Weight from F = mg

The idea

The gravitational force on an object of mass m is F = mg, where g, the acceleration due to the Earth's gravitational force, is 9.8 m s–2, nearly constant near the Earth's surface and independent of the object's mass.

Heavy ball, light ball

You drop a heavy ball and a light ball together from the same height.

Which one do you think speeds up faster as it falls?

• Both speed up at the same rate
• The heavy ball speeds up faster
• The light ball speeds up faster

Drop two balls

Set one ball heavy and one light, then press Drop.

The same g for all

The force the Earth exerts on a mass m is mg, so the heavier ball has the larger weight. But its mass is also larger, so the acceleration F/m is the same, 9.8 m s⁻². Both balls land together.

The gravitational force on an object of mass m is F = mg, where g, the acceleration due to the Earth's gravitational force, is 9.8 m s⁻², nearly constant near the Earth's surface and independent of the object's mass.

Notes

F = mg: the gravitational force on mass m. g = 9.8 m s⁻², nearly constant near the Earth's surface and independent of mass.

Check yourself

What is the gravitational force on an object of mass 5 kg? Use g = 9.8 m s⁻².

Answer: 49 N

F = mg = 5 kg × 9.8 m s⁻² = 49 N.

A barbell has a total mass of 30 kg. What gravitational force acts on it? Use g = 9.8 m s⁻².

Answer: 294 N

F = mg = 30 kg × 9.8 m s⁻² = 294 N, downward.

A 1 kg object and a 10 kg object fall near the Earth's surface. How do their accelerations due to gravity compare?

What is g?

• They are the same, g — correct. Yes!
• The 10 kg object accelerates more. g does not depend on the mass of the object.
• The 1 kg object accelerates more. g does not depend on the mass of the object.
• The mass of the Earth. g is an acceleration, with the unit m s⁻².
• The acceleration due to the Earth's gravitational force, 9.8 m s⁻² — correct. Yes!
• The weight of an object. The weight is the force F = mg. The letter g stands for the acceleration.