Calculating Weight (OCR Gateway GCSE Physics)

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)

• 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 10 N/kg (or m/s²)

Gravitational Potential Energy

• 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 10 m/s²
  • In the absence of air resistance, all bodies near the Earth will fall with the same acceleration regardless of their mass

• The gravitational potential energy (GPE) of an object is defined as:

The energy an object has due to its height in a gravitational field

• This means:
  • If an object is lifted up it will gain GPE
  • If it falls, it will lose GPE

• The GPE of an object can be calculated using the equation:

GPE = m × g × h

• Where:
  • GPE = gravitational potential energy, in Joules (J)
  • m = mass, in kilograms (kg)
  • g = gravitational field strength, in Newtons per kilogram (N/kg)
  • h = height in metres (m)

Step 1: List the known quantities

• • Mass of the man, m = 70 kg
  • Gravitational field strength, g = 10 N/kg
  • Height, h = 3 m

Step 2: Write down the equation for gravitational potential energy

GPE = mgh

Step 3: Calculate the gravitational potential energy

GPE = 70 × 10 × 3 = 2100 J

Step 1: List the known quantities

• • Gravitational field strength on Earth = 10 N/kg
  • Gravitational field strength on the Moon = 2 N/kg
  • Mass of Isabelle, m = 40 kg

Step 2: State the equation linking weight and mass

• • The equation linking weight and mass is:

W = m × g

Step 3: Calculate Isabelle's weight on Earth

• • Substituting the values of mass and Earth's gravitational field strength into the equation gives:

W (Earth) = 40 × 10 = 400 N

Step 4: Calculate Isabelle's weight on the Moon

• • Substituting the values of mass and the Moon's gravitational field strength into the equation gives:

W (Moon) = 40 × 2 = 80 N

Step 5: Comment on the two values of weight

• • Isabelle's weight is greater on Earth than on the Moon
  • This is because the Earth has a larger gravitational field strength than the Moon, so Isabelle's weight force (the force of gravity pulling down on her) is larger on Earth than on the Moon