Give two pairs of scalar and vector quantities.

Speed and velocity; distance and displacement (also mass and weight).

How do you add two vectors by scale drawing?

Draw them to scale head to tail; the resultant joins the start of the first to the end of the second.

How do you find the resultant of two perpendicular vectors by calculation?

Magnitude √(a² + b²); direction from tan θ = b/a.

What are the components of a force F at angle θ to the horizontal?

Horizontal F cos θ; vertical F sin θ.

What is the component of weight W perpendicular to a slope at angle θ?

W cos θ, which the normal contact force balances.

What is the condition for an object to be in equilibrium?

The resultant force on it is zero.

What motion can an object in equilibrium have?

It can be at rest or moving at constant velocity.

How can you solve equilibrium problems by resolving?

Resolve all forces in two perpendicular directions; the sum of components in each direction is zero.

Why is weight a vector but mass a scalar?

Weight is a force and acts towards the centre of the Earth; mass has no direction.

Scalars, vectors and equilibriumAQA A-Level Physics: Flashcards

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What is the difference between a scalar and a vector?

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What is the difference between a scalar and a vector?: A scalar has magnitude only; a vector has magnitude and direction.
Give two pairs of scalar and vector quantities.: Speed and velocity; distance and displacement (also mass and weight).
How do you add two vectors by scale drawing?: Draw them to scale head to tail; the resultant joins the start of the first to the end of the second.
How do you find the resultant of two perpendicular vectors by calculation?: Magnitude √(a² + b²); direction from tan θ = b/a.
What are the components of a force F at angle θ to the horizontal?: Horizontal F cos θ; vertical F sin θ.
What is the component of weight W down a slope at angle θ?: W sin θ.
What is the component of weight W perpendicular to a slope at angle θ?: W cos θ, which the normal contact force balances.
What is the condition for an object to be in equilibrium?: The resultant force on it is zero.
What motion can an object in equilibrium have?: It can be at rest or moving at constant velocity.
What shape do three coplanar forces in equilibrium form when drawn head to tail?: A closed triangle.
How can you solve equilibrium problems by resolving?: Resolve all forces in two perpendicular directions; the sum of components in each direction is zero.
Why is weight a vector but mass a scalar?: Weight is a force and acts towards the centre of the Earth; mass has no direction.

Exam questions on Scalars, vectors and equilibrium

A hiker walks 6.0 km due east and then 8.0 km due north, taking 2.0 hours in total, and stops.
Calculate the direction of the hiker's displacement, giving your answer as an angle east of north.2 marks
A box of weight 60 N is at rest on a rough ramp that is inclined at 30° to the horizontal.
The ramp is raised so that it is inclined at 40° to the horizontal and the box is still at rest. Calculate the frictional force acting on the box.2 marks
A lamp of weight 30 N hangs at rest from the middle of two identical light strings. Each string is attached to a ceiling hook and makes an angle of 25° with the horizontal. The lamp and strings are in equilibrium.
Calculate the tension in each string.3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).