1. Chapter 5 Kinetic Energy
Section 2 Energy
Chapter 5
Kinetic Energy
The energy of an object that is due to the object’s motion is called kinetic energy.
Kinetic energy depends on speed and mass.

2. gravitational PE = mass  free-fall acceleration  height
Section 2 Energy
Chapter 5
Potential Energy
Potential Energy is the stored energy associated with an object because of the position, shape, or condition of the object.
Gravitational potential energy is the energy an object has because of its position in a gravitational field.
Gravitational potential energy depends on height from a zero level and the mass of the object.
PEg = mgh
gravitational PE = mass  free-fall acceleration  height

3. Potential Energy, continued
Section 2 Energy
Chapter 5
Potential Energy, continued
Elastic potential energy is the energy available for use when a deformed elastic object returns to its original configuration.
The symbol k is called the spring constant, a parameter that measures the spring’s resistance to being compressed or stretched.

4. Chapter 5 Mechanical Energy
Section 3 Conservation of Energy
Chapter 5
Mechanical Energy
Mechanical energy is the sum of kinetic energy and all forms of potential energy associated with an object or group of objects.
ME = KE + ∑PE
Mechanical energy is often conserved.
MEi = MEf
initial mechanical energy = final mechanical energy (in the absence of friction)

5. Simple Harmonic Motion
Section 1 Simple Harmonic Motion
Chapter 11
Simple Harmonic Motion
Simple harmonic motion describes any regular vibrations or oscillations that repeat the same movement on either side of the equilibrium position.
Every simple harmonic motion is a back-and-forth motion over the same path. For example, pendulums & springs

6. Measures of Simple Harmonic Motion
Section 2 Measuring Simple Harmonic Motion
Chapter 11
Measures of Simple Harmonic Motion

7. Amplitude, Period, and Frequency in SHM
Section 2 Measuring Simple Harmonic Motion
Chapter 11
Amplitude, Period, and Frequency in SHM
In SHM, the maximum displacement from equilibrium is defined as the amplitude of the vibration.
A pendulum’s amplitude can be measured by the angle between the pendulum’s equilibrium position and its maximum displacement.
For a mass-spring system, the amplitude is the maximum amount the spring is stretched or compressed from its equilibrium position.
The SI units of amplitude are the radian (rad) or degrees and the meter (m).

8. Amplitude, Period, and Frequency in SHM
Section 2 Measuring Simple Harmonic Motion
Chapter 11
Amplitude, Period, and Frequency in SHM
The period (T) is the time that it takes a complete cycle to occur.
The SI unit of period is seconds (s).
The frequency (f) is the number of cycles or vibrations per unit of time.
The SI unit of frequency is hertz (Hz) or cycles/sec.

9. Amplitude, Period, and Frequency in SHM, continued
Section 2 Measuring Simple Harmonic Motion
Chapter 11
Amplitude, Period, and Frequency in SHM, continued
Period and frequency are inversely related:
Thus, any time you have a value for period or frequency, you can calculate the other value.

10. Measures of Simple Harmonic Motion
Section 2 Measuring Simple Harmonic Motion
Chapter 11
Measures of Simple Harmonic Motion

11. Period of a Simple Pendulum in SHM
Section 2 Measuring Simple Harmonic Motion
Chapter 11
Period of a Simple Pendulum in SHM
The period of a simple pendulum depends on the length and on the free-fall acceleration.
The period does not depend on the mass of the bob or on the amplitude (for small angles).
Lab results

12. Section 1 Simple Harmonic Motion
Chapter 11
SHM in springs
The direction of the force acting on the mass (Felastic) is opposite the direction of the mass’s displacement from equilibrium (x = 0).

13. Chapter 11 SHM in springs At equilibrium:
Section 1 Simple Harmonic Motion
Chapter 11
SHM in springs
At equilibrium:
The spring force and the mass’s acceleration become zero.
The speed reaches a maximum.
At maximum displacement:
The spring force and the mass’s acceleration reach a maximum.
The speed becomes zero.

14. Simple Harmonic Motion
Section 1 Simple Harmonic Motion
Chapter 11
Simple Harmonic Motion

15. Force and Energy in Simple Harmonic Motion
Section 1 Simple Harmonic Motion
Chapter 11
Force and Energy in Simple Harmonic Motion

16. spring force = (spring constant  displacement)
Section 1 Simple Harmonic Motion
Chapter 11
Hooke’s Law
The spring force, or restoring force, is directly proportional to the displacement of the mass.
This relationship is known as Hooke’s Law:
Felastic = kx
spring force = (spring constant  displacement)
The quantity k is a positive constant called the spring constant.

17. Section 1 Simple Harmonic Motion
Chapter 11
Spring Constant

18. Chapter 11 Practice Questions
Section 1 Simple Harmonic Motion
Chapter 11
Practice Questions
In pinball games, the force exerted by a compressed spring is used to release a ball. If the distance the spring is compressed is doubled, how will the force change? If the spring is replaced with one that is half as stiff, how will the force acting on the ball change?
If a mass of 0.55 kg attached to a vertical spring stretches the spring 2.0 cm from its original equilibrium position, what is the spring constant?
Suppose the spring from above is replaced with a spring that stretches 36 cm from its equilibrium position.
What is the spring constant?
Is this spring stiffer or less stiff?
How much force is required to pull a spring 3.0 cm from its equilibrium position if the spring constant is 2700 N/m?

19. Chapter 11 Section Review Section 1 Simple Harmonic Motion
Which of these periodic motions are simple harmonic?
a child swinging on a playground swing (θ = 45)
a CD rotating in a player
an oscillating clock pendulum (θ = 10)
A pinball machine uses a spring that is compressed 4.0 cm to launch a ball. If the spring is 13 N/m, what is the force on the ball?
How does the restoring force acting on a pendulum bob change as the bob swings toward the equilibrium position? How do the bob’s acceleration (along the direction of motion) and velocity change?
When an acrobat reaches the equilibrium position, the net force acting along the direction of motion is zero. Why does the acrobat swing past the equilibrium position?

20. Period of a Mass-Spring System in SHM
Section 2 Measuring Simple Harmonic Motion
Chapter 11
Period of a Mass-Spring System in SHM
The period of an ideal mass-spring system depends on the mass and on the spring constant.
The period does not depend on the amplitude.
This equation applies only for systems in which the spring obeys Hooke’s law.

21. Practice: Mass-Spring System
Section 2 Measuring Simple Harmonic Motion
Chapter 11
Practice: Mass-Spring System
A 125 N object vibrates with a period of 3.5 s when hanging from a spring. What is the spring constant of the spring?
A spring of 30.0 N/m is attached to different masses, and the system is set in motion. Find the period and frequency of vibration for masses of 2.3 kg and 15 g.

22. Chapter 11 Section Review
Section 2 Measuring Simple Harmonic Motion
Chapter 11
Section Review
A child swings on a playground swing with a 2.5 m long chain.
What is the period and frequency of the child in motion
A 0.75 kg mass attached to a vertical spring stretches the spring 0.30 m.
What is the spring constant?
The mass-spring system is now placed on a horizontal surface and set vibrating, What is the period of the vibration?