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Chapter 7: Problem 2

If a Saturn \(\mathrm{V}\) rocket with an Apollo spacecraft attached had a combined mass of \(2.9 \times 10^{5} \mathrm{~kg}\) and reached a speed of \(11.2 \mathrm{~km} / \mathrm{s}\), how much kinetic energy would it then have?

Short Answer

Expert verified
Kinetic energy is approximately \(1.82 \times 10^{13}\) Joules.

Step by step solution

01

Write the Formula for Kinetic Energy

The kinetic energy (KE) can be calculated using the formula: \[ KE = \frac{1}{2} m v^2 \] where \(m\) is the mass and \(v\) is the velocity of the object.
02

Identify and Substitute Given Values

From the problem, the mass \(m\) is given as \(2.9 \times 10^5 \text{ kg}\) and the velocity \(v\) is given as \(11.2 \text{ km/s}\). We need to convert velocity into meters per second, so \(11.2 \text{ km/s} = 11200 \text{ m/s}\). Substitute these into the formula.
03

Plug in Values and Calculate

Substitute the values into the equation: \[ KE = \frac{1}{2} \times (2.9 \times 10^5 \, \text{kg}) \times (11200 \, \text{m/s})^2 \]Calculating inside the parentheses first:\[ (11200)^2 = 125440000 \]Now calculate the entire expression:\[ KE = 0.5 \times 2.9 \times 10^5 \times 125440000 \]
04

Simplify and Solve

Calculate the multiplication step by step:1. \( 0.5 \times 2.9 \times 10^5 = 1.45 \times 10^5 \)2. \(1.45 \times 10^5 \times 125440000 = 1.81688 \times 10^{13} \) Thus, the kinetic energy is \(1.81688 \times 10^{13} \, \text{Joules} \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Saturn V Rocket
The Saturn V rocket is one of NASA's most iconic achievements.
Launched for the Apollo missions, this massive vehicle was designed to send astronauts to the Moon. It stood at a towering 111 meters tall and was capable of generating over 34 million newtons of thrust.
Its incredible power made it uniquely suited to carrying the heavy Apollo spacecraft beyond Earth's atmosphere, into space, and to our natural satellite. The Saturn V's role in the successful moon landings of the 1960s and 1970s demonstrates a perfect blend of engineering and physics.
Apollo Spacecraft
The Apollo spacecraft was not just a single vessel, but a combination of different modules that worked together to achieve space exploration on a grand scale.
The spacecraft consisted of the Command Module (CM), which housed the astronauts; the Service Module (SM) that contained essential supplies and propulsion systems;
and the Lunar Module (LM) which was designed to land on the moon's surface. Each part was vital to the mission's success. Together, these modules were carried into space by the Saturn V rocket, showcasing incredible engineering and strategic planning.
Mass and Velocity
Mass and velocity are essential in physics, especially when calculating kinetic energy (KE).
The mass of an object is how much matter it contains, measured in kilograms, while velocity is its speed and direction, usually given in meters per second.
In the case of the Apollo mission scenario, we had a mass of 2.9 x 10鈦� kg for the rocket and the spacecraft.
The velocity, after conversion from 11.2 km/s to meters per second, was 11200 m/s. These two figures are the cornerstone for calculating the rocket's kinetic energy using the formula \( KE = \frac{1}{2} m v^2 \).
Physics Problem Solving
Solving physics problems involves a systematic approach to analyzing given data and applying the right formulas.
Begin by identifying what you know鈥攍ike mass and velocity in this problem.
Next, choose the correct equation, in this case the kinetic energy formula. Substitute your known values in, simplifying where necessary.
Finally, solve the problem step-by-step, double-checking calculations along the way.
  • Understand the problem: Clearly define what you need to solve.
  • Organize given data: Write out the relevant information.
  • Use the right formulas: Apply them accurately.
  • Check your work: Ensure accuracy at each calculation step.
This methodical approach can help you tackle most physics exercises.

