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Gerak dan Perubahan(Tinjauan Fisika)
Elok SudibyoP. Sains – FMIPA Unesa
Materi Perkuliahan:Gerak dan Perubahan (Tinjauan Fisika)
Pertemuan ke:11. Kinematika Linier (Linear Kinematics)12. Kinetika Linier (Linear Kinetics)13. Ujian Subsumatif-114. Kinematika Anguler (Angular Kinematics)15. Kinetika Anguler (Angular Kinetics)16. Ujian Subsumatif-2
LINEAR KINEMATICS
Objectives:When you finish this chapter, you should be able to do the following:• Distinguish between linear, angular, and general
motion.• Define distance traveled and displacement, and
distinguish between the two.• Define average speed and average velocity, and
distinguish between the two.
• Define instantaneous speed and instantaneous velocity.
• Define average acceleration.• Define instantaneous acceleration.• Calculate the distance traveled and displacement,
speed and velocity, and acceleration.
• Use the equations of projectile motion to determine the vertical or horizontal position of a projectile given the initial velocities and time.
Types of Motion
Motion
Linear Motion (Translation)
Rectilinear Motion
Curvilinear Motion
Angular Motion
(Rotation)
General Motion
Rectilinear motion
• Linear Kinematics: describing objects in linear motion (position, distance traveled, displacement, time, speed, velocity, acceleration)
LINEAR KINEMATICS
• Mechanically, position is defined as location an object in space at any particular time.
• Example: A 100-meter swimming race in a 50-meter pool.
Position
• a swimmer’s location at any particular time.
Position
Distance Traveled & Displacement
• Distance:– Length of path which a body covers during motion– Units (SI): meter (m)– Scalar quantity
• Displacement:– The change in position of a body during motion– Units (SI): meter (m)– Vector quantity
Distance & Displacement
• Distance: represented by BLUE colour line• Displacement: represented by YELLOW colour line
Displacement as a Vector
• Vector has:– Magnitude– Direction– Point of origin
• Vector represented graphically by: – Line of action
• Magnitude and Direction quantified using:– Pythagorean Theorem– Trigonometry
Standing Broad Jump take-off
+-
+
-
P2P1
Calculation of Displacement
• Calculation of Magnitude:Resultant displacement (dR)
==
= 0.63 m
• Calculation of Direction:Angle to horizontal (θ)
Tan θ = Opposite / AdjacentTan θ = dV / dH = 0.2 / 0.6
θ = Tan-1 (0.2 / 0.6) θ = 18.8º
2
V
2
H d+d
22 )2.0(+)6.0(
Vertical displacement (dV) = 0.2 m
Horizontal displacement (dH) = 0.6 m
Resultant displacement (dR)
P1
P2
Speed and Velocity
• Average Speed (scalar):– Length of path (distance)
divided by change in time (∆t)
• Average velocity (vector):– Change in position (∆p)
divided by change in time (∆t)
– Displacement (d) divided by change in time (∆t)
If displacement = 50 m
Δt
d=
Δt
Δp=v
If t = 5 s
v = 50 / 5
= 10 m·s-1
Speed and Velocity
• We can think of instantaneous speed as distance traveled divided by the time it took to travel that distance if the time interval used in the measurement is very small.
• If the motion of the object under analysis is in a straight line and rectilinear, with no change in direction, average speed and average velocity will be identical in magnitude.
Velocity as a vector
Average Velocity
• Average velocity not necessarily equal to instantaneous velocity.
Winner of the Men's 100 m at the 2004 Athens Olympics
in 9.85 sAverage velocity:
= 100/9.85= 10.15 m·s-1
Kinematic analysis of 100 m sprint
Kinematic analysis of 100 m sprint
Velocity during 100 m
Average velocity: v = d / ∆t 0-10 m
= 10 / 2.2 = 4.5 m·s-1
10-20 m= 10 / 1.2 = 8.3 m·s-1
20-30 m= 10 / 0.8 = 12.5 m·s-1
30-40 m= 10 / 0.7 = 14.3 m·s-1
40-50 m= 10 / 0.8 = 12.5 m·s-1
50-60 m= 10 / 0.8 = 12.5 m·s-1
60-70 m= 10 / 0.7 = 14.3 m·s-1
70-80 m= 10 / 0.8 = 12.5 m·s-1
80-90 m= 10 / 0.9 = 11.1 m·s-1
90-100 m= 10 / 0.9 = 11.1 m·s-1
Acceleration
• Average Acceleration (a):Change in velocity (∆v) divided by change in time (∆t)
• As with displacement & velocity, acceleration can be resolved into components using trigonometry & Pythagorean theorem
2 1(v - vva = =
t t
)
V1 = 4.5 m·s-1 V2 = 8.3 m·s-1
∆t = 1.2 s
a = (8.3 - 4.5) / 10 = 3.2 m·s-2
Acceleration
• When an object speeds up, slows down, starts, stops, or changes direction, it is accelerating.
• The direction of motion does not indicate the direction of the acceleration.
• Instantaneous acceleration is the acceleration of an object at an instant in time.
Acceleration during 100 m
Acceleration at start of racea = (v2 - v1) / ∆t
= (8.3 - 4.5) / 1.2 Positive Acceleration= 3.2 m·s-2
_____________________________________________________________________________________________________________________________________________
Acceleration during middle of racea = (v2 - v1) / ∆t
= (12.5 - 12.5) / 0.8 Constant Velocity= 0
_____________________________________________________________________________________________________________________________________________
Acceleration at end of racea = (v2 - v1) / ∆t
= (11.1 - 14.3) / 0.9 Negative Acceleration= -3.5 m·s-2
Positive/Negative Acceleration
Velocity Curve for Sprinting
Velocity Curves for Two Sprinters
Bodies projected into the air are projectiles.
Horizontal & Vertical Components:• Vertical is influenced by gravity.• No force (neglecting air resistance) affects the
horizontal.• Horizontal relates to distance.• Vertical relates to maximum height achieved.
Kinematics of Projectile Motion
• Angle of projection
• Projection speed• Relative height of
projection
Factors Influencing Projectile Trajectory
• Perfectly vertical• Parabolic• Perfectly horizontal
Air resistance may cause irregularities.In this chapter, neglecting air resistance.
Angles of Projection
Relative Projection Height
• Maximize the speed of projection• Maximize release height• Optimum angle of projection:
Release height = 0, then angle = 450
Release height, then angle Release height, then angle
Optimum Projection Conditions
Range at Various Angles
Analyzing Projectile Motion
Path of a projectile fired with initial velocity vo at angle qo to the horizontal. Path is shown in black, the velocity vectors are green arrows,
and velocity components are dashed.
General Kinematic Equations for Constant Acceleration in Two Dimensions
• Horizontal (x component):
• Vertical (y component):
Kinematic Equations for Projectile Motion
v = projection speed (m/s)q = angle of projection (degree)h = relative height of projection (m)g = acceleration due to gravity (9,8 m/s2)
TUGAS: BUKTIKAN...!!!
Range of Projectile (R)
• Kerapian pekerjaan (keseriusan dalam mengerjakan tugas).
• Sistematika (keruntutan) tahap-tahap penyelesaian atau pembuktian.
• Kelengkapan tahap-tahap penyelesaian.• Kebenaran pekerjaan.• Tugas ditulis dengan tinta hitam pada kertas double-
folio bergaris.• Ketepatan dalam penyerahan tugas.
Kriteria Penilaian Tugas
THANKS....
WISH FOR GOOD LUCK....
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