Our Dynamic Universe Mechanics
Higher Physics
Our Dynamic Universe
This section will last for 40 hours , covering 6 areas.
· Equations of Motion
· Forces, energy and power
· Collisions and explosions
· Gravitation
· Special relativity
· The expanding universe
· Big Bang Theory
The course is outlined in more detail later . Each area is divided into subsections . You can use this information to check your understanding. The statements are broad therefore it is essential that you read your summary sheets and keep all your work up to date throughout the course.
Assessment
Assessment
Outcome 1 : Practical Write up
1.1 Planning an experiment/practical investigation
1.2 Following procedures safely
1.3 Making and recording observations/measurements correctly
1.4 Presenting results in an appropriate format
1.5 Drawing valid conclusions
1.6 Evaluating experimental procedures
Outcome 2 : KU, Skills , Research and Application
2.1 Making accurate statements
2.2 Describing an application
2.3 Describing a physics issue in terms of the effect on the environment/society
2.4 Solving problems : Predicting, selecting , processing and analyzing.
The 6 key areas are outlined overleaf. For each key area a broad outline of the keys facts is given.
1) Equations of Motion
Equations of motion for objects with constant acceleration in a straight line.
· Candidates should undertake experiments to verify the relationships shown in the equations
Motion-time graphs for motion with constant acceleration
· Displacement-time graphs. Gradient is velocity.
· Velocity-time graphs. Area under graph is displacement. Gradient is acceleration.
· Acceleration-time graphs. Restricted to zero and constant acceleration.
· Graphs for bouncing objects and objects thrown vertically upwards
Motion of objects with constant speed or constant acceleration
· Objects in freefall and the movement of objects on slopes should be investigated.
2) Forces ,Energy and Power
Balanced and unbalanced forces.
The effects of friction. Terminal velocity.
· Forces acting in one dimension only. Analysis of motion using Newton‘s First and Second Laws.
· Friction as a force acting in a direction to oppose motion. No reference to static and dynamic friction.
· Tension as a pulling force exerted by a string or cable on another object.
· Velocity-time graph of falling object when air resistance is taken into account, including changing the surface area of the falling object.
· Analysis of the motion of a rocket may involve a constant force on a changing mass as fuel is used up.
Resolving a force into two perpendicular components
· Forces acting at an angle to the direction of movement.
· The weight of an object on a slope can be resolved into a component acting down the slope and a component acting normal to the slope.
· Systems of balanced and unbalanced forces with forces acting in two dimensions.
Work done, potential energy, kinetic energy and power
· Work done as transfer of energy.
· Conservation of energy.
3) Collisions and Explosions
Elastic and inelastic collisions
· Conservation of momentum in one dimension and in which the objects may move in opposite directions.
· Kinetic energy in elastic and inelastic collisions
Explosions and Newton‘s Third Law.
Conservation of momentum in explosions in one dimension only.
Impulse.
· Force-time graphs during contact of colliding objects.
· Impulse can be found from the area under a force-time graph.
4) Gravitation
Projectiles and Satellites
· Resolving the motion of a projectile with an initial velocity into horizontal and vertical components and their use in calculations.
· Comparison of projectiles with objects in free fall.
· Newton‘s thought experiment and an explanation of why satellites remain in orbit.
Gravity and mass.
· Gravitational Field Strength of planets, natural satellites and stellar objects.
· Calculating the force exerted on objects placed in a gravity field.
· Newton‘s Universal Law of Gravitation.
5) Special Relativity
Introduction to special relativity
· Relativity introduced through Galilean Invariance, Newtonian Relativity and the concept of absolute space.
· Experimental and theoretical considerations (details not required) lead to the conclusion that the speed of light is the same for all observers.
· The constancy of the speed of light led Einstein to postulate that space and time for a moving object are changed relative to a stationary observer.
· Length contraction and time dilation
6) The Expanding Universe
The Doppler Effect and redshift of galaxies.
· The Doppler Effect is observed in sound and light.
· For sound, the apparent change in frequency as a source moves towards or away from a stationary observer should be investigated.
· The Doppler Effect causes similar shifts in wavelengths of light. The light from objects moving away from us is shifted to longer wavelengths — redshift. The redshift of a galaxy is the change in wavelength divided by the emitted wavelength.
· For galaxies moving at non-relativistic speeds, redshift is the ratio of the velocity of the galaxy to the velocity of light.
· (Note that the Doppler Effect equations used for sound cannot be used with light from fast moving galaxies because relativistic effects need to be taken into account.)
Hubble‘s Law.
· Hubble‘s Law shows the relationship between the recession velocity of a galaxy and its distance from us.
· Hubble‘s Law leads to an estimate of the age of the Universe.
Big Bang Theory
· Evidence for Big Bang theory
· Dark matter / Energy
Kinematics
Vectors : Revision
If you want to move a chair the DIRECTION and MAGNITUDE of the applied force must be considered: if you push a chair with a large force to the right it moves to the right and if the applied force is in the opposite direction the chair moves to the left. Force is said to be a VECTOR quantity. Vector quantities have a DIRECTION and MAGNITUDE eg.
Velocity of 50 km h-1 North, Displacement of 100 m East, Acceleration of 5 ms-2 West.
Scalar quantities only have a MAGNITUDE eg.
Mass of 2 kg, Temperature of 20oC, Distance of 1 km.
ADDITION OF VECTORS
Additions of Scalar quantities is straightforward eg. 2kg + 5 kg = 7kg but with Vector quantities the magnitude and direction must be taken into consideration:
Thrust 150N Friction 100N
The frictional force is to the left and we normally indicate this by means of a negative sign ie. - 100N. The thrust is to the right and this is indicated by a positive sign ie. +150N. The RESULTANT force is the vector addition of these two forces:
FR = + 150 + - 100
= + 50N i.e. a force of 50N to the right
The situation is more complex if the quantities are not pushing directly with or against each other. .
