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Wonders of Physics


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Vector Diagram – Parallelogram Method

For Combined Science (Physics), drawing of vector diagram is a must.
In general, two known forces are given and the resultant force of these two forces is to be found using the vector diagram.

There are two methods to draw vector diagram 1) Parallelogram method and 2) Tip-to-tail method. In this post, the parallelogram method is used.

Example 01
Capture 01

Example 02

Capture 02

Example 03

Capture 03

Example 04

Capture 04

Click here to view another post on Closed-Loop Triangle Method (2 forces, 2 unknowns, 1 known)


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Vector Diagrams

Vector diagram is commonly referred to parallelogram rule.

Vector diagrams are generally divded into 3 categories:
1) 2 forces acting on a body, there is a resultant force. (Newton’s 2nd Law)

2) 3 forces acting on a body, the body is at rest / in equilibrium or moving at constant speed. (Newton’s 1st Law, Net force = 0N)
    – The resultant force due to any 2 forces is equal and opposite to the 3rd unknown force.

3) 3 forces acting on a body, the body is at rest / in equilibrium or moving at constant speed (Newton’s 1st Law, Net force = 0N)
    – Only 1 known force, angles given, using closed loop triangle to find the 2 unknown forces.

Let’s look at some examples for each category.

1) 2 forces acting on a body, there is a resultant force. (Newton’s 2nd Law)

2) 3 forces acting on a body, the body is at rest / in equilibrium or moving at constant speed. (Newton’s 1st Law, Net force = 0N)
    – The resultant force due to any 2 forces is equal and opposite to the 3rd unknown force.
    – You can either use parallelogram rule or closed looped triangle.

Example 1: Body at rest – Using Parallelogram Rule

Example 1: Body at rest – Using Closed-Looped Triangle

Example 2: Body at constant speed – Using Parallelogram Rule

Example 2: Body at constant speed – Using Closed-Looped Triangle

3) 3 forces acting on a body, the body is at rest / in equilibrium or moving at constant speed (Newton’s 1st Law, Net force = 0N)
    – Only 1 known force, angles given, using closed loop triangle to find the 2 unknown forces.

Click here to view the construction of vector diagram using Parallelogram Method.


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Resultant force and Vector Diagram

A trolley is acted on by three forces, P, Q and R in magnitude and direction as shown in the figure below. A single force F could balance all three forces. What is the magnitude of F?

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Solutions:There are 3 different forces, P, Q and R acting on the trolley.Consider the forces P and R only, as they are acting perpendicular to each other, the resultant force falls exactly on Q. (using the vector diagram method/parallelogram method).The resultant of P and R is Q, plus the existing Q, will give a final resultant force of 2Q acting on the trolley.