Statics is the branch of mechanics that is concerned with the analysis of (force and torque, or "moment") acting on physical systems that do not experience an acceleration (a=0), but rather, are in static equilibrium with their environment. The application of Newton's second law to a system gives:
F
=
m
a
.
{\displaystyle {\textbf {F}}=m{\textbf {a}}\,.}
Where bold font indicates a vector that has magnitude and direction.
F
{\displaystyle {\textbf {F}}}
is the total of the forces acting on the system,
m
{\displaystyle m}
is the mass of the system and
a
{\displaystyle {\textbf {a}}}
is the acceleration of the system. The summation of forces will give the direction and the magnitude of the acceleration and will be inversely proportional to the mass. The assumption of static equilibrium of
a
{\displaystyle {\textbf {a}}}
= 0 leads to:
F
=
0
.
{\displaystyle {\textbf {F}}=0\,.}
The summation of forces, one of which might be unknown, allows that unknown to be found. So when in static equilibrium, the acceleration of the system is zero and the system is either at rest, or its center of mass moves at constant velocity. Likewise the application of the assumption of zero acceleration to the summation of moments acting on the system leads to:
M
=
I
α
=
0
.
{\displaystyle {\textbf {M}}=I\alpha =0\,.}
Here,
M
{\displaystyle {\textbf {M}}}
is the summation of all moments acting on the system,
I
{\displaystyle I}
is the moment of inertia of the mass and
α
{\displaystyle \alpha }
= 0 the angular acceleration of the system, which when assumed to be zero leads to:
M
=
0
.
{\displaystyle {\textbf {M}}=0\,.}
The summation of moments, one of which might be unknown, allows that unknown to be found.
These two equations together, can be applied to solve for as many as two loads (forces and moments) acting on the system.
From Newton's first law, this implies that the net force and net torque on every part of the system is zero. The net forces equaling zero is known as the first condition for equilibrium, and the net torque equaling zero is known as the second condition for equilibrium. See statically indeterminate.
A physicist who does research in statics is called a statician.
Homework Statement
Look I have an exercise about trusses in vector mechanics. It's the following:
https://scontent-lax3-1.xx.fbcdn.net/hphotos-xfp1/v/t1.0-9/12003339_1645511085733429_8210043018491702007_n.jpg?oh=4955534403fb6f3f5f9a40c9c0b8ecbc&oe=569761ED
I have to determine the forces in...
Homework Statement
Here is the prompt/picture
The hint given is a FBD of the bead is recommended to being this problem. Find the coordinates of B so that both the magnitude and orientation of the elastic cord force can be properly represented. Also, two mutually orthogonal normal force...
Homework Statement
A weight W is supported by bar AO and cables AB, AC, and AD. Point A lies in the xy plane, if the bar and cables have the strengths listed below, determine the largest value W may have.
Hint given: A FBD of joint A is recommendedto being this problem. Bar AO should be...
Homework Statement
A model for the suspension of a vehicle is shown where the spring has stiffness k = 178 N/mm and an unstreched length of 347 mm.
http://imgur.com/1dTVs12
Determine the value P and the force supported by member AB so that the suspension has the equilibrium position shown...
Homework Statement
Suppose I've got a static mass on a downward plane. (For instance a car on a drive way). How would you set up this free body diagram?
Homework Equations
F = f1+f2...etc
The Attempt at a Solution
My preference is A, but I've seen it displayed in examples in my book as B...
Homework Statement
In figure (a), four identical crates weighing 2,000 lb each are stacked one on top of another, and in figure (b) a simple model for determining the deformation of the stack of crates is shown. In this model, each spring has the same stiffness k = 4,500 lb/in. and the forces...
Homework Statement
A collar with a pulley slides on a frictionless vertical bar GH. A string A B C D is wrapped around, where portion AB of the string is horizontal. A spring with 2.5 lb/in. stiffness is placed between the collar and point H. The spring has 7 in. unstreched length and 5 in...
Homework Statement
The top of a ladder of L and mass m is connected to a wall by a horizontal cable. The ladder makes an angle Θ=60 with the horizontal. A woman of mass 2m finds that as she climbs the ladder, the ladder begins to slip when she is one-third of the way up the ladder.
Find the...
Two steel straps are use to hold member BCD level. The size of each strap is 12 mm thick and 50 mm wide. A 16 mm diameter bolt is used to connect thesteel straps to the 89 x 89 mm post at A. A 25 kN is applied at the free end of the cantilever at point D. Determine:
the tensile stress developed...
Homework Statement
A 10.0kg sphere is attached to the incline by a horizontal string. Determine the tension in the string.
Homework Equations
(F⃗ net)x=ΣFx=0
(F⃗ net)y=ΣFy=0
Στ=0
τ = (radial disance)(F)
The Attempt at a Solution
1. I began by determining all the relevant forces associated...
Homework Statement
Homework Equations :
d = sqrt of dx^2 + dy^2 + dz^2
The Attempt at a Solution :[/B]
[/B]
Q1: The second image is the solution diagram. What I don't understand is that why is the force acting from A towards B? Shouldn't it be from B towards A? I'm thinking of it as A as...
