<< Chapter < Page Chapter >> Page >

Simplifying, rearranging terms, and dividing both sides by 2 gives us:

P = 4*Q ( eq. a2 )

Two equations and two unknowns

Including eq. a1 , (repeated below) we now have two equations and two unknowns.

P + Q = W

Inserting the numeric value for W gives us

P + Q = 10, or

Q = 10 - P ( eq. a3 )

Substituting this value of Q into eq. a2 gives us

P = 4*(10 - P), or

P = 40 - 4*P, or

5*P = 40, or

P = 8

which is one of the answers that we are looking for.

Inserting the value for P into eq. a3 gives us

Q = 10 - 8, or

Q = 2

which is the other answer that we are looking for.

A more general case of the trapeze bar

Let's pick another point, label it X, and compute the moments about that point. Those moments must also sum to zero for the bar to be in equilibrium.(The moments computed about any point on the bar must sum to zero for the bar to be in equilibrium.)

The moments about X produced by the three forces are:

  • P: (X-A)*(P)
  • W: (X-C)*(W)
  • Q: (X-B)*(Q)

Let X = 5

Substituting for X gives us:

(5)*(P) - (3)*(10) + (-5)*(Q) = 0

Simplifying, rearranging terms, and diving both sides by 5 gives us:

P - Q - 6 = 0, or

P = Q + 6 ( eq. a4 )

Now we can use this equation along with eq.a1 to solve for Q.

P + Q = 10, from eq.a1 , or

Q = 10 - P

Substituting this value for Q in eq. a4 gives us,

P = 10 - P + 6

Simplifying and dividing both sides by 2 gives us,

P = 8 , which is the same answer as before (which it should be)

Substitution of P back into eq. a1 gives us,

Q = 2

Apply theweight at different locations on the trapeze

If you solve for P and Q for any location of the weight between the ropes, you will find that the values for the upward forces at each end of the bar areinversely proportional to the distance from the weight to that end of the bar.

For example, for equilibrium, using the dimension symbols established for your drawing earlier:

a*P = b*Q

Dividing both sides by a gives:

P = (b/a)*Q

Weight is centered

If b/a = 1 (weight is centered), then:

P = Q meaning that both upward forces are equal.

Weight towards the left end

If b/a = 4 (weight at 2), then:

P = 4*Q meaning that most of the force is being exerted by the rope on the left end.

Weight toward the right

If b/a = 1/4 (weight at 8), then

P = Q/4 meaning that most of the force is being exerted by the rope on the right end.

Weight at the right end

If b/a = 0 (weight at 10, right end of the bar)

P = 0 meaning that all of the force is being exerted by the rope on the right end of the bar.

Because P + Q = W, we conclude that Q = W

The bar is essentially eliminated

The scenario where b/a = 0 essentially eliminates the bar from consideration. The weight is hanging directly on the rope on the right end of the bar and theweightless bar and the other rope are simply floating in the air.

Hypothetical replacement by a single upward force

If we were to draw an imaginary force labeled R pointing directly up from the point C where R is equal to P + Q, we could imagine the forces P and Q as beingreplaced by R. In that case, R would be the resultant of P and Q and would be equal in magnitude and opposite in direction to the downward force W.

Questions & Answers

what is mutation
Janga Reply
what is a cell
Sifune Reply
how is urine form
Sifune
what is antagonism?
mahase Reply
classification of plants, gymnosperm features.
Linsy Reply
what is the features of gymnosperm
Linsy
how many types of solid did we have
Samuel Reply
what is an ionic bond
Samuel
What is Atoms
Daprince Reply
what is fallopian tube
Merolyn
what is bladder
Merolyn
what's bulbourethral gland
Eduek Reply
urine is formed in the nephron of the renal medulla in the kidney. It starts from filtration, then selective reabsorption and finally secretion
onuoha Reply
State the evolution relation and relevance between endoplasmic reticulum and cytoskeleton as it relates to cell.
Jeremiah
what is heart
Konadu Reply
how is urine formed in human
Konadu
how is urine formed in human
Rahma
what is the diference between a cavity and a canal
Pelagie Reply
what is the causative agent of malaria
Diamond
malaria is caused by an insect called mosquito.
Naomi
Malaria is cause by female anopheles mosquito
Isaac
Malaria is caused by plasmodium Female anopheles mosquitoe is d carrier
Olalekan
a canal is more needed in a root but a cavity is a bad effect
Commander
what are pathogens
Don Reply
In biology, a pathogen (Greek: πάθος pathos "suffering", "passion" and -γενής -genēs "producer of") in the oldest and broadest sense, is anything that can produce disease. A pathogen may also be referred to as an infectious agent, or simply a germ. The term pathogen came into use in the 1880s.[1][2
Zainab
A virus
Commander
Definition of respiration
Muhsin Reply
respiration is the process in which we breath in oxygen and breath out carbon dioxide
Achor
how are lungs work
Commander
where does digestion begins
Achiri Reply
in the mouth
EZEKIEL
what are the functions of follicle stimulating harmones?
Rashima Reply
stimulates the follicle to release the mature ovum into the oviduct
Davonte
what are the functions of Endocrine and pituitary gland
Chinaza
endocrine secrete hormone and regulate body process
Achor
while pituitary gland is an example of endocrine system and it's found in the Brain
Achor
what's biology?
Egbodo Reply
Biology is the study of living organisms, divided into many specialized field that cover their morphology, physiology,anatomy, behaviour,origin and distribution.
Lisah
biology is the study of life.
Alfreda
Biology is the study of how living organisms live and survive in a specific environment
Sifune
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




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
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Accessible physics concepts for blind students' conversation and receive update notifications?

Ask