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Hoo Sze Yen

Physics SPM 2008

CHAPTER 2: FORCES AND MOTION

2.1 Linear Motion

Kinematics ­ the study of movement without reference to the forces that cause the movement Linear Motion ­ movement with constant acceleration Classification Physical quantity with... Example Scalar Magnitude only Distance Speed Vector Magnitude and direction Displacement Velocity Acceleration

2.1.1 Equations of Linear Motion

If s = displacement (succession) [m] u = initial velocity [m s-1] v = final velocity [m s-1] t = time [s] s = ½ (u + v) t -- --

a=

From : Insert into

v-u t

:

v = u + at s = ½ (u + u + at) t s = ut + ½ at2

--

From

: :

t=

v-u a

Insert into

s = ½(u + v)

=

(v - u ) t

v2 - u2 2a 2 2 v = u + 2as

--

Chapter 2: Forces and Motion

Page 1 of 11

Hoo Sze Yen

Physics SPM 2008

2.2

Linear Motion Graphs

2.2.1 Ticker timer

Ticker timer used to study movement in a short period of time 50 Hz used to determine: o time o displacement o average velocity o acceleration o type of movement

Explanation Consistent distance = uniform velocity

Movement

Short distance = low velocity Long distance = high velocity Increasing distance = increasing velocity / acceleration Decreasing distance = decreasing velocity / deceleration

2.2.2 Stroboscope

Number of images in one second = number of slits × number of spins per second T= where T = period (time taken per image) [s] n = number of slits on the stroboscope f = number of spins per second [Hz] 1 nf

Chapter 2: Forces and Motion

Page 2 of 11

Hoo Sze Yen

Physics SPM 2008

2.2.3 Linear Motion Graphs

Displacement-time graphs

Velocity = slope of the graph v=0 (a = 0)

Velocity-time graphs

Acceleration = slope of the graph Displacement = area under the graph

v/m s-1

Acceleration-time graphs

Velocity = area under the graph

s/m

a/m s-2

t/s

t/s v/m s-1 a/m s-2

t/s

v= constant (a = 0)

s/m

t/s

t/s v/m s

-1

t/s a/m s

-2

v a= constant

s/m

t/s

t/s v/m s-1 a/m s-2

t/s

v a= constant

s/m

t/s

t/s

t/s v/m s-1 a/m s-2

v a

t/s

t/s a/m s-2

v a

v/m s

-1

t/s

t/s a/m s

-2

a increasing rate

t/s

a decreasing rate

a/m s

-2

t/s

Chapter 2: Forces and Motion

Page 3 of 11

Hoo Sze Yen

Physics SPM 2008

2.3

Inertia

Dynamics ­ the study of movement caused by force Inertia ­ natural characteristics of an object to oppose any attempted change on its original state, whether at rest or in motion ­ tendency of an object to remain at rest, or to keep moving at constant speed in a straight line Newton's First Law of Motion (Law of Inertia) Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it.

2.4

Momentum

Momentum = mass × velocity p = mv

where p = momentum [kg m s-1] m = mass [kg] v = velocity [m s-1]

Principle of conservation of momentum In any collision or interaction between two or more objects in an isolated system, the total momentum before collision is equal to the total momentum after collision.

m1u1 + m2u2 = m1v1 + m2v2 Three situations: 1) Elastic collision: When both objects move separately after collision.

Note: In an elastic collision, the kinetic energy is conserved.

m1u1 + m2u2 = m1v1 + m2v2 2) Inelastic collision: When both objects move together after collision. m1u1 + m2u2 = (m1 + m2)v 3) Explosion: When both objects are stationary before the explosion. 0 = m1v1 + m2v2

Chapter 2: Forces and Motion

Page 4 of 11

Hoo Sze Yen

Physics SPM 2008

2.5

Force

Force changes the size, shape, state of rest, velocity and/or direction of an object. Force is a vector quantity. Newton's Second Law of Motion The acceleration of a body, a, is directly proportional to the net force acting upon it, F, and inversely proportional to its mass, m.

F = ma where F = force [N] m = mass [kg] a = acceleration caused by F [m s-2]

2.5.1 Balanced Forces

Balanced forces = net force is zero

An object that is stationary, or moving with uniform velocity in a straight line, is said to be in a state of balanced forces.

2.5.2 Unbalanced Forces

Unbalanced forces may cause an object to start moving, to speed it up, to slow it down, or to bring it to a stop. The greater the unbalanced force, the greater the acceleration or deceleration produced.

2.5.3 Net Force / Resultant Force

Net force on an object is the overall force resulting from the combination of the individual forces acting upon the object. When the forces are balanced, the net force is zero; as if there is no force acting upon the object. When the forces are unbalanced, the net force is the difference between the forces acting in opposite directions.

