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ME = 13520 joules + 26950 joules = 40470 joules

Validation

Let's see if we can validate that result in some other way.

We know that the mechanical energy of the rocket at rest on the platform was equal to 1470 joules.

We can compute the work done in moving the rocket up by 260 meters by multiplying that distance by the upward force. Thus,

work = distance * thrust, or

work = 260 m * 150N = 39000 joules

Additional mechanical energy

This is the mechanical energy added to the rocket after it left the platform while the engine was burning.The total mechanical energy when the burn ends is the sum of that value and the mechanical energy that it had while at rest on the platform. Thus, the totalmechanical energy at the end of the burn is:

ME = 1470 joules + 39000 joules = 40470 joules

A good match

This value matches the value computed earlier on the basis of the height of the rocket above the surface of the earth and thevelocity of the rocket. Thus, the two approaches agree with one another up to this point.

State at the end of Leg B

Therefore, at the end of Leg B,

  • The total mechanical energy possessed by the rocket is equal to 40470 joules.
  • The gravitational potential energy is 26950 joules
  • The kinetic energy is 13520 joules
  • The rocket is out of fuel and is coasting upward with a velocity of 52 m/s.
  • The only force acting on the rocket is an internal downward force due to gravity, which is equal to 10kg * 9.8m/s^2 = 98 newtons.

Leg C

This is the part of the trip where the rocket coasts from its height at the end of Leg B to the apex of its trip. The continued upward motion is due solely to its kinetic energy at the endof Leg B.

From the end of Leg B when the rocket engine stops burning, until the rocket crashes on the surface of the earth, the only forces acting on the rocket will be the internal force of gravity.

Total mechanical energy is conserved

Since internal forces cannot change the mechanical energy possessed by an object, thetotal mechanical energy for the rocket must remain at 40470 joules for the remainder of the trip.

How long to reach the apex?

We can compute the time required for the rocket to reach the apex as

t = v/g = (52m/s)/(9.8m/s^2) = 5.31 seconds

How far will the rocket travel?

Knowing the time required to reach the apex, we can compute the distance to the apex (during this leg only) as

d = v0*t - 0.5*g*t^2, or

d = (52m/s) * (5.31s) - (0.5) * (9.8m/s^2)*(5.31s)^2, or

d = 138 meters

An additional 138 meters

In other words, the rocket travels an additional 138 meters straight up after the rocket-engine stops burning. This additional travel is due solely to thekinetic energy possessed by the rocket at the end of the burn.

The total height of the apex

Adding 138 more meters to the height at the end of the burn causes the height at the apex to be

height at apex = 275m + 138m = 413 meters

Mechanical energy equals potential energy alone

At that point, the total mechanical energy is equal to the gravitational potential energy because the rocket isn't moving and the kinetic energy has gone to zero.

Questions & Answers

what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
how can I make nanorobot?
Lily
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Accessible physics concepts for blind students. OpenStax CNX. Oct 02, 2015 Download for free at https://legacy.cnx.org/content/col11294/1.36
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