Two forces, each of 10 N, act at a point P as shown in the diagram. The angle between the directions of the forces is 120°.

Question 16

Two forces, each of 10 N, act at a point P as shown in the diagram. The angle between the directions of the forces is 120°.

What is the magnitude of the resultant force?

A 5N                B 10N              C 17N              D 20N

Reference: Past Exam Paper – June 2003 Paper 1 Q3

Solution:

Answer: B. 

Since the angle on the right of the diagonal vector is 120° with the horizontal, the angle on the LEFT of the diagonal vector is 180° – 120° = 60°with the horizontal.

Consider the resultant vector.

Since the 2 vectors given are of the same magnitude, we can assume that the triangle formed when the resultant is formed will at least be an isosceles triangle – that is, the angle that these 2 vectors make with the resultant vector will have the same value. Let this angle be x.

Sum of angles in a triangle is 180°.

60° + x + x = 180°

Angle x = (180° – 60°) / 2 = 60°

Since all the angles are equal in the triangle, it is actually an equilateral triangle. So, the sides will have the same magnitude.

Thus, resultant vector = 10N

The question can also be tackled using sine or cosine rule (depending on the values available).

Complete Fig 1.1 to show each quantity and its unit.

Question 15

Complete Fig 1.1 to show each quantity and its unit. [4]

            Quantity                                  Unit

            speed                                       m s^-1

            density                       

                                                            s^-1

            electric field strength             

                                                            kg m s^-1

Reference: Past Exam Paper – June 2003 Paper 2 Q1

Solution:

Quantity                                  Unit

            speed                                       m s^-1

            density                                    kg m^-3

            frequency                               s^-1

            electric field strength              N C^-1 or V m^-1 or kg m s^-2 C^-1

            momentum or impulse          kg m s^-1

{The unit of density is kg m^-3 (= mass / volume).

A unit of s^-1 means that the quantity is ‘something divided by time’. The numerator should not have any unit. This could be frequency (= 1 / period) or count rate or activity or decay constant.

The question has NOT asked for the SI BASE unit. So, the unit of electric field strength can be given as N C^-1 (= force / charge) or V m^-1 (= p.d. / distance) or in SI base units, kg m² C^-1. However, there was no need to convert into SI base unit as this was not specified in the question.

In the unit kg m s^-1, kg is the unit of mass and m s^-1 is the unit of velocity. The quantity represented by ‘mass × velocity’ is momentum (or impulse).}

Which formula could be correct for the speed v of ocean waves in terms of the density ρ of seawater, the acceleration of free fall g, the depth h of the ocean and the wavelength λ?

Question 14

Which formula could be correct for the speed v of ocean waves in terms of the density ρ of seawater, the acceleration of free fall g, the depth h of the ocean and the wavelength λ?

A v = √gλ                     B v = √(g/h)                 C v = √(ρgh)                D v = √(g/ρ)

Reference: Past Exam Paper – June 2007 Paper 1 Q3

Solution:

Answer: A.

Unit of velocity: m s^-1

Consider the overall unit of the options provided.

The unit of the correct option should have the units of velocity.

Note that square root means ‘a power/index of ½ or 0.5’.

Unit of √(gλ): [ms^-2 m]^0.5 = [m²s^-2]^0.5 = m s^-1 

Unit of √(g/h): [ms^-2 m^-1]^0.5 = [s^-2]^0.5 = s^-1

Unit of √(ρgh): [kgm^-3 ms^-2 m]^0.5 = [kg m^-1 s^-2]^0.5 = kg^0.5 m^-0.5 s^-1

Unit of √(g/ρ): [ms^-2 kg^-1m³]^0.5 = [m⁴ s^-2 kg^-1]^0.5 = m² s^-1 kg^-0.5