7.1P Explain how and why both the weight of any body and the value of g…

The idea

Weight is the force of gravity on a mass, given by W = m × g, so the same body keeps its mass everywhere but its weight changes wherever g changes. The value of g at a surface depends on the mass of the body you stand on and on its radius: a more massive body pulls more strongly, and a larger radius spreads that pull over a greater distance from the centre, weakening it. The Moon has far less mass than the Earth and a smaller radius, and the two effects together give a surface g of about 1.6 N/kg against about 9.8 N/kg on Earth. A 60 kg astronaut therefore weighs about 590 N on Earth but only about 96 N on the Moon, while the 60 kg mass is unchanged.

What earns the marks

• States that mass is unchanged between Earth and the Moon while weight changes because g differs.
• Uses W = m × g to compare the weight of the same body on Earth and on the Moon.
• Explains that g depends on the mass of the body being stood on and on its radius.
• Identifies that the Moon has a smaller mass than the Earth, giving a smaller surface g.
• Recognises that a larger radius reduces the surface value of g for a given mass.

Common mistakes and how to put them right

• Claims that mass changes on the Moon.

  Put it right: Keep mass constant and change only the weight.

• Treats g as a universal constant of 9.8 N/kg everywhere.

  Put it right: Use the surface value of the body concerned.

• Assumes a smaller radius always means a smaller g.

  Put it right: Combine the mass effect with the radius effect.

Exam tips

• Write the equation W = m × g before substituting so the examiner sees the method.
• Quote g as about 9.8 N/kg on Earth and about 1.6 N/kg on the Moon when comparing.
• Explain both factors, mass and radius, rather than only saying the Moon is smaller.