Equations of motion; Scalar and vector quantities, Analysing motion, Questions on motion, Motion graphs, Force vectors, Vector components, Vector components for an object on a slope

Topic 2

Analysing Motion

General Knowledge

Any vector can be resolved into two components at right angles to each other.

What does the gradient on displacement-time graph at a particular time show?

The gradient of a displacement-time graph at a particular time gives the velocity of the object at that time.

General Knowledge

The gradient of a displacement-time graph at a particular time gives the velocity of the object at that time. Gradient=Change in Displacement/Change in Time = Delta s/Delta t =Velocity

What does the gradient on a velocity-time graph at any particular time show?

The gradient of a velocity-time graph at a particular time gives the acceleration of the object at that time.

General Knowledge

The gradient of a velocity-time graph at a particular time gives the acceleration of the object at that time. Gradient=Change in Velocity/Change in Time =Delta v/Delta t =Acceleration

An object lifts off vertically and takes a time of 4s to reach the highest point. What time will it take to fall back to Earth?

4 seconds - assuming no rocket force or air resistance. The acceleration due to gravity is the same in both directions, slowing down on the way up, speeding up on the way back down.

If a question states 'freely under gravity', what information about the equations is being given?

Acceleration = -9.8 ms-2 due to gravity

Name six Vector quantities

Displacement Velocity Acceleration Force Weight Momentum

Name five Scalar quantities

Distance Speed Time Power Energy

(Continuation of previous) Now calculate the maximum height reached by the ball to the nearest metre.

Equation: u = 24.5m{s^{ - 1}} Equation: v = 0 Equation: a = - 9.8m{s^{ - 2}} Equation: t = 2.5s Equation: s = ? Equation: s = ut + (1/2) x at^2 Equation: s = 24.5 times 2.5 + (1/2) x ( - 9.8) x 2.5^2 Equation: s = 61.25 - 30.625 Equation: s = 30.625 Maximum height reached is 31 m.

A nail is fired from a nail gun into a fixed block of wood. The nail has a speed of 380 ms-1 just as it enters the wood as shown in ( http://a.files.bbci.co.uk/bam/live/content/zkjfcdm/large ) The nail comes to rest after penetrating 60 mm into the wood. Find the time taken for the nail to come to rest. Assume that the frictional force on the nail is constant as it penetrates the wood.

Equation: u = 380ms^-1 Equation: v = 0 Equation: a = ? Equation: t = ? Equation: s = 60x10^-3m Equation: sC)t Equation: t = (2 x 0.06)/380 = 3.16x10^- 4s The time taken for the nail to come to rest is 3.16 x 10-4s

Topic 5

Force Vectors

These two components when added together have the same effect as the initial single vector.

Horizontal and vertical components of a vector See ( http://a.files.bbci.co.uk/bam/live/content/zxp97ty/large ) is the same as: See ( http://a.files.bbci.co.uk/bam/live/content/z6nk2hv/large ) Expressed mathematically: Equation: Fx = Fcos (x) and: Equation: Fy = Fsin (x)

See this first before you read question( http://a.files.bbci.co.uk/bam/live/content/zts8mp3/large ) A force of 30 N acts on a box as shown. Find the horizontal and vertical components of the 30 N force. Round the answers to one decimal place.

Horizontal component of force equals: See ( http://a.files.bbci.co.uk/bam/live/content/zhfdxnb/large ) Equation: Fx= Fcos theta = 30cos 40^o = 22.98 Vertical component of force equals: Equation: Fy= Fsin x = 30sin 40^o = 19.28 When rounded off to 1 decimal place: Horizontal component of force equals: Equation: 23.0 N Vertical component of force equals: Equation: 19.3 N

General Knowledge

In ( http://a.files.bbci.co.uk/bam/live/content/z4dngk7/large ) Of the above u, v, a, and s are vector quantities. As such, remember to make vectors going in one direction positive and vectors in the opposite direction negative. Time (t) is a scalar quantity. If any three of the five quantities are known then the other two may be calculated using the following four equations: Equation: v = u + at Equation: s = ut + (1/2) x at^2 Equation: v^2= u^2 + 2as Equation: s= ((u + v)/2) x t

General Knowledge

In this case the weight is the single force and it is resolved into two independent components, one acting along the slope Fs and the other acting perpendicular to the slope Fp. See: http://a.files.bbci.co.uk/bam/live/content/zpyw6sg/large Expressed mathematically: Component of weight parallel to slope equals: Equation: Wsin x = mgsin x Component of weight perpendicular to slope equals: Equation: Wcos x = mgcos x

If a question states 'from rest' what information about the equations is being given?

