2022 A/L Physics Past Paper · Question 01 (English Medium)

Answer: (4) Force, Potential Energy

What the question asks

Find the pair where the first quantity is a vector and the second is a scalar.

What each letter means:

$m$ ($\text{kg}$): mass.

$\vec{v}$ ($\text{m s}^{-1}$): velocity.

$v$ ($\text{m s}^{-1}$): speed.

$P$ ($\text{W}$): power.

$W$ ($\text{J}$): work.

$s$ ($\text{m}$): distance.

$\vec{F}$ ($\text{N}$): force.

$E_p$ ($\text{J}$): potential energy.

$\vec{p}$ ($\text{kg m s}^{-1}$): momentum.

$\vec{\tau}$ ($\text{N m}$): torque.

Relevant theory

A scalar quantity is completely specified by its magnitude.

eg. Mass, time, distance, pressure, energy, density, speed, area, volume, work, power

They have both magnitude and direction and obey the law of vector addition.

eg. Displacement, acceleration, impulse, moment, momentum, magnetic flux density, velocity, force, electric field intensity, gravitational field intensity, weight.

Reading the options

For example, think of a bus trip.

Say how far the bus went. The distance $s$ is one amount. No direction is needed. That is a scalar.

Say how the bus is moving. The velocity $\vec{v}$ needs a direction too, such as north or south. That is a vector.

Now think of a bag on a high shelf. Its potential energy $E_p$ is just an amount of energy. That is a scalar.

Push the bag with your hand. The force $\vec{F}$ pushes one way, so it has a direction. That is a vector.

In words: a scalar has only a size. A vector has a size and a direction.

So $\vec{F}$ and $\vec{v}$ are vectors, and $s$ and $E_p$ are scalars.

The book gives two lists.

Scalars: mass, time, distance, pressure, energy, density, speed, area, volume, work, power.

Vectors: displacement, acceleration, impulse, moment, momentum, velocity, force, weight and others.

Now put each pair against the lists, first and then second.

(1) Mass is a scalar, velocity is a vector.

(2) Power is a scalar, speed is a scalar.

(3) Work is a scalar, distance is a scalar.

(4) Force is a vector, potential energy is a scalar.

(5) Momentum is a vector, torque is a vector.

Only pair (4) is a vector first and a scalar second.

Why the other options fail

Mass is a scalar and velocity is a vector. This pair is the wrong way round.

Power and speed are both scalars. There is no vector in this pair.

Work and distance are both scalars. There is no vector in this pair.

Momentum and torque both have a direction. Both are vectors. There is no scalar here.

Conclusion

Force is a vector and energy is a scalar.

The answer is (4).

Ask one question about each quantity: does it need a direction?

If yes, it is a vector. If no, it is a scalar.

Then read the pair in order, first and second.

Exam tip