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Worksheet · AS 9702 · 1.4 Physical quantities and units

Scalars and vectors: practice

Sorting quantities, resolving into components, resultants of perpendicular vectors, and combining by components. Show your working, and give every vector answer as a magnitude and a direction.

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Name: ________________Class: __________Date: __________
Resolve with Fx = F cos θ and Fy = F sin θ. For perpendicular vectors, magnitude = √(x2 + y2) and direction from tan θ = y / x.
Section A · Recall
A12 marks

Explain the difference between a scalar and a vector quantity.

A23 marks

Sort these into scalars and vectors: mass, velocity, force, temperature, displacement, speed, acceleration, energy, momentum.

Section B · Resolving vectors
B1 to B36 marks

Resolve each force into horizontal and vertical components.

B1. 20 N at 30 degrees above the horizontal. B2. 50 N at 60 degrees above the horizontal. B3. 8.0 N at 45 degrees above the horizontal.
Section C · Resultant of perpendicular vectors
C13 marks

Two forces act at a point: 3.0 N east and 4.0 N north. Find the magnitude and direction of the resultant.

C23 marks

A velocity has components 6.0 m s−1 east and 8.0 m s−1 north. Find the resultant speed and its direction.

Section D · Combining vectors by components
D14 marks

Two forces act at a point: 10 N due east and 10 N at 60 degrees north of east. Using components, find the magnitude and direction of the resultant.

Section E · Application and reasoning
E13 marks

A block of weight 50 N rests on a slope at 30 degrees to the horizontal. Find the component of the weight along the slope and the component perpendicular to the slope.

E23 marks

Two forces of equal size F act at a point. Explain why the resultant can be anything from 0 to 2F, and state the angle between the forces in each of these two cases.

Total: 27 marks. Original work by the TheLucidSTEM team. Written in the style of the papers; no past paper question is reproduced.

Answer key · full worked solutionsclick to reveal
A1. Scalar and vector.

a scalar has magnitude only; a vector has both magnitude and direction.

A2. Sorting.

scalars: mass, temperature, speed, energy. Vectors: velocity, force, displacement, acceleration, momentum.

B1 to B3. Resolving.

B1. Fx = 20 cos 30° = 17.3 N; Fy = 20 sin 30° = 10.0 N.
B2. Fx = 50 cos 60° = 25.0 N; Fy = 50 sin 60° = 43.3 N.
B3. Fx = 8.0 cos 45° = 5.7 N; Fy = 8.0 sin 45° = 5.7 N.

C1. 3.0 N east, 4.0 N north.

R = √(3.02 + 4.02) = 5.0 N; tan θ = 4.0 / 3.0, so θ = 53° north of east.

C2. 6.0 and 8.0 m s−1.

R = √(6.02 + 8.02) = 10.0 m s−1; tan θ = 8.0 / 6.0, so θ = 53° north of east.

D1. Combining by components.

total x = 10 + 10 cos 60° = 10 + 5 = 15 N. Total y = 0 + 10 sin 60° = 8.66 N.
R = √(152 + 8.662) = √(225 + 75) = √300 = 17.3 N. Direction: tan θ = 8.66 / 15, so θ = 30° north of east.

E1. Weight on a slope.

component along the slope = 50 sin 30° = 25 N; component perpendicular to the slope = 50 cos 30° = 43.3 N.

E2. Two equal forces.

the resultant is largest, 2F, when the forces point the same way (angle 0 degrees), and smallest, 0, when they point in opposite directions (angle 180 degrees). For angles between these the resultant lies between 0 and 2F.

Marking note: every vector answer needs a magnitude and a direction stated relative to a named axis. Accept resolving with sine or cosine provided the angle is defined consistently in a labelled diagram.
Original work by the TheLucidSTEM team. Questions are written in the style of the papers; no past paper question is reproduced. Supplied in editable formats so you can adapt them freely.
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