Topic 2: Mechanics

2.1 – Motion

Distance and displacementDistance DisplacementScalar Vector

A scalar quantity which measures how

far two locations are apart from each

other along a certain path.

A vector quantity defined by the length

and direction of the line segment joining

the initial and final positions of an object.

http://www.everythingmaths.co.za/science/grade-10/21-motion-in-one-dimension/

pspictures/1e8543454948498cff6c8afc52243435.png

Speed and velocitySpeed VelocityScalar Vector

Rate of change of distance to time. Rate of change of displacement to time.

Velocity is a measure dependent on the motion of the observer. The relative velocity

of A to B is equal to the vector subtraction of the velocity of B from the velocity of A.

AccelerationAccelerationVector

Rate of change of velocity

Acceleration due to gravity of any free-falling object is given by g=9.81m/s^2. This

value does not depend on the mass of the object.

Take note that acceleration is a vector and thus has a direction. If we assume the

upwards direction to be positive, the acceleration due to gravity would have a

negative value of g=-9.81m/s^2.

Graphs describing motion

Displacement-time graph

http://www.hk-phy.org/contextual/mechanics/kin/motion_graph/5-02.gif

The slope gradient indicates the velocity.

Straight lines imply constant velocity.

Velocity-time graph

http://www.hk-phy.org/contextual/mechanics/kin/motion_graph/5-06.gif

The slope gradient indicates the acceleration.

Straight lines imply constant acceleration.

The area under the lines indicates the change in displacement.

Acceleration-time graph

http://www.hk-phy.org/contextual/mechanics/kin/motion_graph/5-11.gif

Horizontal lines imply constant acceleration.

The area under the lines indicates the change in velocity.

Equations of motion for uniform accelerations =

displacement

u = initial

velocity

v = final

velocity

a =

acceleration

t = time taken

If acceleration is constant (uniform), the following equations can be used

http://1.bp.blogspot.com/-Ir-dVXazGq8/VUWAE7vHAbI/AAAAAAAAE1E/dGfJu1IY-

3Y/s1600/linearformula.png

Projectile motionAn object is said to undergo projectile motion when it follows a curved path due to the

influence of gravity.

http://farside.ph.utexas.edu/teaching/301/lectures/img340.png

http://www.splung.com/kinematics/images/projectiles/vector-components.png

If we assume air resistance to be negligible in a projectile motion:

The horizontal component of velocity is constant

The vertical component of velocity accelerates downwards at 9.81m/s^2

The projectile reaches its maximum height when its vertical velocity is zero

The trajectory is symmetric

http://www.schoolphysics.co.uk/age16-19/Mechanics/Kinematics/text/

Projectiles_and_air_resistance/images/1.png

The presence of air resistance changes the trajectory of the projectile by the

following

The maximum height of the projectile is lower

The range of the projectile is shorter

The trajectory is not symmetric

Fluid resistance and terminal speedAir resistance limits the maximum velocity an object could attain from free-falling. For

example:

If you jump out of a plane and undergo free-falling, you will feel an upward force

exerted on you by the surrounding air due to air resistance.

As you fall faster and faster due to gravity, this upward force exerted by air

becomes greater and greater until it balances your weight. At this point, the net

force acting on you becomes zero, and you no longer accelerate.

This specific velocity at which you stop accelerating during a free-fall is called

the terminal velocity.

http://physics-tutor.site90.net/drupal/files/Fimage006.gif

2.2 – Forces

Objects as point particlesForces change the velocity or shape of objects.

The unit of force is newton (N).

Objects are represented as a point mass to enable the representation for forces as

arrows in free-body diagrams.

Free-body diagramsOn a free body diagram, forces acting on an object are represented as arrows which

stem from a point mass.

The length and direction of the arrows corresponds to the magnitude and the

direction of the forces acting on the body of interest.

https://qph.is.quoracdn.net/main-qimg-53327b3c0b795f33aeba2042e688631a?

convert_to_webp=true

http://img.sparknotes.com/content/testprep/bookimgs/sat2/physics/0011/

pendulum_FBD.gif

Determining the resultant force

1. Resolve all acting forces into horizontal and vertical components

2. Add up the horizontal components

3. Add up the vertical components

4. Combine the sum of horizontal components and the sum of vertical components

Translational equilibriumA body is said to be in translational equilibrium if it the net force acting on the body is

zero. This means the body is either at rest or travels at constant velocity. For

example:

Mass hanging at rest

Elevator moving upwards at constant velocity

Parachutist reaching terminal velocity

Newton’s laws of motionNewton's First Law (Law of Inertia) states that a body remains at rest or travels with

constant speed along a straight line unless acted upon by an external force. (Net

force = 0)

https://www.dlsweb.rmit.edu.au/toolbox/buildright/content/bcgbc4010a/

02_force_systems/03_newtons_first_law/images/page_001.gif

Newton's Second Law states that net force is directly proportional to acceleration and

inversely proportional to mass. (F=ma)

http://hyperphysics.phy-astr.gsu.edu/hbase/imgmec/fmaill.gif

Newton's Third Law states that if a body A exerts a force on body B, then body B

exerts a force of the same magnitude but in the opposite direction of body A.

