(O Level Phy) Be careful of units!

In physics calculations, when a question gives the mass of an object in grams, very likely you will have to convert it to kg because physical quantities are based on SI units. Similarly, when necessary, cm and km will need to be converted to m, and min and h will need to be converted to s. That is why I often encourage students to write units in their working to keep track of the units.

Include units in your working... 

Example: If the mass of a bullet is 20 g, what is its weight?
[Solution]
W = mg = 20 g x 10 N/kg

Look at the units. They clearly tell that you need to convert g to kg so that you can multiply kg and N/kg and cancel the "kg"s to get N which is the unit of weight (a type of force). Therefore, the weight of the bullet
= 0.0020 kg x 10 N/kg
= 0.20 N

Too many times, students forget to convert units causing them to lose marks unnecessarily.

Don't forget to convert g to kg... 

Example: What is the kinetic energy of the 20 g bullet if it is shot out of a gun at 200 m/s?
[Solution]
KE = ½ mv²
= ½ (20 g)(400 m/s)²

Again, do not forget to convert g to kg.

KE = ½ (0.0020 kg)(400 m/s)²
= 160 J

The units of mass m and speed v in the formula of KE are kg and m/s respectively. This is because the formula of KE is derived using F = mass x acceleration where mass is in kg and acceleration is in m/s².

Example: What is the maximum pressure, in Pa, that can be exerted by a brick of density 2  g/cm³

and dimensions 5 cm by 10 cm by 20 cm on a flat ground?



[Solution]
Mass of brick = density x volume = 2  g/cm³ x (5 cm x 10 cm x 20 cm) = 2000 g
Weight of brick = mg = 2000 g x 10 N/kg = 2 kg x 10 N/kg = 20 N

By now, you should know that you have to change 2000 g to 2 kg.

Greatest pressure

= force on the ground / smallest area

= weight of brick / smallest area

= (20 N)/(5 cm x 10 cm)

Now, do you need to convert cm to m? Yes, this is because Pa (pascal) is equivalent to N/m², not N/cm². Of course, if the question requests for pressure in N/cm², there's no need for the conversion. Okay, I shall now leave it to you to continue the working on your own.

Pascal is equal to N/m²...