The acceleration of gravity (gravitational field strength "g") is proportional to the force due to gravity and can be expressed as the ratio of the force of gravity on an object to the mass of the object or:

F = mg  (g = acceleration due to gravity)

It is important not to confuse the force of gravity on an object with the mass of an object (most people do).  The force of gravity on an object is what we know of as the objects weight. Weight is measured in units of force, or Newtons (N) as opposed to units of mass (kg) as is commonly used.

When a man steps onto a weigh scale, he reads a value in kilograms (kg) and says that this value is his weight.  He is mistaken!  His weight is really the force of gravity (in Newtons) which acts on the that mass (kg). 

Example:      The scale which the man stands on reads 70 kg.  The weight of the man is found by calculating the force of gravity on 70 kg:

Fg =  mg   (g = 9.8 m/s²)

Fg = (70 kg)(9.8m/s²)

Fg = 686 kgm/s²

Fg = 686 N 

The man actually weighs 686 N (not 70 kg).  

Since the weight of a man (or any object) depends on the acceleration of gravity (g = 9.8 m/s²), we can see how the weight of an object will change when the gravity changes (on the moon for instance).  This is not so for mass (kg) since mass is a measure of the amount of matter in the object.

***Note: The measurement of weight using a typical bathroom scale takes into account the fact that the acceleration of gravity is 9.8 m/s2 and is calibrated to give a value in kilograms instead of the true units of weight (Newtons).

Try the following problems (see bottom for link to answers):

1. Give the weight (in N) of the following masses (g = 9.8 m/s²):
   1. 150 kg
   2. 1200 kg
2. Give the mass of the following objects (g = 9.8 m/s²):           
   1. A bowling ball weighing 100N
   2. A large crate which weighs 10 000N
3. If a cow is measured to have a weight of 500 N on Earth, what would the weight of the cow be if it were put on a planet where the acceleration of gravity (g) is 11.2  m/s² (remember that the mass of an object does not change when the acceleration of gravity changes)?  
4. If the weight of a box is 200 N, and its mass is 20.1 kg, what is the acceleration of gravity in this place?
5. What is the acceleration of gravity in a place where the cow from question #3 has a weight of 250 N?  

Answers to the above questions