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Equilibrium of Forces

Neil Trivedi

Teacher

Neil Trivedi

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Equilibrium of Forces

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Challenging Question

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Equilibrium of Forces

When an object is in equilibrium, it means there is no resultant (net) force and no resultant moment acting on it. In this section we will be focusing on particles which are dimensionless so will have no moment forces acting on it.

The way to tackle questions like this is to resolve all forces into their horizontal and vertical components, equate them and then solve them either individually or simultaneously.

When setting up the horizontal equation, we equate the leftward and rightward forces, and for the vertical, we equate the upward and downward forces.

Example 1:

A particle of mass kg is attached to one end of a light inextensible string at . The other end of the string is attached to a fixed point . A horizontal force N is applied to the particle at . The particle is held in equilibrium under gravity. Find the tension in the string and the value of .

A single small point is shown on an otherwise blank dark background, representing a reference point (such as the origin) for a coordinate or geometry diagram.

Step 1: Draw a force diagram.

A point has two forces acting on it: a diagonal tension force 𝑇 directed up-left and a vertical downward weight force of 5𝑔, forming a simple force diagram for equilibrium.

We break down the tension to its horizontal and vertical components and add the weight of .

A tension force 𝑇 acting at 60^∘ to the vertical is resolved into components 𝑇 cos 60^∘ upward and 𝑇 sin 60^∘ horizontally left, alongside a downward weight of 5𝑔 at the same point.

Step 2: Resolve the vertical force.

The only two forces are the weight and the vertical component of the tension.

N

Step 3: Resolve the horizontal force.

Here we have the horizontal component of tension and .

N

No answer provided.

Example 2:

A particle of weight N is suspended by two strings from a fixed horizontal ceiling. The particle hangs in equilibrium. The strings are light and inextensible and are inclined at and to the ceiling, as shown in the figure.

Two slanted cables are attached to the ends of a horizontal beam and meet at a single point below, forming a V-shaped support system used for tension and equilibrium analysis.

Find the tension in each of the two strings.

Step 1: Draw a force diagram.

Since we have two strings, we label them individually as and instead of just and break them down to their horizontal and vertical components. We also add in the weight of . Due to alternate angles being equal ( angles), the angles in blue are equal to their respective angles at the ceiling.

Two cables meet at a joint supporting a 65N downward force, with tensions 𝑇_1 at 40^∘ left and 𝑇_2 at 35^∘ right resolved into horizontal components 𝑇_1 cos 40^∘, 𝑇_2 cos 35^∘ and vertical components 𝑇_1 sin 40^∘, 𝑇_2 sin 35^∘.

Step 2: Resolve the horizontal force.

The only two horizontal forces are the horizontal components of the tensions.

Step 3: Resolve the vertical force.

Here we have the vertical components of the tensions and the weight.

Substituting ,

N

We take the exact value of when we calculate .

N

No answer provided.

Challenging Question

Practice Questions

Friction Newton's 2nd Law in 2D with Friction