Static Equilibrium: Proving Forces are Equal

  • Thread starter Thread starter astr0
  • Start date Start date
  • Tags Tags
    Conceptual Forces
AI Thread Summary
In static equilibrium, three forces acting on an object must balance, resulting in a net force of zero. To prove that the forces are equal, one can represent them as vectors forming a triangle, where each force corresponds to a side of the triangle. The relationship between the forces can be established using the sine of the angles between them. By applying trigonometric principles, it can be shown that the ratio of each force to the sine of its corresponding angle is equal. This geometric representation confirms that the forces are indeed in equilibrium.
astr0
Messages
17
Reaction score
0
Three forces act on an object in static equilibrium.
9h56l2.gif


(a) If F1 and F2 represent the magnitudes of the forces acting on the object, show that
ayrpxs.png
.

(b) Show that
2vwimux.png


I know that the sum of all forces needs to be zero if the system is in equilibrium, but I don't know how to prove that each force divided by the sine of theta is equal to each other.
 
Last edited:
Physics news on Phys.org
when you add three forces (in representation ) which are in equilibrium, you get a triangle
this is because the net magnitude is zero. Draw such a diagram and then solve the question
 

Thread 'Rolling without slipping on a curved surface'

Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
View full post »
Thread 'Correct statement about a reservoir with an outlet pipe'

Thread 'Correct statement about a reservoir with an outlet pipe'

The answer to this question is statements (ii) and (iv) are correct. (i) This is FALSE because the speed of water in the tap is greater than speed at the water surface (ii) I don't even understand this statement. What does the "seal" part have to do with water flowing out? Won't the water still flow out through the tap until the tank is empty whether the reservoir is sealed or not? (iii) In my opinion, this statement would be correct. Increasing the gravitational potential energy of the...
View full post »
Thread 'A bead-mass oscillatory system problem'

Thread 'A bead-mass oscillatory system problem'

I can't figure out how to find the velocity of the particle at 37 degrees. Basically the bead moves with velocity towards right let's call it v1. The particle moves with some velocity v2. In frame of the bead, the particle is performing circular motion. So v of particle wrt bead would be perpendicular to the string. But how would I find the velocity of particle in ground frame? I tried using vectors to figure it out and the angle is coming out to be extremely long. One equation is by work...
View full post »

Similar threads

Static equilibrium | Uniform sphere on incline | Determining friction
Replies
43
Views
2K
Equilibrium of Forces and Torques on Sawhorses Supporting a Person on a Board
Replies
6
Views
2K
Three equal forces applied to a rectangle, find net torque direction?
Replies
30
Views
4K
Torque: find the force necessary for a body to be in equilibrium
Replies
6
Views
2K
Equilibrium Forces: Force to Move a Mass
Replies
6
Views
1K
Spring-mediated dipole in a magnetic field
Replies
31
Views
2K
What is the Correct Angle for Tension Force in Arm Mechanics?
Replies
2
Views
2K
To find the resultant of forces on a lamina
Replies
5
Views
3K
Potential energy of an electrostatic system in equilibrium
Replies
14
Views
1K
How to calculate the magnitudes of three forces around a hexagon
Replies
17
Views
2K

Hot Threads

Recent Insights

Back
Top