A level Physics

3.1 Vectors & Scalars
3.2 Moments & Couples
3.3 Equilibrium of Coplanar Forces
3.4 Laws of Friction
3.5 Triangle & Polygon of Vectors
3.6 Velocity & Acceleration
3.7 Equations for Uniform Acceleration
3.8 Projectiles
3.9 Newtons Laws of Motion
3.10 Momentum
3.11 Work, Energy & Power

3.1 Vectors & Scalars ( examples )

Vectors have magnitude & direction______eg. F = ( 4i + 2j ) N
Scalars have magnitude only___________eg. |F| = ( 4² + 2² )^½ = 20^½ N

Examples ( Scalars : distance, speed, mass, energy, charge, current, time, temperature. Vectors : displacement, velocity, acceleration, momentum, force, torque. )

Vector Addition ( parallelpgram rule )______C = A + B______a = |A|, b = |B|, c = |C|

C = A + B ______cosine rule: a² = b² + c² - 2 bc cos a______sine rule:
Components of Vectors
The components of F are resolved into 2 vectors___ horizontal & vertical components of F

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3.2 Moments & Couples ( examples )

The turning effect of a force is the 'turning moment' or 'torque' ( note in equilibrium the total torque about any point = 0 )

Torque, T = Fx___ pivot is at right angles to the screen __ Torque of a couple = Fx__ couple

Experiment with moments

balance with 2 weights ___sum of clockwise moments = sum of anti-clockwise moments ( x₁F₁ = x₂F₂ )

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3.3 Equilibrium of Coplanar Forces ( examples )

For equilibrium components of forces must balance.
plank pivoted against a wall by a string ___sum of clockwise moments = sum of anti-clockwise moments (about a point).

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3.4 Laws of Friction ( examples )___coefficient of friction = m

______ steel on steel mu ~ 0.8, smooth => mu = mu' = 0 ___m' - dynamic friction, m - limiting friction.

use F = ma, equations of motion, g = 9.8 m/s/s ______ Equilibrium => take moments abt. a point

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3.5 Triangle & Polygon of Vectors ( examples )

i) space & ii) force diagrams - statics => equilibrium ___Use cosine or sine rules to find angles & sides.

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3.6 Velocity & Acceleration ( examples )____speed Þ scalar, velocity Þ vector.

velocity, v = ( instantaneous velocity ) - gradient of distance-time graph
acceleration, a = rate of change of velocity.

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3.7 Equations for Uniform Acceleration ( examples )

s-t & v-t graphs

i) a = \ v = u + at____ ii) average velocity, __v_av =
iii) s = ( u + v ) t ,__v = u + at \ s = ( u + u + at ) t ,__s = ut + at²
iv) put t of i) into t of iii) \ into s = ut + at² Þ__v² = u² + 2as .

_______Area under a velocity-time graph___ area = displacement
______________________________________________uniform acceleration

Experiment - study of uniform acceleration

timer => photo-diodes velocity squared vs. acceleration
____________errors : measurement of time ( human )

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3.8 Projectiles ( examples )

projectile - motion under gravity _______ equations - vertical, horizontal motion

time of flight: 2t = , ____range = range , ____trajectory: y = x tan q -
____________________________( sin2q = 2 sinq cosq )____________y = ax + bx² ( parabola )

Experiment - determination of g by free fall

measurement of g height vs. time squared

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3.9 Newtons Laws of Motion ( examples )

Newton's 1^st law: A body is at rest or uniform motion in a straight line, unless acted on by an external force.
Newton's 2^nd law: The rate of change of momentum of a body is proportional to the resultant force acting on it & occurs in the same direction.
____________________F µ a,________ F = ( change in direction F )
Newton's 2^rd law: If body A exerts a force on body B, then body B exerts an equal & opposite force on body A.

_____ F₀ = resultant

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3.10 Momentum ( examples )

F = ____FDt - impulse,___eg. 2mu = m(v - u)____ Force-time graph = impulse

Conservation of momentum

___ before & after collision ___m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂ __( bodies in a system conserve total momentum )

____ collision at an angle ____e = __( coefficient of restitution, 0 < e< 1, elastic = 1 ).

Experiment - study of conservation of linear momentum
______ conservation of momentum - elastic, inelastic

Conservation of energy & momentum

Bullet fired into a block of wood raises above the ground.

______ conservation of momentum & energy

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3.11 Work, Energy & Power ( examples )

Work done = Force ´ distance______W = Fs______\ 1 Joule = 1 Newton ´ 1 metre ( J º Nm )
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W = pDV ( p - pressure, V - volume ).______Kinetic energy, KE = mv²
____________________________________Potential energy, PE = mgh ( º Fs )
____________________________________Power, P =
Derive KE :_____F = ma, ___v² = 2as ( u = 0 ). ___\ as = v²/2 ___\ mas = (º Fs in units).

Conservation of energy

Total energy of a (closed) system is constant - energy is transformed, not created or destroyed.

E_T = PE + KE ( eg. mechanical energy )

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Page Last Updated: November 2005