In classical mechanics, a particle is in mechanical equilibrium if the net force on that particle is zero. By extension, a physical system made up of many parts is in mechanical equilibrium if the net force on each of its individual parts is zero.In addition to defining mechanical equilibrium in terms of force, there are many alternative definitions for mechanical equilibrium which are all mathematically equivalent. In terms of momentum, a system is in equilibrium if the momentum of its parts is all constant. In terms of velocity, the system is in equilibrium if velocity is constant. In a rotational mechanical equilibrium the angular momentum of the object is conserved and the net torque is zero. More generally in conservative systems, equilibrium is established at a point in configuration space where the gradient of the potential energy with respect to the generalized coordinates is zero.
If a particle in equilibrium has zero velocity, that particle is in static equilibrium. Since all particles in equilibrium have constant velocity, it is always possible to find an inertial reference frame in which the particle is stationary with respect to the frame.
1.we know that generally, every force systems can be replaced by a resultant force(R) and a couple(M) at a point O. the position of point O is optional.
but magnitude and direction of M is dependent to this point while magnitude and direction of R is independent.
In static equilibrium R and M...
Homework Statement
A door, essentially a uniform rectangle of height 2.00 m, width 0.87 m, and weight 130.0 N, is supported at one edge by two hinges, one 35.1 cm above the bottom of the door and one 164.9 cm above the bottom of the door. Calculate the horizontal components of the forces on...
Homework Statement
The attached figure shows a weightless bar with several forces applied to it (all in New). The distances are as follow: AB=6m, BC=1m and CD=3m. The question is to calculate DE so there is equilibrium.
Homework Equations
ƩM=0 (Rotational equilibrium)...
Homework Statement
A door made of a uniform piece of wood measures 1 m by 2 m and has a mass of 18kg. The door is entirely supported by two hinges, one at the bottom corner and one at the top corner. Find the force (magnitude and direction) that the door exerts on each hinge. Assume that...
Homework Statement
A 1380 N uniform boom of length ℓ is supported by a cable, as shown. The boom is pivoted at the bottom, the cable is attached a distance 3/4ℓ from the pivot, and a 3604N weight hangs from the boom’s top. Find the tension of the cable.
here is a picture of the diagram...
I do not understand how to solve static equilibrium questions. Like those:
Or this one
http://www.chegg.com/homework-help/questions-and-answers/a-uniform-120-lb-beam-is-supported-in-a-horizontal-positionby-a-pin-and-cable-as-shown-in--q701621
The second one with the pin is especially hard...
Homework Statement
A plank having length L and mass M rests in equilibrium on two supports (1 and 2) that are separated by a distance D. The supports are located at equal distances from the enter of the plank. A mass m hangs from the right end of the plank. If L=6m and D=2m, which of the...
Homework Statement
A uniform beam of length L and mass m shown in the figure below is inclined at an angle of θ to the horizontal. Its upper end is connected to a wall by a rope, and its lower end rests on a rough horizontal surface. The coefficient of static friction between the beam and...
Homework Statement
The figure shows a model of a crane that may be mounted on a truck. A rigid uniform horizontal bar of mass = 90.00 kg and length = 5.200 m is supported by two vertical massless strings. String A is attached at a distance = 1.600 m from the left end of the bar and is...
Homework Statement
If a body is acted upon by clockwise moments of 75 N at 1.25 m
And anticlockwise moments of 50 N at 1.3 m ,
Is it in a state of static equilibrium ?
If not what is required to achieve a state of static equilibrium ?
Homework Equations
sum of all forces on all...
A 736g uniform mass beam is used to suspend a sphere that weighs 5.25N. it is supported by an ideal rope attached to the wall, and one third the length along the beam (from the wall). The angle between the rope ans the beam is 51.0 degrees.
a) draw a free body diagram
b) calculate the...
Homework Statement
Pin C joins members ABC and CDE
Homework Equations
Sum of moments at a point = 0
Sum of vertical forces = 0
Sum of horizontal forces = 0
Weight of triangle acts as a force at its centroid (1/3) its length according to this figure.
The Attempt at a Solution...
Homework Statement
A .110-kg remote control 21.0cm long rests on a table, with a length L overhanging its edge. To operate the power button on this remote requires a force of .365N. How far can the remote control extend beyond the edge of the table and still not tip over when you press the...
Homework Statement
Attached is the picture of the problem and my free body diagram.
The system is in equilibrium.
Homework Equations
Fy = 0 Fx = 0
The Attempt at a Solution
I'm having trouble solving the two equations that I arrive with...
