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Gunpowder rockets

A problem to solve

A fireworks company wants to make a newfirework that will reach a vertical height of 400mcarrying an explosive load of 200g. The explosive

load is to be attached on the top of thegunpowder rocket. The frame and casing of therocket have a combined mass of 1 0g.The rocket is pushed upwards with a gunpowder rocket of efficiency 2 ! "i.e. 2 ! of the chemicalenergy of the gunpowder is converted into kineticenergy of the rocket#.The gunpowder used to power the rocket has an energy density of $.0 %&kg '1 . This means that when 1kg of gunpowder explodes ( burns it releases $.0 million &oules of energy.

Assume that air resistance is negligible

)se the conservation of energy and the e*uations below to answer the following *uestions+1. Assuming that the rocket uses all of its gunpowder in one initial explosion calculate the initial vertical

velocity of the rocket for it to reach an altitude of 400m "use our e*uations of motion to answer this#.

v=0

a= ?

s=400

t=?

u=?

a=-9.81

v^2=u^2+2as

u=v^2-2as

u=0-2 x -9.81 x 400

u=88.6 m/s

2. ,hat mass of fuel will the rocket need to reach an altitude of 400m "you will need to make someestimates here of the mass of gunpowder needed and use trial and error to work this out#

Ek=1/2mv^2

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Ek= x 0.350 x 88.6^2

Ek= 1373.74 J

Mass x ! "#$ % !s&t$ x ''&(& !($= ! "#$ " ) as % &! x*) s& !

0.00185 x 3 x ,= 1387

0.00183 x 0.25 x 3= 0.001373 MJ

t&m s $ 1000000

1.83 # ' 'u )

" t t " m t % " a""a!# t uat& ! 1/4 3 x# = 1374 xk# = 1374/ 1/4 3

1374/ 1/4 3 = 1.83067

$. -ow much kinetic energy will the rocket need at ground level

Ek= 1/2mv^2

Ek= 0.350 x 88.6^2 / 2

=1 373.743

4. mu( #"av&tat& !a) * t !t&a) ! "#$ &)) t " (k t #a&!?

E*=m# ( a!# &! % )ta

E*= 0.350 x 9.81 x 400

E*= 1373.4

am as Ek

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To solve this problem you will have to research the following:Understandings :

Kinetic energy: /nergy that an ob ect(thing possesses due to its motion.

Gravitational potential energy + /nergy that an ob ect(thing possesses while being in agravitational field. The higher up an ob ect is located the more 3/ it has.

Principle of conservation of energy: /nergy cannot be destroyed nor created only transformedfrom one state to another.Efficiency: t refers to how well energy is transformed the state we want.

Energy density: s defined as the amount of energy stored in a given space per unit mass or volume.

Applications and skills: 5iscussing the conservation of total energy within energy transformations 6uantitatively describing efficiency in energy transfers

Data booklet reference:EK = mv 2

E P = mgh

total power

total work = useful power out

Efficiency = useful work out

esearch:

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)se the following sources to help you find an answer. Absorb Advanced 3hysics interactive textbook ' section on ,ork energy and power 7inetic energy 8 ravitational potential energy '

o http+((www.schoolphysics.co.uk(age19'1:(%echanics(5ynamics( ;outube tutorial '