Calculating Weight | Physics for Grade 10 PDF Download

Mass v Weight

• Mass (measured in kilograms, kg) is related to the amount of matter in an object
• Weight (measured in newtons, N) is the force of gravity on a mass
  • The weight of an object and the mass of an object are directly proportional
  • The size of this force depends on the gravitational field strength (often called gravity, g, for short)

Exam Tips

It is a common misconception that mass and weight are the same, but they are in fact very different

• Since weight is a force - it is a vector quantity
• Since mass is an amount - it is a scalar quantity

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Calculating Weight

• Weight, mass and gravitational field strength are related using the equation:
  
• g is known as the acceleration due to gravity or the gravitational field strength
• On Earth, this is equal to 9.81 m/s2 (or N/kg)

Free Fall

• An object in free fall is falling solely under the influence of gravity
• On Earth, all free-falling objects accelerate towards Earth at a rate of 9.81 m/s2
• In the absence of air resistance, all bodies near the Earth will fall with the same acceleration regardless of their mass

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Mass v Weight

• An object’s mass always remains the same, however, its weight will differ depending on the strength of the gravitational field on different planets
• For example, the gravitational field strength on the Moon is 1.63 N/kg, meaning an object’s weight will be about 6 times less than on Earth
  
  On the moon, your mass will stay the same but your weight will be much lower
• The value of g (gravitational field strength) varies from planet to planet depending on their mass and radius
• A few examples of varying gravitational field strength are shown below:
  
  Gravitational field strength of the planets in our solar system

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Solved Example

Example: A student estimates they would have a weight of 190 N on Mars.The gravitational field strength on Earth is 9.8 N/kg. The gravitational field strength on Mars is 3.8 N/kg.Calculate the weight of the student on Earth.

Step 1: List the known quantities
Weight on Mars, WM = 190 N
Gravitational field strength on Mars, gM = 3.8 N/kg
Gravitational field strength on Earth, gE = 9.8 N/kg

Step 2: Write out the equation relating mass and weight and rearrange for mass
W = mg
Divide both sides by g:
m = W/g

Step 3: Calculate the student’s mass
The student’s mass is the same anywhere in the universe

Step 4: Calculate the student’s weight on Earth
W_E = m × g_E = 50 × 9.8 = 490 N