static equilibrium Definition and Topics - 42 Discussions
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.
A diagram of the physical situation is below:
Choosing the positive ##y## direction to be upwards and the positive direction of rotation to be counterclockwise, Newton's linear second law gives:
$$-m_D g + F_L + F_R = 0$$
where ##F_L## is the magnitude of the force exerted on the bar by the...
If I can determine the weight of that heavy object placed on the plank, I will be able to determine the stretch of that wire. But, when using the second condition for static equilibrium (torques of the system equal to 0), I always end up with two unknowns, no matter what point of rotation I...
i really cant understand the answer of this question, is the question 1.3 in fluid mechanics by Frank ,M White
For the triangular element in Fig P1.3, show that a tilted free liquid surface, in contact with an atmosphere at pressure pa, must undergo shear stress and hence begin to flow.
I know I have to find the x and y components of T1 using 400cos(55) and 400sin(55) and I know that the x-component of T1 will = the x-component of T2 but opposite sign to give 0. But idk how to get there and what do to for the y-component. I think I found the weight, I think it’s 32.42g but I’m...
a uniform rod of mass m is placed as shown, with one of its end resting on a smooth wall while 1/4 of the rod's length is sticking out of a rough table. Find the net force the table exert on the rod at the corner.
i drew the free...
A block of uniform density experiences a force F to the right, applied 5/3 m from the bottom of the block. The block is 2 m high and 1 m wide. Take the pivot point to be the point at the bottom right of the block. Find the value of the force that is just able to tip the box...
I'm not used to communicate physics in English, so my language may be a bit off.
This task is fairly simplistic. It's a figure which is held up in points A and B (both having an x and y force exerted on them), and the figure has a joint C. It is depicted in attached files.
Long time reader, first time poster..
I hope someone out there can help me. I'm designing an add-on to an existing piece of equipment and I'm unsure of how to calculate the resultant force output from a hydraulic cylinder.
On a straight push, the chosen hydraulic cylinder has an...
An object is suspended on a frictionless slope inclined plane by a rope parallel to the incline. If the angle of the incline is 25° and the tension on the rope is 5000 N, what is the weight of the object
The Attempt at a Solution
So in my eyes, you...
A meter stick with a mass of 260 g is supported horizontally by two vertical strings, one at the 0-cm mark and the other at the 90-cm mark
A) What is the tension in the string at 0 cm
B) What is the tension in the string at 90 cm
C) The string at the 90-cm mark is cut. What...
An artist must push with a minimum of 75N at an angle of 45° to a picture to hold it in equilibrium. The coefficient of friction between the wall and the picture frame is 0.30. What is the mass of the picture?
The Attempt at a Solution
What I've attempted to do is resolve vertically and horizontally:
After that.... I'm completely stuck. Any help would be appreciated, I've spent so long on this I bet I'm just missing one simple thing.
Thanks in advance
Consider a rigid 2.60-m-long beam (see figure) that is supported by a fixed 1.30-m-high post through its center and pivots on a frictionless bearing at its center atop the vertical 1.30-m-high post. One end of the beam is connected to the floor by a spring that has a force...
Two linear springs with stiffness Kh, Kv are attached to a single mass m at right angle to each other, i.e; one of the spring(Kh) is in the horizontal direction(x-axis) and the other(Kv) is in the vertical direction(y-axis).
A constant force F is being applied to the mass...
free body diagram
I'm having trouble understanding (what I guess should be) a simple concept and so I can't apply it to a project I'm working on (also kind of rusty on torques and mechanics problems)
If I have a hinged beam (of uniform weight) and I lift it from one end and stay...
I was working on a pulley system as shown here:
The mass on the right and left side is equivalent, and I am solving for when the system is in static equilibrium. Theta is the angle between the rope on either side of one of the pulleys. H and y are both measured from the original position of...
A bridge, constructed of 11 beams of equal length L and negligible mass, supports an object of mass M as shown in the picture.
Assuming that the bridge segments are free to pivot at each intersection point, what is the tension T in the horizontal segment directly above the...
I have a 3 pulley system statically balanced hanging weights at a determined relative angle (we are taking into account friction). If I change the position of one pulley, angles will remain the same. However, if I have a 4 pulley system, at the same conditions, changing one's position will...
This question pertains to the classic ladder-leaning-against frictionless wall scenario. The system is in static equilibrium. The ladder is thin and can be assumed to be made of a homogeneous material so that the center-of-mass lies at the geometric center.
The forces in this scenario is...
1. Homework Statement
The door has a mass of 30 kg, is 200 cm long and 90 cm wide. The hinges are installed at 25 cm from the bottom (R2) and 25 cm from the top (R1). What are is the magnitude of the force exerted by each hinge on the door? The door is in a state of static equilibrium...
Given three spring scale readings, positioned at unknown angles, find the mass of the weight hanging from all three scales without using trig, and without measuring the angles. You have only a yard stick. This is a static equilibrium problem.
If you were to look at a simple 2D or 3D static equilibrium diagram, where a mass is suspended by multiple ropes at different angles, my gut feeling is that there is a fairly simple proportion between the distance between the center of mass and the rope (the distance created opposite of the...
There is a diving board held up by two pillars A and B, and there is a diver standing on it's edge. What are the directions of the forces exerted at points A and B? Picture Below:
F_NET = 0
The Attempt at a Solution
I thought both A and B were...
You are holding a sign as shown below. The sign (including the horizontal bar it hangs from) has a mass of 2.20 kg and is 40.5 cm wide. The sign is hanging from a 1.03 m tall, 4.46 kg vertical post. The sign is symmetric with a uniform mass distribution as implied by the...
For my physics lab, they had us do a simple static equilibrium experiment where we rested a ruler on a fulcrum (at its center of mass) and then attached varying amounts of weight on either end at different distances from the fulcrum. This screenshot is the data we recorded...