide the oxygen atoms necessary for the chemical reaction that produces thrust. Common oxidizers include liquid oxygen, nitrogen tetroxide, and ammonium perchlorate. The choice of oxidizer significantly affects the rocket's performance and handling characteristics.
29. How does the rocket's velocity affect its fuel efficiency?
As a rocket's velocity increases, its fuel efficiency generally improves. This is because the kinetic energy imparted to the exhaust gases relative to the Earth decreases, meaning more of the engine's energy goes into accelerating the rocket itself. However, this effect is somewhat offset by the increased power needed to accelerate the remaining fuel to the higher velocity.
30. How do different propellant combinations affect rocket performance?
Different propellant combinations offer varying levels of specific impulse, density, storability, and handling safety. For example, liquid hydrogen and liquid oxygen offer very high specific impulse but low density, requiring large tanks. Kerosene and liquid oxygen provide less specific impulse but are denser and easier to handle. The choice of propellants significantly impacts the rocket's design, performance, and suitability for different missions.
31. What is the Oberth effect, and how is it used in space missions?
The Oberth effect is the phenomenon where a rocket engine produces more useful energy when fired at high speeds. It occurs because the propellant itself has more kinetic energy at higher velocities, which is converted to even more kinetic energy when expelled. Space missions often use this effect by timing engine burns at the point of highest velocity in an orbit, typically at the closest approach to a gravitational body.
32. How do rockets maintain their orientation and stability during flight?
Rockets maintain orientation and stability through a combination of techniques:
33. What is the significance of the rocket's mass ratio?
The mass ratio is the ratio of the rocket's initial (fueled) mass to its final (empty) mass. It's a crucial factor in the rocket equation and determines the maximum change in velocity the rocket can achieve. A higher mass ratio generally allows for greater Δv (change in velocity), but it's limited by structural considerations and diminishing returns as described by the rocket equation.
34. How does atmospheric pressure affect rocket engine performance?
Atmospheric pressure significantly affects rocket engine performance, especially at lower altitudes. Higher atmospheric pressure at sea level creates back pressure on the engine nozzle, reducing its efficiency. As the rocket ascends and atmospheric pressure decreases, the engine becomes more efficient. This is why some rockets have altitude-compensating nozzles or multiple stages optimized for different atmospheric conditions.
35. How do rockets change direction in space?
Rockets change direction in space primarily through:
36. What is the significance of the rocket's center of mass and center of pressure?
The center of mass is the average position of the rocket's mass, while the center of pressure is the point where aerodynamic forces effectively act. For stability, the center of mass should be ahead of the center of pressure. As the rocket burns fuel, these points shift, which must be accounted for in the rocket's design and flight controls to maintain stability throughout the flight.
37. How do rockets achieve escape velocity?
Rockets achieve escape velocity (about 11.2 km/s for Earth) through sustained acceleration. They don't need to reach this speed instantly; instead, they continuously accelerate, often using multiple stages. The rocket gains speed as it climbs, benefiting from reduced atmospheric drag and gravity. Orbital velocity (about 7.8 km/s) is often achieved first, with additional burns used to reach escape velocity if needed.
38. What is the purpose of baffles in rocket engines?
Baffles in rocket engines serve several purposes:
39. What is the role of pressurization in liquid-fueled rockets?
Pressurization in liquid-fueled rockets serves to:
40. How do rocket engineers balance thrust-to-weight ratio?
Balancing thrust-to-weight ratio is crucial in rocket design:
41. How do rockets handle the extreme vibrations during launch?
Rockets manage extreme vibrations through:

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