Form 5 - Understanding Forces in Equilibrium

 To understand Forces in Equilibrium in Form 5 DLP Physics, here's a structured explanation:

Key Concepts

1. Definition:

   • When an object is in equilibrium, the resultant force acting on it is zero, meaning:

     • The object is at rest (static equilibrium), or

     • The object is moving with a constant velocity (dynamic equilibrium).

2. Conditions for Equilibrium:

   • First Condition: The vector sum of all forces acting on the object is zero:

$$\mathrm{\Sigma }{F}_x=0\text{and}\mathrm{\Sigma }{F}_y=0\backslash Sigma\; F\_x\; =\; 0\; \backslash quad\; \backslash text\{and\}\; \backslash quad\; \backslash Sigma\; F\_y\; =\; 0$$

• Second Condition: The net torque acting on the object is zero:

$$\mathrm{\Sigma }\tau =0\backslash Sigma\; \backslash tau\; =\; 0$$

Force Diagram:

• Draw all forces acting on the object using a free-body diagram (FBD).

• Label the forces clearly (e.g., weight, normal force, tension, friction).

Steps to Solve Equilibrium Problems:

1. Identify all forces acting on the object and their directions.

2. Resolve any inclined forces into horizontal ($F_{x}F\_x$) and vertical ($F_{y}F\_y$) components.

$$F_x=F\cos \theta ,F_y=F\sin \theta F\_x\; =\; F\; \backslash cos\; \backslash theta,\; \backslash quad\; F\_y\; =\; F\; \backslash sin\; \backslash theta$$

3. Apply the conditions of equilibrium:

   • For horizontal forces: $\mathrm{\Sigma }{F}_x=0\backslash Sigma\; F\_x\; =\; 0$

   • For vertical forces: $\mathrm{\Sigma }{F}_y=0\backslash Sigma\; F\_y\; =\; 0$

4. If torques are involved, identify the pivot point and ensure:

$$\mathrm{\Sigma }\tau =0\backslash Sigma\; \backslash tau\; =\; 0$$

Applications:

• Calculating tension in strings or cables.

• Balancing beams on a pivot.

• Solving problems with ladders, bridges, or objects on inclined planes.

Example Problem:

A 10 kg box is suspended by two ropes at angles of 30° and 45° to the horizontal. Find the tension in each rope.

1. Draw a free-body diagram.

2. Resolve the tension forces into components.

3. Apply equilibrium equations:

$$\mathrm{\Sigma }{F}_x=0\text{and}\mathrm{\Sigma }{F}_y=0\backslash Sigma\; F\_x\; =\; 0\; \backslash quad\; \backslash text\{and\}\; \backslash quad\; \backslash Sigma\; F\_y\; =\; 0$$

4. Solve for the tensions.