Resultant Forces (Cambridge (CIE) IGCSE Physics): Revision Note

Effects of forces

• A force is defined as:

A push or a pull that acts on an object due to the interaction with another object

• Forces can have a variety of effects on an object

• Forces can change an object's

  • speed

  • direction

  • shape

  • size

A thrust force can cause a car to speed up, a gravitational force can cause a comet to change direction, compression forces can cause a spring to change shape

• The effects of forces on an object often depend on the type of force acting

  • The push force (thrust) of an engine can cause a car to speed up, whilst the force exerted by the brakes (friction) can cause it to slow down

  • The gravitational pull of the Sun on a comet causes the comet to change direction

  • When two opposing forces push on each end of a spring, the spring changes shape (it compresses)

Resultant forces on a straight line

What is a resultant force?

• A resultant force is the single force that has the same effect as all the forces acting on an object

• When multiple forces act on one object along the same straight line, the forces can be combined to produce one net force that describes the combined action of all of the forces

• This single resultant force determines:

  • The direction in which the object will move as a result of all of the forces

  • The magnitude of the net force experienced by the object

Balanced and unbalanced forces

• The forces acting on an object can be described as balanced or unbalanced

• Forces are balanced if multiple forces along the same straight line act in opposing directions with an equal magnitude in each direction

  • The effects of the forces then cancel out

  • There is no resultant force along that straight line

• Forces are unbalanced if the effects of the forces acting in each straight line do not cancel out

  • There is a resultant force in one or more lines of direction

• Consider the forces acting on a book at rest on a table:

  • The gravitational pull of the Earth on the book (weight) acts in a downward direction

  • The push force of the table on the book (normal contact force) acts in the upward direction

  • The forces are equal in magnitude and opposite in direction

  • The forces are therefore balanced

  • There is no resultant force acting on the book

Zero resultant force on a book resting on a table

A book resting on a table is an example of balanced forces

Calculating resultant force

• 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 one value is assigned as positive and one as negative

• So the resultant force acting on the object is

$\mathrm{resultant}\mathrm{force}=5+\left(-5\right)$

$\mathrm{resultant}\mathrm{force}=0\mathrm{N}$

• 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 does not 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

$\mathrm{resultant}\mathrm{force}=3+7$

$\mathrm{resultant}\mathrm{force}=10\mathrm{N}$

• 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

$\mathrm{resultant}\mathrm{force}=\left(-7\right)+3$

$\mathrm{resultant}\mathrm{force}=-4\mathrm{N}$

• In this case, the box will move to the left due to the resultant force of 4 N

Zero and non-zero resultant forces

Zero and non-zero resultant forces acting on three objects