Resultant Forces (Oxford AQA IGCSE Combined Science Double Award)
Revision Note
Written by: Leander Oates
Reviewed by: Caroline Carroll
Resultant Forces
What is a resultant force?
When a number of forces are acting on a single object, the forces can be replaced by a single force that has the same effect on the motion of the object as all the original forces acting together
This single force is called the resultant force
The resultant force determines:
The direction in which the object will move as a result of all of the forces
The magnitude of the final force experienced by the object
What is a Free-Body force diagram?
Free-body force diagrams are vector diagrams showing the multiple forces acting on a single object
The vectors can be drawn onto a picture of the object, or the object can be represented by a dot
Free-Body force diagram of a car
The vertical forces add together
In the example of the car, the normal contact force and the weight are equal in magnitude and opposite in direction
Therefore, the vertical forces add up to zero
We say the forces are balanced
The horizontal forces add together
In the car example, the thrust force has a greater magnitude than the frictional force and acts in the opposite direction
Therefore, the net horizontal force is in the forward direction
Taking all the forces into account, the resultant force is in the forward direction
A non-zero resultant force will cause a change in the object's motion
A change in the object's motion is an acceleration
In the example of the forward travelling car, the car will accelerate or speed up
Examiner Tips and Tricks
Force diagrams are any diagrams which show forces acting, free-body force diagrams specifically show the forces acting on a single object. You don't need to know this terminology for your exam, but you do need to recognise if the forces shown in a diagram are acting on a single object or on multiple objects.
Calculating resultant forces
Force is a vector quantity, it has both magnitude and direction
When adding forces together it is important to assign positive and negative values to show the direction in which the forces are acting
If a 5 N force acts to the right and a 5 N force acts to the left on an object, then we assign one of the values as positive and one as negative
So the resultant force acting on the object is
The forces acting on the object are equal in magnitude and opposite in direction therefore they cancel one another out
This is like two people pushing a box with equal force from opposite sides, the box doesn't move
If two people push the box from the same side in the same direction, one with a 3 N force and one with a 7 N force, then the forces will add together and the box will move in the direction of the resultant force
If two people push the box in opposite directions, one with a 7 N force to the left (negative) and one with a 3 N force to the right (positive), then the forces will add together and the box will move in the direction of the resultant force
Zero and Non-Zero resultant forces
Worked Example
Calculate the magnitude and direction of the resultant force in the diagram below.
Answer:
Step 1: Assign a direction to the forces
Forces acting to the right are positive
Forces acting to the left are negative
Step 2: Add together all the forces acting on the object
Step 4: State the magnitude and direction of the resultant force
The resultant force is 2 N to the left
Examiner Tips and Tricks
Mathematically, it doesn't matter which direction you assign to be positive or negative, as long as you are consistent throughout your calculation.
Using scale diagrams to determine resultant force
There are two methods that can be used to combine vectors using a scale diagram: the triangle method and the parallelogram method
To combine vectors using the triangle method:
Step 1: link the vectors head-to-tail
Step 2: the resultant vector is formed by connecting the tail of the first vector to the head of the second vector
Step 3: The magnitude of the resultant vector can be found by measuring the length of the arrow
To combine vectors using the parallelogram method:
Step 1: link the vectors tail-to-tail
Step 2: complete the resulting parallelogram
Step 3: the resultant vector is the diagonal of the parallelogram
Step 4: The magnitude of the resultant vector can be found by measuring the length of the arrow
Triangle and Parallelogram method of combining vectors
Worked Example
Two ropes are used to pull a shopping trolley out of a ditch. The angle between the forces is 40°
Draw a vector diagram to determine the magnitude of the resultant force from the ropes on the shopping trolley.
Answer:
Step 1: Draw the known vectors on the scale diagram
Select a suitable scale that allows room for the parallelogram to be constructed
The scale used here is 2 cm = 100 N
Draw the vectors tail to tail at an angle of 40°
Step 2: Construct the parallelogram
The lines should be the same length as the vectors and at the same angles
Step 3: Draw the resultant vector
Draw in the resultant vector as the diagonal of the parallelogram
Step 4: Determine the magnitude of the resultant force
Measure the length of the vector
Use the scale to work out the magnitude
The scale is 2 cm = 100 N
Therefore, 1 cm = 50 N
An answer between 280 N and 290 N would gain the mark
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