This pair of forces is called an action-reaction pair, which must act on two different

bodies.

http://www.physchem.co.za/OB11-mec/graphics/law3_f1.gif

Solid frictionFriction is a non conservative force which opposes motion. If there is no motion, then

there will be no force caused by friction.

For two solid surfaces moving over each other, the friction will be affected by the

nature (roughness etc) of the two surfaces. However, the surface area and velocity of

the object does not affect the friction.

There are also two types of friction for solid surfaces: static friction and kinetic

friction. Static friction is that which stops objects from beginning to move. Kinetic

friction is that which slows objects down when they are moving. Static friction is

always larger than kinetic friction.

These two types of friction are defined individually by their constants µs and

µk respectively.

The forces of friction are also dependent on the normal force the surface is applying,

leading to Friction force =<µs*Normal force for objects that are not moving and

Friction force=µs *Normal force for objects that are moving.

http://ffden-2.phys.uaf.edu/211_fall2002.web.dir/ben_townsend/frictiongraph.JPG

2.3 – Work, energy and power

Kinetic energyKinetic energy (KE) is the energy of a body due to its motion and is given by the

equation

http://www.one-school.net/Malaysia/UniversityandCollege/SPM/revisioncard/physics/

forceandmotion/images/kineticenergyformula.png

Gravitational potential energyThe gravitational potential energy (GPE) of an object changes with its height and is

given by the equation

http://www.one-school.net/Malaysia/UniversityandCollege/SPM/revisioncard/physics/

forceandmotion/images/gravitationalpeformula.png

Elastic potential energyElastic energy is potential energy stored as a result of the deformation of an elastic

object such as the stretching of a spring and is given by the equation

http://www.one-school.net/Malaysia/UniversityandCollege/SPM/revisioncard/physics/

forceandmotion/images/eleasticpeformula.png

http://srikant.org/core/img244.png

Work done as energy transferWork done measures the transfer of energy due to a force and is a scalar quantity.

The work done W by a force F on an object is given by the equation

http://www.one-school.net/Malaysia/UniversityandCollege/SPM/revisioncard/physics/

forceandmotion/images/workformula.png

http://www.one-school.net/Malaysia/UniversityandCollege/SPM/revisioncard/physics/

forceandmotion/images/workandenergy_clip_image002.jpg

In a force-displacement graph, work done is the area under the curve.

http://www.phys.ttu.edu/~rirlc/Image551.gif

Power as rate of energy transferPower (P) is the work done or the energy output per time given by the equation:

http://www.one-school.net/Malaysia/UniversityandCollege/SPM/revisioncard/physics/

forceandmotion/images/powerformula.png

For constant force acting on an object with constant velocity, the power is given by

the equation: P=Fv.

Principle of conservation of energyEnergy can neither be created nor destroyed; it can only be changed from one form

to another. For example:

An electrical heater transforms electrical energy to thermal energy.

A falling object transforms potential energy to kinetic energy.

Total energy of an isolated body remains constant. In other words, ΔKE+ΔPE=0

EfficiencyEfficiency is the ratio of useful energy output to energy input as a percentage given

by the equation

http://www.one-school.net/Malaysia/UniversityandCollege/SPM/revisioncard/physics/

forceandmotion/images/efficiencyformula.png

2.4 – Momentum and impulse

Newton’s second law expressed in terms of rate of

change of momentumThe linear momentum (p) is given by the equation

http://www.one-school.net/Malaysia/UniversityandCollege/SPM/revisioncard/physics/

forceandmotion/images/momentumformula.png

The linear momentum (p) is a vector with the same direction as the velocity of an

object.

The change of momentum of an object is called impulse.

Rearranging the formula describing Newton's second law results in the following

expression

http://zonalandeducation.com/mstm/physics/mechanics/momentum/

introductoryProblems/imp1.gif

Impulse and force–time graphsImpulse is given by the area of a force-time graph.

http://tap.iop.org/mechanics/mechanics_images/img_mid_39660.gif

Conservation of linear momentumThe law of conservation of linear momentum states that the sum of initial momentum

is equal to the sum of final momentum in a closed system and can be given by the

equation

http://www.one-school.net/Malaysia/UniversityandCollege/SPM/revisioncard/physics/

forceandmotion/images/momentumformula2.png

Elastic collisions, inelastic collisions and explosionsType Total momentum Total kinetic energy

Elastic Conserved Conserved

Inelastic Conserved Not conserved

Explosion Conserved Not conserved

http://www.thetrc.org/pda_content/texasphysics/e-BookData/Images/SB/58/LR/

Elastic%20and%20Inelastic%20Collisions.png

http://www.physicsclassroom.com/Class/momentum/u4l2e1.gif