# Evan's Space

## Wonders of Physics ## Work Done, Energy and Power are Scalar Quantities

Work Done, Kinetic Energy (KE), Gravitational Potential Energy (GPE) and Power are all SCALAR quantities.

Many have asked if Work Done is scalar or vector? Though from our textbook, Work Done = Force x distance in the direction of the force.

In other words, Work Done = Force x Displacement

We already know that Force is a vector. Weight being a force, is also a vector quantity. Displacement is distance in a specific direction, hence it is a vector quantity too. In tertiary education, you will learn in details that the product (multiplication) of two vectors will result in a scalar or dot product.

Since it is out of syllabus, it will be good to use other ways to help you to understand and recall.

Method 1 Remember vector x vector will end up a scalar. Similar to (-)x(-) = (+) Method 2 Consider moving a box up to a certain height, work done or gain in GPE is constant regardless of the path it takes (diagonal or vertical). Hence direction is not important, therefore GPE  is a scalar. When considering KE, since KE = 1/2mv2 , similar to Method 1, v2 is actually velocity x velocity. Hence it product of 2 vectors, resulting in KE being a scalar.

Power = Energy Conversion/ time    or     Work Done / time,
since energy, work done and time are scalar, Power is a scalar quantity.

Other important note: Power = Rate of work done = Rate of energy conversion.

## Work Done, Energy and Power are Scalar Quantities

Work Done, Kinetic Energy (KE), Gravitational Potential Energy (GPE) and Power are all SCALAR quantities.

Many have asked if Work Done is scalar or vector? Though from our textbook, Work Done = Force x distance in the direction of the force.

In other words, Work Done = Force x Displacement

We already know that Force is a vector. Weight being a force, is also a vector quantity. Displacement is distance in a specific direction, hence it is a vector quantity too. In tertiary education, you will learn in details that the product (multiplication) of two vectors will result in a scalar or dot product.

Since it is out of syllabus, it will be good to use other ways to help you to understand and recall.

Method 1 Remember vector x vector will end up a scalar. Similar to (-)x(-) = (+) Method 2 Consider moving a box up to a certain height, work done or gain in GPE is constant regardless of the path it takes (diagonal or vertical). Hence direction is not important, therefore GPE  is a scalar. When considering KE, since KE = 1/2mv2 , similar to Method 1, v2 is actually velocity x velocity. Hence it product of 2 vectors, resulting in KE being a scalar.

Power = Energy Conversion/ time    or     Work Done / time,
since energy, work done and time are scalar, Power is a scalar quantity.

Other important note: Power = Rate of work done = Rate of energy conversion.

## N2007P1Q27 – Current Electricity – Brightness of bulbs

X and Y are lamps with filaments made of the same material. The filament of lamp X is thicker and shorter than that of lamp Y. Each lamp is connected to the mains and switched on. Which is the brighter lamp and which lamp has the larger resistance?

 Brighter lamp Larger resistance A X X B X Y C Y X D Y Y

Solutions: Option B

Using the formula, R = ρl/A     (ρ: resistivity (Ωm), l: length (m) and A: cross-sectional area (m2) Since both are of the same material, resistivity ρ is the same. X is thicker (cross-sectional area) and shorter, X will have lower resistance than Y.

Hence Y has larger resistance. Both are then connected to mains.

You can assume they are connected individually as shown below. Potential difference across each bulb is the same as the mains.

Since brightness depends on power, using P = IV, bulb X is brighter.