The document is a multi-part physics problem involving the analysis of dropping objects through air resistance and into snow.
The first part asks the student to show that the speed of a raindrop falling under gravity and gaining mass over time will eventually become constant, deriving an expression for the terminal speed.
The second part involves calculating the loss of mechanical energy when a sliding block hits a spring and experiences friction slowing its motion.
The third part examines using a ballistic pendulum to measure the speed of a bullet by calculating momentum and energy transfers between the bullet and suspended block.
The final part evaluates whether parachutes would be needed to drop soldiers packed into hay bales, based on observing the sinking
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This articles aims to explain how one can relatively easily calculate the pressure drop within a condenser or an evaporator, where two-phase flow occurs and the Navier-Stokes equation becomes very tedious.
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Full download: https://goo.gl/MyzREj
principles of soil dynamics pdf
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Methods to determine pressure drop in an evaporator or a condenserTony Yen
This articles aims to explain how one can relatively easily calculate the pressure drop within a condenser or an evaporator, where two-phase flow occurs and the Navier-Stokes equation becomes very tedious.
Principles of soil dynamics 3rd edition das solutions manualHuman2379
Full download: https://goo.gl/MyzREj
principles of soil dynamics pdf
soil dynamics and liquefaction
fundamentals of soil dynamics and earthquake engineering
principles of foundation engineering
Dynamics of structures 5th edition chopra solutions manualSchneiderxds
Download at: https://goo.gl/bVUnH2
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All of material inside is un-licence, kindly use it for educational only but please do not to commercialize it.
Based on 'ilman nafi'an, hopefully this file beneficially for you.
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Newton™s Laws; Moment of a Vector; Gravitation; Finite Rotations; Trajectory of a Projectile with Air Resistance; The Simple Pendulum; The Linear Harmonic Oscillator; The Damped Harmonic Oscillator
Stationary Quantum State: introduced by Niels Bohr, 1913:
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A Synthesis Problem combining Transverse velocity, Archimedes' principle, and (though knowledge of it is optional) fundamental frequencies/harmonics. Submission for UBC Phys101.
Problem abbreviated from Sears and Zemansky's University Physics with Modern Physics 13th ed. Problem 15.81
This presenations provides an outlook of what we anticipate with the structured data hub: to create linkable datasets, enhance the use of provenance, add quality flags to data, answer new questions and finally, borrow from and provide to public sources such as dbpedia
Dynamics of structures 5th edition chopra solutions manualSchneiderxds
Download at: https://goo.gl/bVUnH2
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dynamics of structures (5th edition) pdf
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dynamics of structures: theory and applications to earthquake engineering 5th edition
All of material inside is un-licence, kindly use it for educational only but please do not to commercialize it.
Based on 'ilman nafi'an, hopefully this file beneficially for you.
Thank you.
Newton™s Laws; Moment of a Vector; Gravitation; Finite Rotations; Trajectory of a Projectile with Air Resistance; The Simple Pendulum; The Linear Harmonic Oscillator; The Damped Harmonic Oscillator
Stationary Quantum State: introduced by Niels Bohr, 1913:
A property of a stationary quantum state of a physical system of constant energy is that probability to find a particle in any element of volume is independent of the time. A stationary quantum state may be defined as a condition of a system such that all observable physical properties are independent of the time.
Synthesis Problem of Transverse Speed and Archimedes' PrincipleArnold Choa
A Synthesis Problem combining Transverse velocity, Archimedes' principle, and (though knowledge of it is optional) fundamental frequencies/harmonics. Submission for UBC Phys101.
Problem abbreviated from Sears and Zemansky's University Physics with Modern Physics 13th ed. Problem 15.81
This presenations provides an outlook of what we anticipate with the structured data hub: to create linkable datasets, enhance the use of provenance, add quality flags to data, answer new questions and finally, borrow from and provide to public sources such as dbpedia
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Vendor Product Addon by CedCommerce is a powerful Magento extension that fulfills most of the needs of the vendors/admin and includes all the product features which required in a marketplace. It adds all the product types including configurable, bundle, grouped and product Custom Options along with up sells, related and cross sells product features. It is an addon for CedCommerce Marketplace Basic.
