Edexcel IGCSE Physics · Spec 1.5-1.7E
Force & Weight: The Equations (Worked Examples)
Worked examples using the force and weight equations.
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Force & Weight: The Equations (Worked Examples)
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Explained
Two equations with the same shape
Weight equals mass times gravitational field strength, W equals m g. Resultant force equals mass times acceleration, F equals m a.
They have the same structure, and that is not a coincidence. Weight is the force gravity exerts, and g is the acceleration it would produce, so the second equation applied to gravity alone gives the first.
Using W equals m g
Mass in kilograms, g in newtons per kilogram, weight in newtons.
A 60 kg person on Earth, with g about 10 N/kg, weighs 600 N. The same person on the Moon, where g is about 1.6 N/kg, weighs about 96 N. The mass has not changed at all.
To find a mass from a weight, divide by g. A 250 N object on Earth has a mass of 25 kg.
Using F equals m a
The F is the resultant force, not any single force acting. If several forces act, work out the resultant first, and only then use the equation.
A 1200 kg car with a resultant force of 3600 N accelerates at 3600 divided by 1200, which is 3 m/s squared.
To find a force, multiply. To find a mass, divide the force by the acceleration. The unit of acceleration is metres per second squared, and forgetting the squared is a common slip when writing the answer.
When both appear together
Many questions need both equations in sequence, and the order matters.
A falling object with air resistance: find its weight with W equals m g, subtract the air resistance to get the resultant force, then use F equals m a to find the acceleration.
A mass hanging over a pulley pulling a trolley: the pulling force is the weight of the hanging mass, so multiply by g first, and only then divide by the total mass being accelerated.
Going straight to F equals m a with a mass in kilograms as though it were a force is the error that pulley questions are designed to catch.
What the mark scheme accepts and rejects
An Edexcel International GCSE Physics mark scheme shows how flexible the examiners are about route. Asked for a force, it accepts using F equals m a together with acceleration equals change in velocity over time, allows an error carried forward from the earlier part, ignores the sign, and accepts any answer that rounds to the expected value for both marks.
Another mark scheme allows the use of 9.8 or 9.81 for g as well as the value printed in the paper, and instructs the examiner to ignore the word gravity written in place of g.
So several different correct methods and several slightly different constants are all acceptable. What is not acceptable appears in a third: substitution into an incorrectly arranged formula scores zero.
The pattern across all of these is the same. Write the equation as it stands, put the numbers in, and rearrange afterwards. The examiners will forgive a rounding difference, a missing sign and a slightly different constant, but not a rearrangement that was already wrong before the numbers arrived.
Checking an answer
Weight in newtons should be roughly ten times the mass in kilograms on Earth. An answer close to the mass itself means g was left out; an answer a thousand times too big usually means grams were not converted to kilograms.
For F equals m a, a heavy object with a modest force should accelerate slowly. If your acceleration comes out larger than g for something being pushed along the ground, check the arithmetic before you write it down.
Spec 1.5-1.7E
What you need to know
- Use W equals m g to find weight
- Use F equals m a to find a force, mass or acceleration
- Rearrange both equations confidently
Active recall
Quick check
Answer each question before opening the answer.
What is the equation linking force, mass and acceleration?
Force = mass × acceleration (F = m × a).
What is the weight of a 5 kg mass where g = 10 N/kg?
50 N (5 × 10).
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