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Measurement of Mass and weight
Mass is the amount of matter contained in a substance while weight is the pull of gravity on an object.
The SI unit for mass is the Kg while weight is the newton (N).Other sub-multiples used are grams (g), milligrams (mg) and tonnes (t).
1 kg = 1,000 g = 1,000,000 mg=100 tonnes.
Mass is constant regardless of place while weight changes with place.
The weight of an object is defined as the force of gravity on the object and may be calculated as the mass times the acceleration of gravity, w = mg. Since the weight is a force, its SI unit is the newton.
The relationship between mass and weight is given by the following formula,
W = mg
Where W = weight of object, M= mass of object
g = gravitational force.
(At the Earth’s surface, where g=9.8 m/s2 )
Differences Between Mass and Weight
Mass |
Weight |
ü It is the quantity of matter in a body ü It is measured in kilograms ü It is the same everywhere ü It is measured using a beam balance ü Has magnitude only Weight |
ü It is the pull of gravity on a body ü It is measured in newton’s ü It changes from place to place ü It is measured using a spring balance ü Has both magnitude and direction |
Example 1.
An object has a mass of 100 kilograms. What is its weight on the surface of the earth?”
Solution
We have both m and g. m equals 100 kg, and g equals 9.8 m/s2, because we’re looking for the weight of the object on the surface of the earth.
F = 100 kg x 9.8 m/s2.
On the surface of the earth, an object with a mass of 100 kg will weigh approximately 980 Newtons. F = 980 N.
Example 2
An object has a mass of 40 kilograms. What is its weight on the surface of the moon?”
Solution
We have both m and g. m equals 40 kg, and g equals 1.6 m/s2, because we’re looking for the weight of the object on the surface of the moon this time.
F = 40 kg x 1.6 m/s2.
On the surface of the moon, an object with a mass of 40 kg will weigh approximately 64 Newtons. F = 64 N.
Example 3
An object weighs 549 Newtons on the surface of the earth. What is its mass?”
Solution
For this problem, we have to work backwards. We already have F and we have g. We just need m.
549 = m x 9.8 m/s2.
Instead of multiplying, we divide. Specifically, we divide F by g. An object weighing 549 Newtons on the surface of the earth will have a mass of about 56 kilograms.
m = 56 kg.