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the immunity of models against localized universal attacks by up to 40%. We evaluate our proposed approach
using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
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CFD analysis is incredibly effective at solving mysteries and improving the performance of complex systems!
Here's a great example: At a large natural gas-fired power plant, where they use waste heat to generate steam and energy, they were puzzled that their boiler wasn't producing as much steam as expected.
R&R and Tetra Engineering Group Inc. were asked to solve the issue with reduced steam production.
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Based on our results, Tetra Engineering installed covering plates to reduce the bypass flow. This improved the boiler's performance and increased electricity production.
It is always satisfying when we can help solve complex challenges like this. Do your systems also need a check-up or optimization? Give us a call!
Work done in cooperation with James Malloy and David Moelling from Tetra Engineering.
More examples of our work https://www.r-r-consult.dk/en/cases-en/
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It is now-a-days very important for the people to send or receive articles like imported furniture, electronic items, gifts, business goods and the like. People depend vastly on different transport systems which mostly use the manual way of receiving and delivering the articles. There is no way to track the articles till they are received and there is no way to let the customer know what happened in transit, once he booked some articles. In such a situation, we need a system which completely computerizes the cargo activities including time to time tracking of the articles sent. This need is fulfilled by Courier Management System software which is online software for the cargo management people that enables them to receive the goods from a source and send them to a required destination and track their status from time to time.
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Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
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The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
1. Problem 3.18
A raindrop of initial mass 0M starts falling from rest under the influence of gravity.
Assume that the drop gains mass from the cloud at a rate proportional to the product of its
instantaneous mass and its instantaneous velocity:
€
dM
dt
= kMV , where k is a constant.
Show that the speed of the drop eventually becomes effectively constant, and give an
expression for the terminal speed. Neglect air resistance.
Solution:
According to equation (3.11),
dt
Pd
F
r
r
= ,
where gMF
rr
= , and VMP
rr
=
write the equation in its scalar form, one obtains:
dt
dM
V
dt
dV
M
dt
MVd
Mg +==
)(
since kMV
dt
dM
= , we see that:
2
kMV
dt
dV
MMg +=
that is: g
dt
dV
kV =+2
Then we can see, as the drop falls, it’s velocity increases due to gravity. However, there
is a limit for this velocity because as the drop speeds up, its acceleration decreases rapidly
and will become negligible as the time goes to infinity. So the speed of the drop will
eventually become constant.
To compute the terminal constant speed, we could set 0=
dt
dV
Then we have: gkVt =2
Or
k
gVt =
Problem 4.2
2. A block of mass M slides along a horizontal table with speed 0v . At 0=x it hits a spring
with spring constant k and begins to experience a friction force. The coefficient of
friction is a variable and is given by bx=µ , where b is a constant. Find the loss in
mechanical energy when the block has first come momentarily to rest.
Solution:
Write the position where the block has first come momentarily to rest as 1x . So 01 =v
According to the work-energy theorem:
∫=−=−=−
1
0
2
0
2
0
2
0
2
1 )(
2
1
2
1
0
2
1
2
1
x
dxxFMvMvMvMv (*)
and we know that bMgxkxuMgkxxF −−=−−=)(
then (*) is just:
2
1
0
2
0 )(
2
1
)(
2
1 1
xbMgkxdxbMgkMv
x
+−=+−=− ∫
or
01 )(
v
bMgk
Mx
+
=
the mechanical energy we have at this point:
)(22
1
0
2
02
1
'
bMgk
kMv
kxUKE
+
=+=+=
the mechanical energy we lost:
2
0
22
02
0
)(2)(22
1
' v
bMgk
gbM
bMgk
kMv
MvEE
+
=
+
−=−
Problem 4.3
3. A simple way to measure the speed of a bullet is with a ballistic pendulum. This consists
of a wooden block of mass M into which the bullet is shot. The block is suspended from
cables of length l, and the impact of the bullet causes it to swing through a maximum
angle φ . The initial speed of the bullet is v, and its mass is m.
a. How fast is the block moving immediately after the bullet comes to rest? (assume that
this happens quickly)
b. Show how to find the velocity of the bullet by measuring m, M, l, and φ .
