# Section 3.4.1 - Mechanics

3.4.1.1 Scalars and vectors Nature of scalars and vectors. Examples should include: velocity/speed, mass, force/weight, acceleration, displacement/distance.
The addition of vectors by calculation or scale drawing.

Calculations will be limited
to two perpendicular vectors.

Scale drawings may involve vectors at angles other than 90°.

Don't forget to use the interactive XL spreadsheet on vectors and projectiles
The resolution of vectors into two components at right angles to each other; Examples should include the components of forces along and perpendicular to an inclined plane.

Note that the data sheet does NOT give you the basic trig info. You need to KNOW that!

Also you need to know Pythagoras' Theorem

Conditions for equilibrium for two or three coplanar forces acting at a point; Appreciation of the meaning of equilibrium in the context of an object at rest or moving with constant velocity.

Problems may be solved either by using resolved forces or by using a closed triangle. MS 0.6, 4.2, 4.4, 4.5 / PS 1.1 Investigation of the conditions for equilibrium for three coplanar forces acting at a point using a force board.
3.4.1.2 Moments

Moment of a force about a point defined as force × perpendicular distance from the point to the line of action of the force;

'torque' as a term has now been removed from the syllabus - but it doesn't hurt you to know it....

moment = Fd

Don't forget the interactive XL spreadsheet on moments

Couple as a pair of equal and opposite forces

Moment of a couple defined as force × perpendicular
distance between the lines of action of the forces
.

The principle of moments and its applications in simple balanced situations.

For equilibrium:

Σ clockwise moments = Σ anticlockwise moments

Centre of mass

Knowledge that the position of the centre of mass of uniform regular solid is at its centre.

Calculations of the position of the centre of mass of a regular lamina are not expected.
3.4.1.3 Motion along a straight line Displacement

Displacement is distance moved in a particular direction. You must understand the difference between distance and displacement!
speed   You met speed at KS3
velocity MS 3.6, 3.7 / PS 1.1, 3.1 - Distinguish between instantaneous velocity and average velocity
and acceleration.
Representation by graphical methods of uniform and non-uniform acceleration;
MS 3.5, 3.6 Measurements and calculations from displacement–time, velocity–time and acceleration–time graphs.

You need to know the dynamics graphs that you met at GCSE

You have to know how to draw graphs to a high standard  - and how to find gradients and areas under graphs (differentiation and integration will not be called for)

Interpretation of velocity-time and displacement-time graphs for uniform and non-uniform acceleration; eg graphs for motion of bouncing ball. Need to understand the physical significance of areas under graph lines and gradients.

Area under a v/t graph between two times is the distance travelled in that time interval

Gradient of s/t graph is velocity and gradient of a/t graph is acceleration

Equations for uniform acceleration

Don't forget the interactive XL Spreadsheets

Acceleration due to gravity, g;

Required practical 3: Determination of g by a freefall method.

MS 0.3, 1.2, 3.7 / AT d Students should be able to identify random and systematic errors in the experiment and suggest ways to remove them.

MS 3.9 Determine g from a graph

3.4.1.4 Projectile motion

Independent effect of motion in horizontal and vertical directions of a uniform gravitational field.

Problems will be solvable using the equations of uniform acceleration. The memorising of projectile equations is not required.

Don't forget the interactive XL Spreadsheets

Qualitative treatment of friction.

Qualitative treatment of lift and drag forces.

Distinctions between static and dynamic friction will not be tested. PS 2.2, 3.1 Investigation of the factors that determine the motion of an object through a fluid.

Terminal speed

Knowledge that air resistance increases with speed.

Qualitative understanding of the effect of air resistance on the trajectory of a projectile and on the factors that affect the maximum speed of a vehicle.

3.4.1.5 Newton’s laws of motion Knowledge and application of the three laws of motion in appropriate situations.

You met these at GCSE

Make sure you can quote them!

But note that Ft = Δmv is on the A2 syllabus not the AS one!

as is conservation of momentum - so don't worry about it at AS!

For constant mass, F = ma Interactive XL Spreadsheet

PS 4.1 / MS 0.5, 3.2 / AT a, b, d Students can verify Newton’s second law of motion.

MS 4.1, 4.2 Students can use free-body diagrams.

3.4.1.6 Momentum

Momentum

Principle applied quantitatively to problems in one dimension.

momentum = mass × velocity

p = mv

MS 2.2, 2.3 Students can apply conservation of momentum and rate of change of momentum to a range of examples.

Force as the rate of change of momentum

#### F= ∆(mv)/ t∆

Impulse = change in momentum

#### F∆t =∆(mv)

where F is constant

Recall the terms momentum and impulse and their units.

Interpret force v. time graphs - area under the graph is the impulse.

Significance of area under a force-time graph.

Principle of conservation of linear momentum applied to problems in one dimension.

Elastic and inelastic collisions; explosions.

Quantitative questions may be set on forces that vary with time.

Impact forces are related to contact times (eg kicking a football, crumple zones, packaging).

Appreciation of momentum conservation issues in the context of ethical transport design.

Quote the principle of conservation of linear momentum.

Explain the difference between elastic and inelastic collisions.

Momentum Structured questions

Momentum Multiple Choice

3.4.1.7 Work, energy and power

Energy transferred, W = Fs cos θ

rate of doing work = rate of energy transfer,

P = ∆ W /∆ t = Fv

efficiency = useful output power /input power

MS 0.3 / PS 3.3, 4.1 / AT a, b, f. Investigate the efficiency of an electric motor being used to raise a mass through a measured height.

Students should be able to identify random and systematic errors in the experiment and suggest ways to remove them

Significance of the area under a force–displacement graph.

Quantitative questions may be set on variable forces.

Efficiency can be expressed as a percentage.

3.4.1.8 Conservation of energy Applied to examples involving gravitational
potential energy
, kinetic energy and work done against resistive forces - such as friction and air resistance.

MS 0.4, 2.2 Estimate the energy that can be derived from food consumption.