# Evan's Space

## Wonders of Physics ## Finding resultant force from 2 forces at 0 to 90 degree Refer to the video tutorial for the explanation.

## Vector Diagram – Parallelogram Method for 4 different kinds of questions

For Combined Science Physics Olevel, when constructing vector diagram, a method called Parallelogram Method is commonly used.

Parallelogram Method is used when 2 forces are known, and the resultant (net) force R, can be found.

Below show 5 different variations of questions when can be solved by using Parallelogram Method:

(A) Body has acceleration, forces are unbalanced, there is a resultant force R (Newton’s 2nd law)
(B) Body at rest, all forces are balanced, there is no resultant force R (Newton’s 1st law)
(C) Body moving at constant velocity, all forces are balanced, there is no resultant force (Newton’s 1st law)
(D) Finding unknown force (with resultant force R  + another known force are given)
(F) Vector diagram is applicable to all vector quantities (with magnitude and direction). Not just for forces.

Click here to view video tutorials on how to construct parallelogram step-by-step    For Pure Physics, another method is the closed-loop triangle, where only 1 known force with 2 other unknown force. Click here to view the video tutorials.

## 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 02 Example 03 Example 04 Click here to view another post on Closed-Loop Triangle Method (2 forces, 2 unknowns, 1 known)

Click here to view how parallelogram method is applied to various kind of questions

## N2008/P1/Q5 – Closed Loop Triangle for System in Equilibrium

A heavy sack is suspended from a ceiling by a rope.
The sack is then pulled to one side and held stationary. Which diagram represents the forces acting on the sack in its new position? Solutions: Ans: D ## 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.

## 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? 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.