Solution:
a. As we assume that this happens quickly, total momentum is conserved. That is:
')( vmMmv += , where 'v is the speed of the block and the bullet after the “collision”.
Solve this equation, we get:
mM
mv
v
+
='
b. As the block swings, its mechanical energy is conserved. So we have:
φcos0'
2
1 2
MglMglMvE −=−=
or
)cos1(2' φ−= glv
plug in the equation for 'v obtained in part a, we have:
)cos1(2 φ−=
+
gl
mM
mv
or
)cos1(2 φ−
+
= gl
m
mM
v
Problem 4.5
4. Mass m whirls on a frictionless table, held to circular motion by a string which passes
through a hole in the table. The string is slowly pulled through the hole so that the radius
of the circle changes from 1l to 2l . Show that the work done in pulling the string equals
the increase in kinetic energy of the mass.
Solution:
Suppose that the mass has velocity 1v when the radius is 1l , 2v when the radius is 2l ,
rv when the radius is r.
Newton’s 2nd
law: amF
rr
= , where θθ
ˆˆ araa r +=
r
as in plane polar coordinate system.
Here as we are pulling the string slowly, we have rFF r
ˆ−=
r
, as rF is the amplitude of the
force. (note: the force is pointing to the origin, which gives us a minus sign as here we
choose rˆ to be our positive direction)
So we know that: rr maF = , and 0=θa .
As in plane polar coordinate system, θθθθ ˆ)2(ˆ)( 2 &&&&&&&
r
rrrrra ++−=
We get that )( 2
θ&&& rrmFr −−= , and 0
)(1
2
2
==+
dt
rd
r
rr
θ
θθ
&
&&&&
From the 2nd
equation, we know that θ&2
r , which is just rrv , is a constant.
So
r
lv
vr
11
= ,
2
11
2
l
lv
v =
As we pull the string really slow, we could take 0=r&& . Then we have:
3
2
1
2
1
2
2
r
lv
m
r
v
mmrF r
r === θ&
so the work we have done in pulling the string:
)
2
1
2
1
( 2
1
2
2
2
1
2
13
2
1
2
1
2
1
2
1
ll
lmvdr
r
lv
mrdFW
l
l
l
l
−=−=⋅= ∫∫
rr
, as we know ∫
−−
−= 23
2
1
rr
and the increase in kinetic energy of the mass:
W
ll
lmvv
l
lv
mmvmvE =−=−=−=Δ )
2
1
2
1
()(
2
1
2
1
2
1
2
1
2
2
2
1
2
1
2
12
2
2
1
2
12
1
2
2
Problem 4.12
5. During the Second World War the Russian, lacking sufficient parachutes for airborne
operations, occasionally dropped soldiers inside bales of hay onto snow. The human body
can survive an average pressure on impact of 30 2
/inlb .
Suppose that the lead plane drops a dummy bale equal in weight to a loaded one from an
altitude of 150 ft, and that the pilot observes that it sinks about 2 ft into the snow. If the
weight of an average soldier is 144 lb and his effective area is 5 2
ft , is it safe to drop the
men?
Solution:
Suppose we drop the dummy bale at ah , it stops at last at bh . And for the ground we have
0=h .
the work-energy theorem gives
∫ ⋅=−
b
a
ab RdFKK
rr
if we think of an average N
r
as the force the snow acts on the dummy bale after it hits the
ground, the equation is just:
)0()(00 −+−−=− bab hNhhmg
that is:
b
ab
h
hhmg
N
)( −
=
the pressure will be:
b
ab
Sh
hhmg
S
N
P
)( −
==
as 22
5,150,2,/8.9,144 ftSfthfthsmglbm ab ==−===
we get ginlbgftlbP ×=×
−×
−−×
= 22
/2.15/
)2(5
)1502(144
, where we have used the fact
that inft 121 =
as the human body can survive an average pressure on impact of 30 2
/inlb , which is
almost twice as big as the pressure on the dummy bale, we could say it is safe to drop the
men.