Scalars & Vectors (Cambridge (CIE) A Level Physics)

The relationship can be used to model a spherical raindrop falling vertically in the air.

Fig 1.1 shows the forces acting on the raindrop as it accelerates downwards.

The raindrop has a radius of 1.5 mm and falls at a velocity of 3.5 m s⁻¹. The constant k has a magnitude of 0.0124 in air.

Other than the resistive force F described in (b), two other forces, X and Y, act on the raindrop drop as it falls through the air. 

(i) State the names of forces X and Y.

[2]

(ii) Calculate the magnitude of the resistive force F in µN.

[2]

(iii) Force X has a value of 137 µN and force Y has a value of 0.18 µN. 

Using Fig. 1.1, determine the magnitude and direction of the resultant force on the raindrop.

[3]

On a windy day, the resultant force on the raindrop is 105 µN at an angle of θ to the vertical as shown in Fig. 1.2. 

Use your answer to (c)iii to show that the angle θ between the resultant and the vertical is about 47°.

(i) State the difference between a scalar quantity and a vector quantity.

[1]

(ii) Underline all the vectors in the list below.

 [1]

Two gusts of wind exert forces of magnitude 5.5 N and 11.9 N on a wind turbine at a point O. Both forces act away from point O and the angle between them is 30°.

Fig. 1.1 shows two lines at an angle of 30° to one another. 

Fig. 1.1

On Fig. 1.1, draw a vector diagram to determine the magnitude of the resultant of the two forces.

Fig. 1.1 shows a 2 tonne wrecking ball being used on a demolition site. 

The ball is suspended from a cable which makes an angle θ with the vertical. The ball is pulled into the position shown by a rope that is kept horizontal. The tension in the rope is 6400 N.

Write expressions for tension T using

(i) the vertical component of the tension in the cable

[2]

(ii) the horizontal component of the tension in the cable. 

[2]

Determine

(i) the angle θ the cable makes with the vertical

[2]

(ii) the magnitude of the tension T in the cable

[2]

On the same demolition site, there is a uniform beam supported by two light cables, AB and AC, which are attached to a single steel cable from a crane, as shown in Fig. 1.2.

The beam is stationary and in equilibrium.

Fig. 1.2

Draw the vector triangle for this situation labelling the tension in both cables and the weight of the beam. 

The tension in the cable AB is 9 N and the tension in the cable AC is 12 N.

Calculate the resultant force required in the beam BC to keep the system in equilibrium.