Initial speed u = 0

( Look at this first then read question: http://a.files.bbci.co.uk/bam/live/content/z9wsr82/large ) A ball is projected vertically upwards with an initial velocity of 24.5 ms-1. The effects of air resistance may be neglected: Calculate the time taken for the ball to reach its maximum height.

Let unknown vector quantities go in the positive direction for vectors. Vertical motion is a constant acceleration of 9.8 ms-2 towards the centre of the Earth. Equation: u = 24.5m{s^{ - 1}} (upwards) Equation: v = 0 (stationary at top) Equation: a = - 9.8m{s^{ - 2}} (acceleration is faster in downwards direction) Equation: t = ? Equation: s = ? Equation: v = u + at Equation: 0 = 24.5 + ( - 9.8)t Equation: t = 2.5s

Topic 4

Motion Graphs

General Knowledge

Physics can be described as modelling the natural world using mathematics. In the case of moving objects, physics can accurately record and even predict the movement of objects using a set of physical laws and equations. These equations have helped launch space vehicles and are responsible for the realism of many computer games.

Topic 3

Questions on Motion

Topic 1

Scalar and vector quantities

When do Scalar quantities change?

Scalar quantities change when their magnitude changes.

What are Scalar quantities?

Scalar quantities have only magnitude (size). For example, 11 m and 15 m s-1 are both scalar quantities.

See this first before you read question( http://a.files.bbci.co.uk/bam/live/content/z2tcjxs/large ) Two forces of value 100 N act on the object shown below. Find the resultant force on the object.

See this first before you read answer ( http://a.files.bbci.co.uk/bam/live/content/zmh4q6f/large ) Length of vectors consistent with scale. By scale drawing: Scale 1 cm = 10 N Size of resultant force = 100 N Direction of resultant displacement = 60° to either force

A 10 kg box slides down a frictionless slope. The slope is at 30° to the horizontal. Find the component of the weight acting parallel to the slope.

See: http://a.files.bbci.co.uk/bam/live/content/znvjtfr/large The component of weight parallel to the slope is: Equation: Wsin x = mgsin x Equation: = 10 x 9.8 x sin 30^o Equation: = 49N

How do you find the difference in two Scalar quantities?

The difference in two scalar quantities = large value - small value

How do you find the difference in to Vector quantities?

The difference in two vectors quantities = final vector - initial vector

When can the equations of Motion only be used?

The equations of motion can only be used for an object travelling in a straight line with a constant acceleration.

What five quantities do the equations of motion relate to?

The equations of motion relate to the following five quantities: u - initial velocity v - final velocity a - acceleration t - time s - displacement

What is the result of adding vectors called?

The result of adding vectors together is called the resultant.

Which of the three motion graphs do you think is most useful?

The velocity time graphs give all three variables for motion-velocity which can be read off at any time. Area is displacement and gradient is acceleration.

Topic 6

Vector Components

Topic 7

Vector Components for an Object on a Slope

When do Vector quantities change?

Vector quantities change when: their magnitude changes their direction changes their magnitude and direction both change e.g. A geostationary satellite is in orbit above the Earth. It moves at constant speed but its velocity is constantly changing (since its direction is always changing).

What are Vector quantities?

Vector quantities have both magnitude (size) and direction. For example, 11 m east and 15 ms-1 at 30° to the horizontal are both vector quantities.

General Knowledge

When adding two vectors together: the greatest (maximum) resultant is equal to their sum the smallest (minimum) resultant is equal to their difference the resultant can have any value between these limits depending on the angle between the two vectors In problems, vectors may be added together by scale diagram or mathematically.

When it comes to adding vector quantities what should you always remember and take into account?

When adding vector quantities remember that the directions have to be taken into account.

(From Previous Flashcard) If the slope is steeper, how does this affect the two components?

mgsin x parallel to slope will increase and mgcos x will decrease

(From Previous Flashcard) Now find the acceleration of the box down the incline.

a=? F=49N m=10kg F=ma 49=10 x a a=49/10 a=4.9ms^-2

The velocity-time and acceleration-time graphs for common motions are shown

http://a.files.bbci.co.uk/bam/live/content/z8qy4wx/large http://a.files.bbci.co.uk/bam/live/content/zd7v9j6/large http://a.files.bbci.co.uk/bam/live/content/zw23kqt/large

(From Previous Flashcard) How will this affect the acceleration?

mgsin theta will cause increased force and mgcos x will decrease and friction as there will be less force pushing the block onto the surface