Physical Quantities and Measurement

State how a vector quantity differs from a scalar quantity.

Underline all the vector quantities in the list.

acceleration distance energy mass momentum temperature

Fig. 1.1 shows a passenger running across a large ship at right angles to the direction in which the ship is moving.

The passenger runs across the ship at $2.4\text{ m / s}$ due north.

The large ship is travelling due east at $6.8\text{ m / s}$.

Determine, either graphically or by calculation, the resultant velocity of the passenger. Give the direction in which the passenger is moving relative to due north.

Show how the answer is obtained.

velocity = ______ $\text{m / s}$ at ______ $^\circ$ from due north

State the difference between a scalar quantity and a vector quantity.

______

State two examples of each type of quantity.

scalar quantity

1. ______
2. ______

vector quantity

1. ______
2. ______

Fig. 1.1 shows the direction and size of two vectors P and Q.

In the space next to Fig. 1.1, draw a labelled vector diagram to show the resultant vector obtained by adding vector P to vector Q.

Draw vector P, vector Q and the resultant vector to the same scale as in Fig. 1.1.

In the space below draw, to scale, a vector diagram of these displacements.

State the scale of your diagram.
On your diagram, show the two displacements and the resultant displacement.
Determine the size (magnitude) and direction of the resultant displacement.

scale = ______
size = ______
direction = ______

Another journey covers a distance of $700\text{ m}$. Describe how it is possible that this journey has no resultant displacement.

State how a vector quantity differs from a scalar quantity.

State one other vector quantity and one other scalar quantity.

vector quantity ______
scalar quantity ______

An aeroplane flies through the air in a straight line, with its engines at full power. The weight of the aeroplane is $160\ \text{kN}$. There is also a force of $320\ \text{kN}$ acting upwards on the aeroplane at $30^\circ$ to the horizontal.

In the space below, use a graphical method to determine the size and the direction of the resultant of these two forces. Use a scale of $1.0\ \text{cm} : 40\ \text{kN}$.

size of resultant force = ______
direction of resultant force = ______

As the aeroplane accelerates, the pilot keeps the engines at constant power. The aeroplane eventually reaches a constant speed.

(1) Explain why the aeroplane stops accelerating and reaches a constant speed.

(2) When travelling at a constant speed, the pilot directs the aeroplane into a tight turn that follows a circular path.

Explain why the aeroplane is accelerating even though its speed is not changing.