AQA · GCSE · Physics
Course version: 8463 · Version from Sept 2016
Newton's Second Law: force, F, in newtons, N
In F = m a, the symbol F stands for force measured in newtons, N. One newton is the force needed to give a 1 kg mass an acceleration of 1 m s⁻², so 1 N = 1 kg m s⁻².
Checked against the AQA 8463 specification (opens in a new tab) on .
- Point 4 of 11
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
In F = m a, the symbol F stands for force measured in newtons, N. One newton is the force needed to give a 1 kg mass an acceleration of 1 m s⁻², so 1 N = 1 kg m s⁻². Force is a vector: it has size and direction, and the direction of the resultant force determines the direction of the acceleration. When several forces act, F means the resultant force, found by combining them along the line of motion. For example, a 2 kg trolley pushed with 10 N forward while friction acts with 4 N backward has a resultant force of 10 N − 4 N = 6 N, giving a = 6 ÷ 2 = 3 m s⁻². Always record force in newtons, not kilograms, and give direction where a question asks for it.
What earns the marks
- State that force is measured in newtons, symbol N, and that 1 N is the force giving a 1 kg mass an acceleration of 1 m s⁻².
- Recognise force as a vector quantity with both magnitude and direction, and state the direction of the resultant force when required.
- Distinguish force in newtons from mass in kilograms, explaining that weight is a force while mass is not.
- Combine multiple forces to find the resultant force in newtons before using it in F = m a.
- Use the relationship 1 N = 1 kg m s⁻² to check that units in a calculation are consistent.
Common mistakes and how to put them right
Treating newtons and kilograms as interchangeable.
Put it right by remembering that mass is measured in kilograms and force in newtons, and that weight equals mass times gravitational field strength.
Giving a force without direction when the question asks for the resultant force.
Put it right by stating the direction, such as 6 N forwards.
Adding all quoted forces regardless of direction.
Put it right by subtracting forces that act in the opposite direction along the line of motion.
Exam tips
- Write the unit N after every force value in your working, and convert any value given in kilonewtons by multiplying by 1000.
- When a question asks for the resultant force, show the addition or subtraction of the individual forces before stating the final value and direction.
- Use the definition of the newton to justify unit conversions, for example explaining that kg m s⁻² is equivalent to N.
Try the lesson
The start of the Newton's Second Law: force, F, in newtons, N lesson, made from checked teaching notes for this specification point.
Have a go first
In the equation F = m a, what is the unit of the quantity represented by the symbol F?
Listen
In F = m a, the symbol F stands for force measured in newtons, N. One newton is the force needed to give a 1 kg mass an acceleration of 1 m s⁻², so 1 N = 1 kg m s⁻². Force is a vector: it has size and direction, and the direction of the resultant force determines the direction of the acceleration. When several forces act, F means the resultant force, found by combining them along the line of motion. For example, a 2 kg trolley pushed with 10 N forward while friction acts with 4 N backward has a resultant force of 10 N − 4 N = 6 N, giving a = 6 ÷ 2 = 3 m s⁻². Always record force in newtons, not kilograms, and give direction where a question asks for it. A strong answer earns marks for these points. State that force is measured in newtons, symbol N, and that 1 N is the force giving a 1 kg mass an acceleration of 1 m s⁻². Recognise force as a vector quantity with both magnitude and direction, and state the direction of the resultant force when required. Distinguish force in newtons from mass in kilograms, explaining that weight is a force while mass is not. Combine multiple forces to find the resultant force in newtons before using it in F = m a. A common slip: Treating newtons and kilograms as interchangeable. Instead, remembering that mass is measured in kilograms and force in newtons, and that weight equals mass times gravitational field strength. Exam tip: Write the unit N after every force value in your working, and convert any value given in kilonewtons by multiplying by 1000.
See it
Key words
Say what each word means before you turn the card.
Force as a vector quantity
Try answering aloud or in your head before turning the card.
The newton as the SI unit of force
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Resultant force and direction
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Distinguishing force from mass
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See every definition
- Force as a vector quantity
- Force has size and direction, and the direction of the resultant force determines the direction of the acceleration.
- The newton as the SI unit of force
- Force is measured in newtons, N, and one newton is the force needed to give a 1 kg mass an acceleration of 1 m s⁻².
- Resultant force and direction
- When several forces act, F means the resultant force, found by combining them along the line of motion, and its direction should be stated where a question asks for it.
- Distinguishing force from mass
- Force is recorded in newtons, not kilograms, and weight is a force while mass is not.
Label the diagram
Some boxes have lost their names. Pick the right name for each number.
1Box 1
2Box 2
3Box 3
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