I use +x to the right, and +y up...
The result I got seemed sort of messy and I'm not sure I've gotten the basic idea correctly, so I thought I'd make it sure. I think this was the easiest problem we had to solve for charge distributions and point charges and whatnot, so I know for sure I'll have to practice more if I made any big...
Homework Statement
A hiker, who weighs 985 N is strolling through the woods and crosses a small horizontal bridge. the bridge is uniform, weighs 3610 N, and rests on two concrete supports, one at each end. he stops one - fifth of the way along the bridge. What is the magnitude of the force...
This is the final question on a static equilibrium quiz i had today (physics 12). when comparing answers (as you tend to do after the quiz "did you get x for question y?"), half of my friends (all of equal ability in the course) got a different answer from me, and the other half the same. I am...
Homework Statement
In the figure below, the driver of a car on a horizontal road makes an emergency stop by applying the brakes so that all four wheels lock and skid along the road. The coefficient of kinetic friction between tires and road is 0.36. The separation between the front and rear...
Homework Statement
a. A uniform beam is hanging from a poing 1.00 m to the right of its center. The beam weights 140 N and makes an angle of 30° with the vertical. At the right-hand end of the beam, a 100-N weight is hung; an unknown weight w hangs at the left end. If the system is in...
In a static equililibrium lab, what are some reasons why the sums of the forces and/or torques may not be equal to zero. The forces in N are very close to zero (as my professor said they should be) and the torques in N-cm are not anywhere close to zero. I know the torques are greater than their...
Static Equilibrium Problem
Homework Statement
A uniform bar of length 16 m and mass 8 kg is
attached to a wall with a hinge that exerts a
horizontal force Hx and a vertical force Hy on
the bar. The bar is held by a cord that makes
a 90 degree angle with respect to the bar and 45 degree...
Hello every one
I am confused between two support type:
the pin, and the link
On the textbook, it says, the pin prevents the object from translating vertically and horzontally, therefore, it provides fx and fy reaction forces.
but another type of support is much identical to the pin...
Homework Statement
A ladder is made in the shape of the letter A. Treat the two sides of the ladder as identical uniform rods, each weighing 455 N, with a length of 3.60 m. A frictionless hinge connects the two ends at the top, and a horizontal wire, 1.20 m long, connects them at a distance...
I was tasked with redesigning our system to hydrostatically test valves. I had to incorporate a drip test downstream of the valve that would be the determining factor whether the valve was leaking or not. The system I came up with has 3/8" ID tubing (app. 10 ft) running from the downstream of...
Homework Statement
See Picture: I am only stuck on Part (c) where it asks to calculate the force as the bookcase starts to tip.
Homework Equations
sigma Fx=0, sigma Fy=0, sigma tau=0
The Attempt at a Solution
I am setting up the problem by picking an axis that runs through the...
Been working on this problem
http://www.flickr.com/photos/archiphoto77/6179533925
(SEE LINK FOR PHOTO OF PROBLEM)
for quite some time now, and the components don't quite add up for me so I am just a tad exasperated... In the x-z projection, I see two forces acting along the x-axis---one...
Homework Statement
Find H as a function of L and XHomework Equations
http://imageshack.us/photo/my-images/28/project1questoin.png/
http://imageshack.us/photo/my-images/28/project1questoin.png/
The Attempt at a Solution
my answer came out to a ridiculous solution and I am not really sure if it...
Homework Statement
http://img849.imageshack.us/img849/3716/staticeqpulley.jpg
Hopefully the image showed up. If not, here's the link: [PLAIN]http://img707.imageshack.us/img707/3716/staticeqpulley.jpg"
Sorry for the low quality pictures. Hopefully it will do though. The question is: Relate...
Homework Statement
My problem is getting the SOLVE() function to work correctly. I have used it plenty of times in the past, but when I put in these 4 equations to solve simultaneously, it gives me the wrong answers. My Professor said that TI-89's sometimes have problems when having to solve...
Homework Statement
It's not possible for me to solve this problem.
Maybe work/energy relations is required ?
Homework Equations
I've ended up with polynomiums of 3. and 4. degree, trying to find the roots.
But finding the...
Homework Statement
I have been given two forces and have to calculate the magnitude and direction of the third force that will result in equilibrium. The two forces I have been given are:
F1 = 2.156N at 48 degrees
F2 = 4.508N at 203 degreesHomework Equations
I used both the cosine law (c^2...
