# 3.7 Further applications of newton’s laws of motion  (Page 2/6)

 Page 2 / 6

Discussion

The numbers used in this example are reasonable for a moderately large barge. It is certainly difficult to obtain larger accelerations with tugboats, and small speeds are desirable to avoid running the barge into the docks. Drag is relatively small for a well-designed hull at low speeds, consistent with the answer to this example, where ${F}_{\text{D}}$ is less than 1/600th of the weight of the ship.

In the earlier example of a tightrope walker we noted that the tensions in wires supporting a mass were equal only because the angles on either side were equal. Consider the following example, where the angles are not equal; slightly more trigonometry is involved.

## Different tensions at different angles

Consider the traffic light (mass 15.0 kg) suspended from two wires as shown in [link] . Find the tension in each wire, neglecting the masses of the wires.

Strategy

The system of interest is the traffic light, and its free-body diagram is shown in [link] (c). The three forces involved are not parallel, and so they must be projected onto a coordinate system. The most convenient coordinate system has one axis vertical and one horizontal, and the vector projections on it are shown in part (d) of the figure. There are two unknowns in this problem ( ${T}_{1}$ and ${T}_{2}$ ), so two equations are needed to find them. These two equations come from applying Newton’s second law along the vertical and horizontal axes, noting that the net external force is zero along each axis because acceleration is zero.

Solution

First consider the horizontal or x -axis:

${F}_{\text{net}x}={T}_{\text{2}x}-{T}_{\text{1}x}=0.$

Thus, as you might expect,

${T}_{\text{1}x}={T}_{\text{2}x}.$

This gives us the following relationship between ${T}_{1}$ and ${T}_{2}$ :

${T}_{1}\phantom{\rule{0.25em}{0ex}}\text{cos}\phantom{\rule{0.25em}{0ex}}\left(\text{30º}\right)={T}_{2}\phantom{\rule{0.25em}{0ex}}\text{cos}\phantom{\rule{0.25em}{0ex}}\left(\text{45º}\right).$

Thus,

${T}_{2}=\left(1\text{.}\text{225}\right){T}_{1}.$

Note that ${T}_{1}$ and ${T}_{2}$ are not equal in this case, because the angles on either side are not equal. It is reasonable that ${T}_{2}$ ends up being greater than ${T}_{1}$ , because it is exerted more vertically than ${T}_{1}$ .

Now consider the force components along the vertical or y -axis:

${F}_{\text{net}\phantom{\rule{0.25em}{0ex}}y}={T}_{\text{1}y}+{T}_{\text{2}y}-w=0.$

This implies

${T}_{\text{1}y}+{T}_{\text{2}y}=w.$

Substituting the expressions for the vertical components gives

${T}_{1}\phantom{\rule{0.25em}{0ex}}\text{sin}\phantom{\rule{0.25em}{0ex}}\left(\text{30º}\right)+{T}_{2}\phantom{\rule{0.25em}{0ex}}\text{sin}\phantom{\rule{0.25em}{0ex}}\left(\text{45º}\right)=w.$

There are two unknowns in this equation, but substituting the expression for ${T}_{2}$ in terms of ${T}_{1}$ reduces this to one equation with one unknown:

${T}_{1}\left(0\text{.}\text{500}\right)+\left(1\text{.}\text{225}{T}_{1}\right)\left(0\text{.}\text{707}\right)=w=\text{mg},$

which yields

$\left(1\text{.}\text{366}\right){T}_{1}=\left(\text{15}\text{.}\text{0 kg}\right)\left(9\text{.}{\text{80 m/s}}^{2}\right).$

Solving this last equation gives the magnitude of ${T}_{1}$ to be

${T}_{1}=\text{108 N}.$

Finally, the magnitude of ${T}_{2}$ is determined using the relationship between them, ${T}_{2}$ = 1.225 ${T}_{1}$ , found above. Thus we obtain

${T}_{2}=\text{132 N}.$

Discussion

Both tensions would be larger if both wires were more horizontal, and they will be equal if and only if the angles on either side are the same (as they were in the earlier example of a tightrope walker).

how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Do somebody tell me a best nano engineering book for beginners?
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
what is nano technology
what is system testing?
preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
Berger describes sociologists as concerned with
Got questions? Join the online conversation and get instant answers!