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To solve an integrated concept problem, we must first identify the physical principles involved and identify the chapters in which they are found. Part (a) of this example asks for weight. This is a topic of dynamics and is defined in Dynamics: Force and Newton’s Laws of Motion . Part (b) deals with electric force on a charge, a topic of Electric Charge and Electric Field . Part (c) asks for acceleration, knowing forces and mass. These are part of Newton’s laws, also found in Dynamics: Force and Newton’s Laws of Motion .

The following solutions to each part of the example illustrate how the specific problem-solving strategies are applied. These involve identifying knowns and unknowns, checking to see if the answer is reasonable, and so on.

Solution for (a)

Weight is mass times the acceleration due to gravity, as first expressed in

w = mg . size 12{w= ital "mg"} {}

Entering the given mass and the average acceleration due to gravity yields

w = ( 4.00 × 10 15 kg ) ( 9 . 80 m/s 2 ) = 3 . 92 × 10 14 N . size 12{w= \( "44" "." "00" times "10" rSup { size 8{ - "15"} } `"kg" \) \( 9 "." "80""m/s" rSup { size 8{2} } \) =3 "." "92" times "10" rSup { size 8{ - "14"} } N} {}

Discussion for (a)

This is a small weight, consistent with the small mass of the drop.

Solution for (b)

The force an electric field exerts on a charge is given by rearranging the following equation:

F = qE . size 12{F= ital "qE"} {}

Here we are given the charge ( 3.20 × 10 –19 C is twice the fundamental unit of charge) and the electric field strength, and so the electric force is found to be

F = ( 3.20 × 10 19 C ) ( 3 . 00 × 10 5 N/C ) = 9 . 60 × 10 14 N . size 12{F= \( 3 "." "20" times "10" rSup { size 8{ - "19"} } C \) \( 3 "." "00" times "10" rSup { size 8{5} } "N/C" \) =9 "." "60" times "10" rSup { size 8{ - "14"} } N} {}

Discussion for (b)

While this is a small force, it is greater than the weight of the drop.

Solution for (c)

The acceleration can be found using Newton’s second law, provided we can identify all of the external forces acting on the drop. We assume only the drop’s weight and the electric force are significant. Since the drop has a positive charge and the electric field is given to be upward, the electric force is upward. We thus have a one-dimensional (vertical direction) problem, and we can state Newton’s second law as

a = F net m . size 12{a= { { ital "net"`F} over {m} } `} {}

where F net = F w size 12{F=F - w} {} . Entering this and the known values into the expression for Newton’s second law yields

a = F w m = 9.60 × 10 14 N 3.92 × 10 14 N 4.00 × 10 15 kg = 14 . 2 m/s 2 . alignl { stack { size 12{a= { {F - w} over {m} } } {} #size 12{ {}= { {9 "." "60" times "10" rSup { size 8{ - "14"} } N - 3 "." "92"` times "10" rSup { size 8{ - "14"} } N} over {4 "." "00" times "10" rSup { size 8{ - "15"} } ital "kg"} } } {} # ="14" "." 2m/s rSup { size 8{2} } {}} } {}

Discussion for (c)

This is an upward acceleration great enough to carry the drop to places where you might not wish to have gasoline.

This worked example illustrates how to apply problem-solving strategies to situations that include topics in different chapters. The first step is to identify the physical principles involved in the problem. The second step is to solve for the unknown using familiar problem-solving strategies. These are found throughout the text, and many worked examples show how to use them for single topics. In this integrated concepts example, you can see how to apply them across several topics. You will find these techniques useful in applications of physics outside a physics course, such as in your profession, in other science disciplines, and in everyday life. The following problems will build your skills in the broad application of physical principles.

Unreasonable results

The Unreasonable Results exercises for this module have results that are unreasonable because some premise is unreasonable or because certain of the premises are inconsistent with one another. Physical principles applied correctly then produce unreasonable results. The purpose of these problems is to give practice in assessing whether nature is being accurately described, and if it is not to trace the source of difficulty.

Problem-solving strategy

To determine if an answer is reasonable, and to determine the cause if it is not, do the following.

  1. Solve the problem using strategies as outlined above. Use the format followed in the worked examples in the text to solve the problem as usual.
  2. Check to see if the answer is reasonable. Is it too large or too small, or does it have the wrong sign, improper units, and so on?
  3. If the answer is unreasonable, look for what specifically could cause the identified difficulty. Usually, the manner in which the answer is unreasonable is an indication of the difficulty. For example, an extremely large Coulomb force could be due to the assumption of an excessively large separated charge.

Questions & Answers

are nano particles real
Missy Reply
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
Lale Reply
no can't
where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
has a lot of application modern world
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
yes that's correct
I think
Nasa has use it in the 60's, copper as water purification in the moon travel.
nanocopper obvius
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
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
analytical skills graphene is prepared to kill any type viruses .
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Berger describes sociologists as concerned with
Mueller Reply
what is hormones?
How we can toraidal magnetic field
Aditya Reply
How we can create polaidal magnetic field
Mykayuh Reply
Because I'm writing a report and I would like to be really precise for the references
Gre Reply
where did you find the research and the first image (ECG and Blood pressure synchronized)? Thank you!!
Gre Reply
Practice Key Terms 8

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Source:  OpenStax, Physics 101. OpenStax CNX. Jan 07, 2013 Download for free at http://legacy.cnx.org/content/col11479/1.1
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