Homework Statement
A bridge truss extends x = 214 m across a river (Fig. P12.68) where θ = 35°. The structure is free to slide horizontally to permit thermal expansion. The structural components are connected by pin joints, and the masses of the bars are small compared with the mass of a 1270...
Homework Statement
A nonuniform fire escape ladder is 6.0 long when extended to the icy alley below. It is held at the top by a frictionless pivot, and there is negligible frictional force from the icy surface at the bottom. The ladder weighs 250 , and its center of gravity is 2.0 along the...
Homework Statement
The uniform rod in the figure is supported by two strings. The string attached to the wall is horizontal, and the string attached to the ceiling makes an angle of ϕ with respect to the vertical. The rod itself is tilted from the vertical by an angle θ. If ϕ = 29.9°...
1. A gymnast of weight 720 N is holding himself in the cross position on the high rings. He is quite still. A free-body force diagram for the gymnast shows the two upward pulls of the rings on the hands, each, size 380 N. Calculate the angle between the wires supporting the rings and the...
Homework Statement
Homework Equations
M=fd
M= r x F
The Attempt at a Solution
this question really loses me. I'm not sure what exactly it is asking for, much less how to solve it. I am assuming it want's the force on A and E? I suppose I need to find the moment about each...
Homework Statement
Calculate minimal force P of the brakes during the stopping of the wheel.
http://img823.imageshack.us/img823/6017/problemzy.jpg
Solution is P=34.3 [N]
Homework Equations
(Written on scan above)
The Attempt at a Solution...
Homework Statement
At what distance "d", from point "A", the board with the person will slide whereas
http://img267.imageshack.us/img267/6139/skkkkkkk.jpg
Uploaded with ImageShack.us
Homework Equations
Weight of board = 50 [kg]
Weight of person = 100[kg]
Frictional coefficient...
Okay, me and my friend have been working on this problem for a while and it just been a headache catalyst for us...your help is called upon, people of the internet.
Homework Statement
A system of weights is in equilibrium.
Calculate the distance "s" where
WD = 5[N]
WF = 5 [N]
WE =...
Homework Statement
Two workers carry a beam at the length of 3 meters. One worker holds the beam at the edge and carries 0.4 of the beam's weight. At what distance (x) from the other edge holds the second worker?
Homework Equations
None.
The Attempt at a Solution
The solution is...
Homework Statement
A charge -q and a charge 4/9q are located at coordinates x = 0 and x = a, respectively. If you place a third charge so that all three are in static equilibrium, justify that its position and its charge,respectively, can only be
x=3a Q=-4q
Homework Equations...
Static Equilibrium...don't understand something
http://img135.imageshack.us/img135/4664/helpo.jpg
Look at the equation at "sum of all forces on y axis" and please tell me: How the heck did 0.4Na -mg = 0 turn into Na = 2.5m g?
Hi
I have posted the picture of the problem. I have already done the problem but I have some
questions. Here the trailer is accelerating due to the applied force P. I used an inertial frame of
reference at some distance to the left of the car.And then did the torque calculations with...
one end of a uniform 10 meter long rod weighing 50 Newtons is supported by a cable at an angel of 53 deg with the rod the other end rests against the wall where is is held by a friction us=2 . determine the minimum distance x from the left end of the rod at which a block weighing 20 Newtons can...
Homework Statement
A large crate weighing 4520 N rests on four 12-cm-high blocks on a horizontal surface (figure below). The crate is 2.0 m long, 1.2 m high, and 1.2 m deep. You are asked to lift one end of the crate using a long steel pry bar. The fulcrum on the pry bar is 11 cm from the end...
Homework Statement
I have a question about rotational static equilibrium. When we consider the static equilibrium of a system, I realized that most people only consider the net torque acting on the system. Why don't we need to consider the net force acting on the system?
For instance:
A...
Homework Statement
A uniform ladder of mass m and length l leans at an angle theta against a frictionless wall. If the coefficient of static friction between the ladder and the ground is mu, determine a formula for the minimum angle at which the ladder will not slip.
Homework Equations...
Homework Statement
Please help me do these :
[PLAIN]http://broadcastsol.com/321.JPG
Prob1
The mechanical system of massless members is shown in the figure. Determine the relationship between two forces P1 and P2 to keep the system in equilibrium at position as showing in the...
Homework Statement
[PLAIN]http://broadcastsol.com/123.JPG
Prob. 1. The structure of massless members is shown in the figure. Determine the reaction forces at the supports C, and forces in the rod EF and DG. Givens: P, a, b, c.
Prob. 2.
The structure of massless members is shown...