Homework Statement
Blocks A and B each weight 170 lb and rest on frictionless surfaces. They are connected to one another by cable AB. Determine the force P required to hold the blocks in the equilibrium position shown and the reactions between the blocks and surfaces.
Hint given: This...
Homework Statement
The dimension h is to be determined to that a worker can comfortably slides boxes weighing up to 106 lb up and down a frictionless incline. If the worker can apply a 50 lb horizontal force to the box, what is the largest value h should have?
Hint given: Before taking any...
Homework Statement
I attached a picture of the question.
Homework Equations
∑Fx=0
∑Fy=0
100kg(9.8)= 981 N
I am not sure how to start this problem. Everything else in this chapter is a breeze so perhaps a small insight or how to start would be sufficient, thanks.
Homework Statement
Two 20 lb forces are applied to a ratchet wrench down at A and up at B to loosen bolt β. Find the sum of the moments of the two forces about the axis (x) of the bolt.
Homework Equations
What are the moments at point A, B, and Q?
How do I find the moment about the x-axis and...
Homework Statement
The Tensions in four cables are equal:
|T1| = |T2| = |T3| = |T4| = T
Determine the value of T so that the four cables exert a totl force of 12,500-lb magnitude on the support.
(Inser a picture of 4 connected cables angled 9, 29, 40, 51 degrees respectively)
My question...
This is a diagram of a pitot-static tube. My question is however not related to its applications but rather, what causes the liquid to rise up the static tube? The static tube is at right angles to the fluid flow. I understand that this is a very basic question but I can't seem to get my head...
Homework Statement
http://cisephysics.homestead.com/files/NewSanFranciscoBridge.pdf
My question is on this problem. For some reason, I have trouble seeing which direction the force is pushing when it comes to statics. In this case, why is the column pushing up? I thought it would be going down...
1. Homework Statement
Find forces P,F,and THomework Equations
Fx = 0
Fy = 0
The Attempt at a Solution
So far I only got force T from getting the moment from point b. Don't know how-to start getting force P and F since they're both at the same point. Any help will be much obliged thank you
[/B]
I need to find tensions in suspensions wires on the picture:
I wrote 4 equilibrium equations for moments in A, B, C, D and equilibrium about y-axis, but i got matrix with rank two.
\begin{pmatrix}
3 & 2 & 1 & 0 \\
0 & 1 & 2 & 3 \\
-1 & 0 & 1 & 2 \\
-2 & -1 & 0 & 1 \\
1 & 1 &...
Homework Statement
Member BC exerts on Member AC a force P directed along line knowing that P must have a 325 N horizontal component, determine (a) the magnitude of the force P,
Homework Equations
Trig I suppose
The Attempt at a Solution
So I'm not sure if this correct
I found two angles...
Homework Statement
Two tugboats are pulling a barge. if the resultant of the forces exerted by the tugboats is a 5000-lb force directed along the axis of the barge, determine
(a) the tension in each of the ropes, give then alpha = 45 (b) the value for alpha for which the tension in rope 2 is...
I drew a FBD about point A and came up with the two equations:
∑Fx=0 20sinθ - T-ab(cos70)=0
ΣFy =0 -20cosθ + T-ab(sin70) -20=0
My answer is not coming out so I either messed up on the FBD or the equations, some help would be appreciated. I'm on 3-10 by the way.
1. Homework Statement
The tension in the cable is 800LBs. Find the depth of water that produces this tension. The gate is hinged at B; the cable is attached at A. (Figure 1)Homework EquationsThe Attempt at a Solution
OK, so this is just 2 opposing lever arms: the tension in the cable is...
Homework Statement
I just don't understand how to set the problem for the free body diagram (point (a) and (b)). Can someone help me with this problem? Thank you in advance.
Homework Statement
Please if anyone could help me with this question .
Two wires AC and BC are attached to the top of pole CD . The force exerted by the pole at C is vertical and the 2.5 kN force applied at C is horizontal and makes an angle α with the direction of the x-axis .
Find the...
Homework Statement
Two masses m and M (where M = 2m) are attached with strings. One mass m is suspended from a single verticle string held by two strings each at 45 degrees to the horizontal. The suspending string to the left at 45 degrees is attached to a fixed point. The string on the right...
Homework Statement
A dockworker adjusts a spring line (rope) which keeps a ship from drifting alongside a wharf. If he exerts a pull of 190 N on the rope, which has 1.25 turns around the mooring bit, what force T can he support? The coefficient of friction between the rope and the cast-steel...
Problem is here,
http://s24.postimg.org/3y6wpyncl/frame.png
I'm looking at this problem with the top and bottom beams being separate members and doing a FBD of both separately. However I'm unsure about the points where we have tension/compression. Like at point B, do I include a y component...