Chapter 2: Forces and Motion

Page 5 of 11

Hoo Sze Yen

Physics SPM 2008

2.6

Impulse and Impulsive Force

Impulse = change of momentum Ft = mv ­ mu

Impulsive force is the change of momentum in a very short period of time. Impulsive force = rate of change of momentum mv - mu F= t where Ft = impulsive [kg m s-1] F = impulsive force [N] m = mass [kg] u = initial velocity [m s-1] v = final velocity [m s-1]

2.7

Safety Features in Vehicles

1. Padded dashboards 2. Shatterproof windscreen glass 3. Inflatable airbags 4. Collapsible steering wheels 5. Headrest 6. Padded seats 7. Seatbelt 8. Antilock brake systems (ABS) 9. Variable-ratio response steering systems 10. Intelligent speed adaptation systems 11. Reverse collision warning systems 12. Bumper bars

2.8

Gravity

All objects are pulled towards the centre of the earth by a force known as the earth's gravitational force. Any object dropped towards earth which falls under the influence of the earth's gravitational force (without any influence of other external forces, such as air friction) is said to be going through a free fall. In reality, free falls only happen within a vacuum space. An object undergoing free fall will fall at the rate of gravitational acceleration which is at a constant of 9.81 m s-1. The gravitational acceleration is not influenced by the size or mass of the object.

Chapter 2: Forces and Motion

Page 6 of 11

Hoo Sze Yen

Physics SPM 2008

2.8.1 Weight

Weight = gravitational force acting on the respective object W = mg where W = weight [N] m = mass [m] g = gravitational acceleration [m s-2]

2.8.2 Lifts

R a

a=0 F = R ­ mg =0 R = mg

W = mg

a = +ve () F = R ­ mg ma = R ­ mg R = ma + mg Common formula: R = mg + ma

a = -ve () F = mg ­ R ma = mg ­ R R = mg ­ ma

a = g (free fall) F = mg ­ R mg = mg ­ R R=0

2.8.3 Pulleys

Motion and acceleration in this direction

T

T

Based on the force formula: F = ma F = Net force acting on the system m = Total mass of the system a = Acceleration of the system F1 ­ F2 = (m1 + m2) a To find out the rope tension: F = ma F1 ­ T = m1a T = F2 ­ m2a

F2 F1

2.9

Forces in Equilibrium

Equilibrium: - resultant force = 0 - acceleration = 0 (stationary or uniform velocity)

Newton's Third Law For every action there is an equal and opposite reaction.

Chapter 2: Forces and Motion

Page 7 of 11

Hoo Sze Yen

Physics SPM 2008

2.9.1 Nett / Resultant Forces

Using the parallelogram method

2.9.2 Force Resolution

Reversing the parallelogram method

Fx = F cos Fy = F sin

2.9.3 Inclined Planes

m2 m1 R Fr

W=mg

R = mg cos Fr = mg sin where W = weight of object [N] m = mass of object [kg] g = gravitational acceleration [m s-2] R = reaction caused by weight of object perpendicular to plane [N] Fr = friction caused by weight of object parallel to plane [N]

Chapter 2: Forces and Motion

Page 8 of 11

Hoo Sze Yen

Physics SPM 2008

2.10 Work

Work done by a constant force to move an object = displacement × force parallel to direction Note: Work is a scalar quantity W = Fs where W = work [J] F = force creating the work [N] s = displacement [m]

Energy is the potential or ability of a system to do work. (scalar quantity) Power is the rate of work done or rate of energy transfer

P=

where P = power [J s-1] W = work [J] E = energy [J] t = time [s]

W E = t t

2.10.1

Potential Energy

Potential energy is the energy within an object because of its position or state. Gravitational potential energy: E = mgh where E = potential energy [J] m = mass [kg] g = gravitational acceleration [m s-2] h = height of the location of the object [m] Elastic potential energy: W = ½ Fs where W = work done [J] F = force exerted [N] s = extension or compression of the spring [m]

F/N

s/m

Chapter 2: Forces and Motion

Page 9 of 11

Hoo Sze Yen

Physics SPM 2008

2.10.2

Kinetic Energy

Kinetic energy is energy acquired by an object during movement. E = ½ mv2 where E = kinetic energy [J] m = mass [kg] v = velocity of the object [m s-1] The law of conservation of energy states that energy may neither be created nor destroyed; it can only change shape.

2.11 Power

Power is the rate at which energy is used.

P=

E t

2.12 Efficiency

Efficiency is the ratio at which the output power is compared to the input power. Efficiency = Output power × 100% Input power

2.13 Elasticity

Elasticity is the ability of an object to return to its original shape and size after the applied external force applied onto it has been removed.

2.13.1

Hooke's Law

Hooke's Law states that the extension or compression of a spring is directly proportional to the force acting on it provided the elastic limit of the spring has not been exceeded.

Chapter 2: Forces and Motion

Page 10 of 11

Hoo Sze Yen Spring extension, x (cm)

Physics SPM 2008

Elastic limit

Tension force, F

F = kx where F = force exerted on the spring [N] k = spring constant [N m-1] x = spring extension / compression [m]

2.13.2 Spring stiffness

Factors which affect the stiffness of a spring: 1) Length of spring 2) Diameter of wire 3) Diameter of coil 4) Type of material

2.13.3 Spring systems

Parallel arrangement Series arrangement

W W

The load is equally distributed among the The same load is applied to each spring. springs. If n springs are used: Total extension = nx If n springs are used: x Total extension = n

Chapter 2: Forces and Motion

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11 pages

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