Mass and weight
Section: Dynamics | Syllabus: Cambridge AS Level Physics 9702
What is Mass? Mass can be defined as the quantity of matter in an object. It is a scalar quantity which has no direction associated with it. Mass The quantity of matter in an object; a measure of its resistance to change in motion (inertia).
Mass is constant for any object that is at rest or travelling much slower than the speed of light. The SI unit used in equations is the kilogram (kg) . Inertia: Golf vs. Table Tennis Ball Think of a table tennis ball and a golf ball.
Both have a diameter of about 40 mm, but their masses are very different: Table tennis ball: 2.7 g (filled with air) Golf ball: 46 g (solid rubber) If you blow on both, the table tennis ball is easier to move because it has less mass, and therefore less inertia (resistance to change in motion).
What is Weight? Weight and mass are often confused in everyday speech, but they are distinct in physics. Weight is the force of gravity on an object. Weight is a vector quantity measured in Newtons (N) .
It acts in the same direction as gravity (on Earth, towards the centre of the Earth). Unlike mass, weight is not constant ; it varies according to the strength of the gravitational field. Diagram: Mass vs Weight Comparison Illustrate a person standing on Earth (g=9.81) and the Moon (g=1.6).
Show that their 'bulk' (mass) is identical, but the downward force arrow (weight) is much smaller on the Moon. Gravitational Field Strength (g) A gravitational field describes any place where the effects of gravity can be detected.
All objects have weight when they are in a gravitational field. W = mg Where: W = Weight / Gravitational Force (N) m = Mass (kg) g = Gravitational field strength (N kg^-1) or acceleration of free fall (m s^-2) Near the Earth's surface, g = 9.81 N kg^-1 = 9.81 m s^-2 .
Relationship Between Newton's Second Law and Gravity Comparing W = mg with Newton's second law (F = ma) shows that g is the acceleration of the mass m. Since g is constant in a uniform gravitational field, all masses have the same acceleration when they fall vertically, provided gravity is the only force acting.
Worked Example: Constant Acceleration of Free Fall Question: Compare the acceleration of a 1 kg mass and a 2 kg mass dropped together (ignoring air resistance). Solution For each mass, the acceleration is given by a = fraction = fraction.
1 kg Mass: Weight W = 1 × 9.81 = 9.81 N a = 9.81 kg m s^-21 kg = 9.81 m s^-2 2 kg Mass: Weight W = 2 × 9.81 = 19.62 N a = 19.62 kg m s^-22 kg = 9.81 m s^-2 Both masses experience the same acceleration despite having different weights.
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