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Section 1 periodic Motionpptx

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Chapter 1
Section 1: Periodic Motion
Learning Objectives
1
Describe Simple Harmonic
Motion
2
Calculate the energy stored
in spring
3
Identify the factors affecting
Pendulum’s period
Key Vocabulary
1.
Periodic Motion
2.
Simple Harmonic Motion
3.
Resonance
Warmer Activity
• From the following clip:
• What is special about this motion !? Try
to describe it with your own words
• Do you know what we call such motion.
Periodic Motion
• Periodic motion occurs when objects move in a repetitive way along
a particular path in a fixed interval of time. Which forms a beautiful repeated
motion like a “harmony” .
Simple Harmonic Motion
• Recall wave characteristic:
•Amplitude is the maximum displacement
or distance reached by an object from the
equilibrium position.
•Period is the time needed for an object to
complete one cycle.
• Simple Harmonic Motion: Any system in which the force acting to
restore an object to its equilibrium position (Net force = 0) is directly
proportional to the displacement of the object.
Activity (1):
Spring – Mass Experiment
• Perform the following experiment and write down your observations
about S.H.M:
https://phet.colorado.edu/sims/html/masses-andsprings/latest/masses-and-springs_en.html
Mass on a spring system
• Observations:
• We can observe that spring force increase as
displacement increase
• Spring force always opposes motion (toward
equilibrium position ( x=0 )
• The time needed across the min. & max. position
(Period) is constant.
• Restoring force: Is the force responsible for this
kind of motion (S.H.M) and its always directed
toward the equilibrium position (X=0)
• And in this example, it’s the spring force where its
directed opposite to the direction of motion to
restore the normal position of the spring (toward
equilibrium) causing a repetitive motion through
fixed time interval
Hooke’s Law
• Based on the experiment we did of Mass-spring system:
1. Find the relation between Spring force – Displacement
2. What if you changed the spring to a stronger one !?
Hooke’s Law
• In Hooke’s Law:
• K : represents the spring constant that depends on the
stiffness of the spring and some other properties.
• It represents the slope of the force magnitude Vs.
displacement ( N/m)
• Steeper slope will give a larger K. Which means that the spring
is harder to stretch
NEGATIVE SIGN means that spring force opposes motion
Objects that obeys Hooke’s law called elastic objects
Hooke’s Law valid for a certain limits, if the spring stretched
further this limit. Then deformation will happen
Elastic Potential Energy
• Once we apply an external force to stretch or compress the spring, A
WORK is done and stored as a potential energy in the spring.
• This potential energy stored is called Elastic potential energy
• Elastic potential energy = Area under the curve
• P.E = (area of triangle) = ½ × Base × Height
• Base = ∆x
• Height = Force = kx (according to hook’s law)
Elastic Potential Energy
• Use the previous experiment then write-down your observation from
the energy graph:
 We apply the law of conservation of energy:
Potential Energy converted into Kinetic energy, and repeat.
1. Max. Potential Energy occurs at (max. compression or extension
position) where at this instant velocity is ZERO ( K.E = 0 )
2. Max. Kinetic Energy occurs at (max. velocity), when displacement is
ZERO (Equilibrium) where elastic potential energy is equal to ZERO
Activity (2)
Activity 3
• Perform the following experiment: and answer the given questions
https://phet.colorado.edu/sims/html/pendulumlab/latest/pendulum-lab_en.html
• Q1) What is the location of Max. Potential Energy
• Q2) Is it considered as periodic motion !! Explain !?
• Q3) What happen to the time period once you:
• Change the mass of the hanged ball
• Change the Length of the rope
• Manipulate the gravity value
• Q4) What are the factors that affects the period of this pendulum ?
Pendulum
The component of the gravitational force in the direction of the
pendulum’s circular path is a restoring force.
• This force is Max. & Min. at the highest point on right and left
(where velocity is zero)
• At equilibrium point velocity is max. and the restoring force is
zero.
• Only for a small angles (less than 15) the force is proportional
to the displacement from the equilibrium >>> simple
harmonic motion
• Masses are called Bob.
Activity 4
Resonance
• See the given video to visualize resonance:
Resonance
• Resonance: Is a force applied to a vibrating or oscillating object at a
time interval equal to the period of oscillation
• It cause an increment of the amplitude in the vibration
• Resonance is a simple harmonic motion causes a larger displacement
as energy added in small increments
• Resonance can cause useful increase in amplitude or catastrophic
result.
• https://www.twig-world.com/film/resonance-1428/
Activity 5
• Apply your understanding of resonance using the following
simulation:
• https://phet.colorado.edu/en/simulation/legacy/resonance
Check your understanding
Let's play:
https://kahoot.it/challenge/0476052?challenge-id=86fdb651-f1b84548-859b-a7e0a8874730_1693727624340
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