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Most popular questions from this chapter

On August \(10,1972,\) a large meteorite skipped across the atmosphere above the western United States and western Canada, much like a stone skipped across water. The accompanying fireball was so bright that it could be seen in the daytime sky and was brighter than the usual meteorite trail. The meteorite's mass was about \(4 \times 10^{6} \mathrm{~kg}\) : its speed was about \(15 \mathrm{~km} / \mathrm{s}\). Had it entered the atmosphere vertically, it would have hit Earth's surface with about the same speed. (a) Calculate the meteorite's loss of kinetic energy (in joules) that would have been associated with the vertical impact. (b) Express the energy as a multiple of the explosive energy of 1 megaton of \(\mathrm{TNT}\), which is \(4.2 \times 10^{15} \mathrm{~J}\). (c) The energy associated with the atomic bomb explosion over Hiroshima was equivalent to 13 kilotons of TNT. To how many Hiroshima bombs would the meteorite impact have been equivalent?

A constant force of magnitude \(10 \mathrm{~N}\) makes an angle of \(150^{\circ}\) (measured counterclockwise) with the positive \(x\) direction as it acts on a \(2.0 \mathrm{~kg}\) object moving in an \(x y\) plane. How much work is done on the object by the force as the object moves from the origin to the point having position vector \((2.0 \mathrm{~m}) \hat{\mathrm{i}}-(4.0 \mathrm{~m}) \hat{\mathrm{j}} ?\)

A force \(\quad \vec{F}=(3.00 \mathrm{~N}) \hat{\mathrm{i}}+(7.00 \mathrm{~N}) \hat{\mathrm{j}}+(7.00 \mathrm{~N}) \hat{\mathrm{k}}\) acts on a \(2.00 \mathrm{~kg}\) mobile object that moves from an initial position of \(\vec{d}_{i}=(3.00 \mathrm{~m}) \hat{\mathrm{i}}-(2.00 \mathrm{~m}) \hat{\mathrm{j}}+(5.00 \mathrm{~m}) \hat{\mathrm{k}}\) to a final position of \(\vec{d}_{f}=-(5.00 \mathrm{~m}) \hat{\mathrm{i}}+(4.00 \mathrm{~m}) \hat{\mathrm{j}}+(7.00 \mathrm{~m}) \hat{\mathrm{k}}\) in \(4.00 \mathrm{~s} .\) Find \((\mathrm{a})\) the work done on the object by the force in the 4.00 s interval, (b) the average power due to the force during that interval, and (c) the angle between vectors \(\vec{d}_{i}\) and \(\vec{d}_{f}\)

During spring semester at MIT, residents of the parallel buildings of the East Campus dorms battle one another with large catapults that are made with surgical hose mounted on a window frame. A balloon filled with dyed water is placed in a pouch attached to the hose, which is then stretched through the width of the room. Assume that the stretching of the hose obeys Hooke's law with a spring constant of \(100 \mathrm{~N} / \mathrm{m} .\) If the hose is stretched by \(5.00 \mathrm{~m}\) and then released, how much work does the force from the hose do on the balloon in the pouch by the time the hose reaches its relaxed length?

Boxes are transported from one location to another in a warehouse by means of a conveyor belt that moves with a constant speed of \(0.50 \mathrm{~m} / \mathrm{s}\). At a certain location the conveyor belt moves for \(2.0 \mathrm{~m}\) up an incline that makes an angle of \(10^{\circ}\) with the horizontal, then for \(2.0 \mathrm{~m}\) horizontally, and finally for \(2.0 \mathrm{~m}\) down an incline that makes an angle of \(10^{\circ}\) with the horizontal. Assume that a \(2.0 \mathrm{~kg}\) box rides on the belt without slipping. At what rate is the force of the conveyor belt doing work on the box as the box moves (a) up the \(10^{\circ}\) incline, (b) horizontally, and (c) down the \(10^{\circ}\) incline?
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