Homework Statement
So I was working on this problem, and my only questions are wether BE and CE can be assumed to be no force members? Also if I am not sure a member is a no force member, will it be revealed once I do the calculations,
Homework Equations
ΣF = 0
The Attempt at a Solution
I...
Homework Statement
The smooth homogeneous sphere rests in the 132° groove and bears against the end plate, which is normal to the direction of the groove. Determine the angle θ, measured from the horizontal, for which the reaction on each side of the groove equals the force supported by the end...
hello all,
I am in the process of measuring coefficients of a rectangular panel using given table in textbooks to obtain them.
I have attached a simple figure of two situations; left is my current situation to analyze- a clamped end and compressive force on the other end.
The situations...
Homework Statement
Homework Equations
F^2 (resultant ) = F1^2 + F2^2 -2F1F2cos(theta)
The Attempt at a Solution
i calculated the magnitude using the equation above and it ended up being :
F (resultant) = F sqrt(2-2cos(theta))
i don't know how to solve for the angle.
Homework Statement
Determine the height h above the base B at which the resultant of the three forces acts.
Homework Equations
M=Fd
The Attempt at a Solution
not sure how to get the height here. thanks
im assuming the distance they are asking is less than 72 in. but I am not sure how to...
1. The problem statement, all variables and /known data
Help! I'm stuck on an exceedingly simple statics problem, number 2.24 in the New Millennium edition of exercises for the Feynman lectures.
The problem consists of an inclined plane (inclination angle 30 degrees) on wheels with a...
I'm having trouble number 2.61. I have the answers, but I don't understand why they are doing what they're doing.
They have this for (Fx)1:(Fx)1=(80 lb)*cos(30)*cos(40)=53 lb
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Hi All
I am currently doing a 1st year engineering course. The course is called applied mechanics and focusses on statics. Could someone recommend a good introductory statics textbook.
The link below is the unit outline for my course...
I've been dealing with the concept of moment this whole year, in statics/dynamics but I've never really completely understood it, just rather memorized it.
What I think moment is:
If some point on a body has moment, then this means it wants to rotate. So moment is essentially what causes...
For example, a 1-m bar fixed to a wall holding a weight of 100 N, like this:
How will the free body diagram of the second case different from the first?
Homework Statement
I am to find the reactions of a 3 pin frame.
Homework EquationsThe Attempt at a Solution
So how do I know which direction to label the horizontal reactions? In the diagram HA and HF are in the same direction, I was under the impression that reactions are opposite to applied...
Homework Statement
The 180-lb tree surgeon lowers himself with the rope over a horizontal limb of the tree. If the coefficient of friction between the rope and the limb is 0.60, compute the force (P) which the man must exert on the rope to let himself down slowly.
Homework Equations
T1/T2...
Homework Statement
A refrigerator with a mass of 100kg measures 150cm high by 75 cm wide by 75 cm deep. How much force applied horizontally at the top edge of the front will make it start tipping backward? Assume that the center of mass is at the center of the refrigerator.
Homework Equations...
Hi all, my professor has hinted at proposing a question of this sort to us for a shear and bending moment diagram. Now while I am comfortable with having [either] a uniformly distributed load or a varying one, I'm not sure how to deal with both. I can't seem to find anything in my textbook to...
Homework Statement
find internal normal, shear, and moment forces at point C, P=8kn
The Attempt at a Solution
for the most part I can solve this entire question but looking at the solution for it one of my equations is different and I cannot figure out why.
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Homework Statement
Door weighs 20kg, and is held open by force P at doorknob opposing 15kg weight attached at C and wrapped around pulley. Theta is 90 degrees, so door is on x axis. Find torques on hinges A & B[/B]Homework Equations
P is 118.8N in -k direction, which agrees with answer in...
Homework Statement
Given: T(sub-B) plus T(sub-B) prime = 36. Both T(sub-C) values are 0. T (sub-D) =36 and T (sub-D) prime = 12. Find values of T (sub-B) and T (sub-B) prime[/B]Homework Equations
OK, so we need to find the wrap angle, which should be 180 + 30 -22, which comes to 188...
Homework Statement
Calculate the stress in every segment of the system. AD and BC are laton and AB is steel.
Homework Equations
geometry compatibility-δ(A/D) +δ(A/B) - δ(C/B) = 0
F(D) - F(C) - 50 =0
The Attempt at a Solution
I supossed that DA and BC are in compression and AB is in...
Homework Statement
http://oi59.tinypic.com/2lacy0o.jpg
Homework Equations
P = ?
T2/T1 = e^(u)(θ)
M = 150 N*m
The Attempt at a Solution
[/B]
T2/T1 = e(.4)(7π/6)
T2/T1 = 5.466
I don't even think I'm on the right track.
hey guys. bellow is an upside down cone frustum with the dimensions given bellow where the green R is the radius of the larger circle and the blue r is the radius of the smaller circle and the red h to be the height of the object
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