Presentation on theme: "Physics Beyond 2000 Chapter 1 Kinematics Physical Quantities Fundamental quantities Derived quantities."— Presentation transcript:
Physics Beyond 2000 Chapter 1 Kinematics
Physical Quantities Fundamental quantities Derived quantities
Fundamental Quantities QuantitySymbolSI Unit Massmkg Lengthlm Timets Others--
Derived Quantities Can be expressed in terms of the basic quantities Examples –Velocity –Example 1 –Any suggestions?
Derived Quantities More examples
Standard Prefixes Use prefixes for large and small numbers Table 1-3 Commonly used prefixes – giga, mega, kilo – centi, milli, micro, nana, pico
Significant Figures The leftmost non-zero digit is the most significant figure. If there is no decimal point, the rightmost non-zero digit will be the least significant figure. If there is a decimal point, the rightmost digit is always the least significant figure. The number of digits between the Most significant figure and least significant figure inclusive.
Scientific Notation Can indicate the number of significant numbers
Significant Figures Examples 5 and 6. See if you understand them.
Significant Figures Multiplication or division. –The least number of significant figures. Addition or subtraction. –The smallest number of significant digits on the right side of the decimal point.
Measurement Mass –Triple beam balance –Electronic balance
Measurement Computer data logging
Error Treatment Personal errors –Personal bias Random errors –Poor sensitivity of the apparatus System errors –Measuring instruments –Techniques
Accuracy and Precision Accuracy –How close the measurement to the true value Precision –Agreement among repeated measurements – Largest probable error tells the precision of the measurement
Accuracy and Precision Examples 9 and 10
Accuracy and Precision Sum and difference –The largest probable error is the sum of the probable errors of all the quantities. –Example 11
Accuracy and Precision Product, quotient and power –Derivatives needed
Kinematics Distance d Displacement s
Average Velocity Average velocity = displacement time taken
Instantaneous Velocity Rate of change of displacement in a very short time interval.
Uniform Velocity Average velocity = Instantaneous velocity when the velocity is uniform.
Speed Average speed Instantaneous speed
Speed and Velocity Example 13
Relative Velocity The velocity of A relative to B The velocity of B relative to A
Relative Velocity Example 14
Acceleration Average acceleration Instantaneous acceleration
Average acceleration Average acceleration = change in velocity time Example 15
Instantaneous acceleration Example 16
Velocity-time graph v-t graph v t Slope: = acceleration
v-t graph Uniform velocity: slope = 0 v t
v-t graph Uniform acceleration: slope = constant v t
Falling in viscous liquid Acceleration Uniform velocity
Falling in viscous liquid v t acceleration: slope=g at t=0 uniform speed: slope = 0
Bouncing ball with energy loss Falling: with uniform acceleration a = -g. Let upward vector quantities be positive.
v-t graph of a bouncing ball Uniform acceleration: slope = -g v t falling
Bouncing ball with energy loss Rebound: with large acceleration a. Let upward vector quantities be positive.
v-t graph of a bouncing ball Large acceleration on rebound v t falling rebound
Bouncing ball with energy loss Rising: with uniform acceleration a = -g. Let upward vector quantities be positive.
v-t graph of a bouncing ball Uniform acceleration: slope = -g v t falling rebound rising
v-t graph of a bouncing ball falling and rising have the same acceleration: slope = -g v t falling rebound rising The speed is less after rebound
Linear Motion: Motion along a straight line Uniformly accelerated motion: a = constant velocity time v u t0
Uniformly accelerated motion u = initial velocity (velocity at time = 0). v = final velocity (velocity at time = t). a = acceleration v = u + at
Uniformly accelerated motion = average velocity time v u t0 velocity
Uniformly accelerated motion time v u t0 velocity s = displacement = s = area below the graph
Equations of uniformly accelerated motion
Uniformly accelerated motion Example 17
Free falling: uniformly accelerated motion Let downward vector quantities be negative a = -g
Free falling: uniformly accelerated motion a = -g
Free falling: uniformly accelerated motion Example 18
Parabolic Motion Two dimensional motion under constant acceleration. There is acceleration perpendicular to the initial velocity Examples: –Projectile motion under gravity. –Electron moves into a uniform electric field.
Monkey and Hunter Experiment gun bullet aluminium foil electromagne t iron ball
Monkey and Hunter Experiment gun bullet aluminium foil electromagne t iron ball The bullet breaks the aluminium foil.
Monkey and Hunter Experiment gun bullet electromagne t iron ball Bullet moves under gravity. Iron ball begins to drop.
Monkey and Hunter Experiment gun bullet electromagne t Bullet is moving under gravity. Iron ball is dropping under gravity.
Monkey and Hunter Experiment gun electromagne t
Monkey and Hunter Experiment gun electromagne t The bullet hits the ball!
Monkey and Hunter Experiment The vertical motions of both the bullet and the iron are the same. The vertical motion of the bullet is independent of its horizontal motion.
Projectile trajectory y x
y x u u = initial velocity = initial angle of inclination
Projectile trajectory y x u v = velocity at time t = angle of velocity to the horizontal at time t v Horizontal line
Projectile trajectory y x u = x-component of u = y-component of u
Projectile trajectory y x u
Projectile trajectory: accelerations y x u
Projectile trajectory y x u v Horizontal line vertical line = x-component of v = y-component of v
Projectile trajectory: velocity in horizontal direction y x u v Horizontal line
Projectile trajectory: velocity in vertical direction y x u v vertical line Horizontal line
Projectile trajectory: displacement y x x = x-component of s y = y-component of s s s = displacement
Projectile trajectory: horizontal displacement y x s s = displacement
Projectile trajectory: vertical displacement y x s s = displacement
Equation of trajectory: a parabolic path y x s s = displacement
Projectile trajectory: direction of motion y x u v Horizontal line vertical line Angle represents the direction of motion at time t.
Projectile trajectory: direction of motion y x u v Horizontal line vertical line
Projectile trajectory Example 19
Projectile trajectory: maximum height H y x u H At H, = 0
Projectile trajectory: range R y x u At R, y = 0 R
Projectile trajectory: maximum range R max y x u R max is maximum when
Projectile trajectory: maximum range R max y x u R max R is maximum when
Projectile trajectory: maximum range R max y x u R max
Projectile trajectory: time of flight t o y x u At time= t o, y = 0 R toto
Projectile trajectory: two angles for one range y x 1 R 2 u u 1 = - 2