What is the difference between scalars and vectors, and what types of force are there?
Scalars, vectors and forces: the difference between scalar and vector quantities, contact and non-contact forces, weight and the resultant of several forces.
A focused answer to AQA GCSE Physics 4.5.1, covering the difference between scalar and vector quantities, contact and non-contact forces, weight and gravity, and how to find the resultant of forces acting in a line.
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What this dot point is asking
AQA wants you to distinguish scalar and vector quantities, classify forces as contact or non-contact, calculate weight, and find the resultant of forces acting along a line. This is part of topic 4.5.1 of the AQA GCSE Physics (8463) specification.
Scalars and vectors
Contact and non-contact forces
The key idea behind non-contact forces is that they act through a field, so the two objects do not need to be touching. A magnet attracts a steel paperclip across a gap through its magnetic field, and the Earth pulls on the Moon across empty space through its gravitational field. Contact forces, by contrast, only exist where surfaces meet, such as friction between a tyre and the road or the normal contact force from a table pushing up on a book resting on it. Being able to classify a named force as contact or non-contact is a standard one-mark exam task.
Weight
Mass is a scalar (the amount of matter, in kilograms); weight is a vector (a force, in newtons). They are directly proportional, . Because the field strength differs from place to place, the same object weighs less on the Moon (where is about ) than on Earth, while its mass stays the same. Weight is measured with a calibrated spring balance (a newtonmeter), which works because the extension of the spring is proportional to the force pulling on it. The point at which weight is taken to act, the centre of mass, is the single point where all the object's mass can be considered to be concentrated; for a uniform symmetrical object this is at its geometric centre.
Resultant force
The resultant force is what determines how an object's motion changes, through Newton's second law. If the resultant force is zero, the forces are balanced and the object stays at rest or keeps moving at a constant velocity. If the resultant is not zero, the object accelerates in the direction of the resultant. For forces that are not in a straight line, AQA higher-tier candidates use a scale drawing: the forces are drawn end to end as arrows (a vector diagram), and the resultant is the single arrow drawn from the start of the first to the end of the last, with its length giving the size and its direction read from the diagram.
Try this
Q1. State the difference between a scalar and a vector quantity. [2 marks]
- Cue. A scalar has magnitude only; a vector has magnitude and direction.
Q2. Calculate the weight of a bag on Earth (). [2 marks]
- Cue. .
Exam-style practice questions
Practice questions written in the style of AQA exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.
AQA 20184 marksA skydiver of mass is falling. The gravitational field strength is . Calculate the weight of the skydiver, and calculate the resultant force on the skydiver at the moment air resistance acting upwards is , stating its direction.Show worked answer →
First find the weight using , acting vertically downwards (2 marks). The two forces act along the same vertical line in opposite directions, so the resultant is the difference: (1 mark), directed downwards because the weight is larger than the air resistance (1 mark). Markers reward the correct weight, subtracting the opposing forces rather than adding them, and stating the direction. A common error is to add the two forces; forces in opposite directions partly cancel.
AQA 20213 marksExplain the difference between mass and weight, and explain why an object's weight is different on the Moon but its mass is the same.Show worked answer →
Mass is the amount of matter in an object, a scalar measured in kilograms, and it does not depend on location (1 mark). Weight is the force of gravity acting on that mass, a vector measured in newtons, given by (1 mark). On the Moon the gravitational field strength is much smaller than on Earth (about one sixth), so the weight is smaller, but the mass is unchanged because the amount of matter has not changed and mass does not depend on the gravitational field (1 mark). Markers reward the scalar-vector distinction, the equation , and the reasoning that only changes between the Earth and the Moon.
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Sources & how we know this
- AQA GCSE Physics (8463) specification — AQA (2016)