A woman is rowing a boat at 5 m s-1 West across a river which is flowing at 6 m s-1 South.
5m s-1 west River flow
B A
6m s-1 south
C
The woman will actually end up at C due to the river current.
The resultant velocity of the woman can be found (a) Scale diagram or (b) Trigonometry.
(a) The 2 motions can be represented by VECTORS : (drawn to scale 1 cm : 2 m s-1)
5ms-1 Motion of boat 6ms-1
These are then added HEAD to TAIL as indicated.
5 A (starting point)
O
6 7.8
C (finishing point)
The Resultant is drawn from A to C and is measured then converted to m s-1 using the scale and the angle O measured. Angle 0 = 50.20.
The resultant velocity is 7.8 m s-1 , 219.80.. ( the 219.80 is a bearing from north )
Use your stunning mathematical abilities to work out the solution to this. In other words use Pythagoras Theorem and your Trigonometry (ask if your answers do not match those above).
Components of Vectors ( extra piece of work )
We can RESOLVE or split any vector into 2 COMPONENTS at 90o to each other eg.
Find the vertical and horizontal components of the velocity of a rocket fired at 400 m s-1 at an angle of 30o to the horizontal.
400 m s-1
1. Draw the Vector 30o
2. Complete a right angled triangle making the original vector the hypotenuse
3. Use your trigonometry to work out the vertical and horizontal components ie.
Cos q = a/h therefore a = h. cosq
Sin q = o/h therefore o = h.sin q
Complete this for the situation above (vx = 346m s-1 and vy = 200 m s-1)
DISTANCE AND DISPLACEMENT : Revision
Distance has a magnitude only and can be represented by a number and is a SCALAR quantity whereas DISPLACEMENT is a VECTOR quantity and must be represented by a magnitude and direction eg.
Two towns A and B are separated by mountains, the distance as the crow flies is 60km but to travel between the towns a twisty mountain road of length 100km must be traversed.
The total distance travelled is thus 100 km . Town B is 600 east of A i.e. a bearing of 0600
The displacement is 60km ,60o
B
N
A
SPEED and VELOCITY : Revision
The average speed of an object can be found by: v = d/t and is thus a SCALAR QUANITY. For the above case if a car takes 2 hours to traverse the road then the average speed = 100 /2 = 50 km h-1. The average displacement is described as the displacement/time (s/t) and is thus a VECTOR QUANTITY.
v = s/t = 60/2 = 30 km h-1 ,060o
A bouncing ball provides a further example of the difference between Velocity and Speed:
A
C Consider the ball bouncing from A to the floor at
B then bouncing up to C then down to D again on
the floor. When released the ball accelerates
downwards at -9.8 m s-2 until it hits the floor at
point B. It bounces back up to C and is still
Floor B D experiencing gravitational force and hence slows down.
FRICTION is IGNORED in the above example as the ball bounces to the original height it was released from after bouncing off the floor ie. NO ENERGY LOSSES.
But a velocity time graph must take into consideration the direction of the motion. Displacement downwards is normally assigned a NEGATIVE sign.
ACCELERATION
Acceleration is defined as the rate of change of velocity ie.
and is thus a VECTOR QUANTITY
Acceleration and Velocity Time Graphs
You should be able to sketch velocity time and acceleration time graphs if given the displacement time graphs for motions or sketch the acceleration and displacement time graphs if given the velocity time graph or sketch a displacement time and velocity time if given the acceleration time graph.
(a) CONSTANT Velocity
The velocity time graph is illustrated below:
v ( m s-1 )
0 t ( s )
The slope of this graph tell us what the acceleration is ie.
slope = (Change in velocity) / time for change ie. acceleration.
The slope is ZERO and so the acceleration time graph is a straight line along the x-axis.
a (m s-2)
0 t ( s )
UNIFORM Acceleration
the acceleration time graph is illustrated below (for 2 m s-2)
a (m s-2)
2
0 5 10 15 t ( s )
At time = 5s the velocity = 5 x 2 = 10 m s-1
At time = 10s the velocity = 10 x 2 = 10 x 2 = 20 m s-1 and so on (Providing the initial velocity is ZERO)
v (m s-1)
30
20
10
0 5 10 15 t ( s )
.
At time = 5s the displacement, s, =0.5 x 5 x10 = 25 m
At time = 10 s the displacement, s, = 0.5 x 20 x 10 = 100 m and so on
s (m)
200
100
0 5 10 15 t ( s )
Complete similar graphs to those shown above for uniform acceleration of -3 m s-2 with an initial velocity of 12 m s-1.
Acceleration and Velocity Time Graphs
Sketch the shape of the graphs below :
(a) CONSTANT Velocity
s v a
0 t 0 t 0 t
(b) UNIFORM Acceleration
s v a
0 t 0 t 0 t
(c) UNIFORM negative acceleration with an initial positive velocity.
s v a
0 t 0 t 0 t
EQUATIONS OF MOTION
There are 3 equations of motion which must be remembered. These equations can be used to describe the motion of an object undergoing UNIFORM Acceleration.
(There is a 4th equation : average velocity = total displacement /time)
v2 = u2 + 2.a.s. v = final velocity
u = initial velocity
s = u.t. + ½at2 s = displacement
t = time
v = u + a.t a = acceleration
When using these equations of motion you MUST remember that you are dealing with VECTOR quantities and that the direction must be taken into consideration.
velocity (ms-1) The object starts with velocity, u, at
time = 0 s and accelerates uniformly
v to velocity, v, after a time of t seconds.