9.1Contact and non-contact forces
A force is a push or pull that acts on an object due to the interaction with another object. All forces between objects are either:
• contact forces — the objects are physically touching • non-contact forces — the objects are physically separated.
Examples of contact forces include friction, air resistance, tension and normal contact force. Examples of non-contact forces are gravitational force, electrostatic force and magnetic force.
Force is a vector quantity.
You should be able to describe the interaction between pairs of objects which produce a force on each object, with the forces represented as vectors.
The key idea is that forces come in pairs, and the pair acts on two different objects. A book resting on a table: the book pushes down on the table, and the table pushes up on the book with an equal force in the opposite direction. Drawn as vectors, the two arrows are the same length and point opposite ways — but each is drawn on a different object.
Common mistake
Weight is a non-contact force, even for an object sitting on the ground. The Earth pulls the object without touching it; the contact force from the ground pushing up is a separate, different force.
- Force
- a push or pull that acts on an object due to the interaction with another object
- Contact force
- a force acting where the objects are physically touching, such as friction, air resistance, tension and normal contact force
- Non-contact force
- a force acting where the objects are physically separated, such as gravitational, electrostatic and magnetic force
9.3Resultant forces
A number of forces acting on an object may be replaced by a single force that has the same effect as all the original forces acting together. This single force is called the resultant force.
You should be able to calculate the resultant of two forces that act in a straight line. Forces in the same direction add; forces in opposite directions subtract, and the resultant acts in the direction of the larger force.
Worked example
A car experiences a driving force of 3200 N forwards and a total resistive force of 1900 N backwards. Calculate the resultant force.
- The two forces act in a straight line but in opposite directions, so subtract.
- 3200 − 1900 = 1300.
- The larger force is forwards, so the resultant acts forwards.
- State both the size and the direction, because force is a vector.
Answer: 1300 N forwards
- Resultant force
- a single force that has the same effect as all the original forces acting on an object together
9.3–9.5Free body diagrams and resolving forcesHigher tier
Higher tier students should be able to describe examples of the forces acting on an isolated object or system, and use free body diagrams to describe qualitatively examples where several forces lead to a resultant force on an object, including balanced forces when the resultant force is zero.
A free body diagram shows one object on its own, with an arrow for every force acting on it and nothing else. Drawing it that way stops you mixing in forces that act on other objects — a common source of error.
When the forces are balanced the resultant is zero, and the object either stays still or continues at a constant velocity.
A single force can be resolved into two components acting at right angles to each other. The two component forces together have the same effect as the single force.
You should be able to use vector diagrams to illustrate resolution of forces, equilibrium situations, and to determine the resultant of two forces, to include both magnitude and direction — scale drawings only.
"Scale drawings only" is an important limit: you will never be asked to use trigonometry here. The method is to draw carefully and measure.
Worked example
A force of 5.0 N acts north and a force of 3.0 N acts east on the same object. Describe how to find the resultant by scale drawing.
- Choose and state a scale, for example 1 cm represents 1.0 N.
- Draw the 5.0 N force as a 5 cm arrow pointing north.
- From the head of that arrow, draw the 3.0 N force as a 3 cm arrow pointing east.
- Draw a single arrow from the tail of the first to the head of the second — this is the resultant.
- Measure its length and convert using the scale, and measure its angle from north with a protractor.
Answer: The resultant measures about 5.8 cm, so about 5.8 N, at roughly 31° east of north. Give both the magnitude and the direction, since a resultant is a vector.
Common mistake
State the scale on a vector diagram and draw the arrows head to tail. Drawing both arrows from the same point and joining the ends gives the wrong answer, and an unstated scale means the measurement cannot be marked.
Before you practise
- A contact force needs the objects to be touching; a non-contact force acts at a distance through a field.
- Gravitational, electrostatic and magnetic forces are non-contact; friction, tension, air resistance and the normal contact force are contact forces.
- The resultant is the single force that would have the same effect as all of them together.
- Forces in a straight line add if they are in the same direction and subtract if they oppose.
- A free body diagram shows one object, with every force on it drawn as an arrow from its centre, labelled and to scale.
- Resolve a force into two perpendicular components by drawing a scale diagram and completing the rectangle.
- In equilibrium the resultant is zero and a scale drawing of the forces closes into a shape.