Lesson 5: Elastic Potential Energy and SHM
Overview:
In this lesson you will be introduced to elastic potential energy and Simple Harmonic Motion. We will focus on on Elastic Potential Energy.
Curriculum Expectations:
Overall Expectations:
C3. Demonstrate an understanding of work, energy, momentum, and the laws of conservation of energy and conservation of momentum, in one and two dimensions.
Specific Expectations:
C2.1 Use appropriate terminology related to energy and momentum, including, but not limited to:
work, work–energy theorem, kinetic energy, gravitational potential energy, elastic potential energy, thermal energy, impulse, change in momentum–impulse theorem, elastic collision, and inelastic collision.
C2.3 Use an inquiry process to analyse, in qualitative and quantitative terms, situations involving work, gravitational potential energy, kinetic energy, thermal energy, and elastic potential energy, in one and two dimensions (e.g., a block sliding along an inclined plane with friction; a cart rising and falling on a roller coaster track; an object, such as a mass attached to a spring pendulum, that undergoes simple harmonic motion), and use the law of conservation of energy to solve related problems.
C3.1 Describe and explain Hooke’s law, and explain the relationships between that law, work, and elastic potential energy in a system of objects.
C3.2 Describe and explain the simple harmonic motion (SHM) of an object, and explain the relationship between SHM, Hooke’s law, and uniform circular motion.
C3. Demonstrate an understanding of work, energy, momentum, and the laws of conservation of energy and conservation of momentum, in one and two dimensions.
Specific Expectations:
C2.1 Use appropriate terminology related to energy and momentum, including, but not limited to:
work, work–energy theorem, kinetic energy, gravitational potential energy, elastic potential energy, thermal energy, impulse, change in momentum–impulse theorem, elastic collision, and inelastic collision.
C2.3 Use an inquiry process to analyse, in qualitative and quantitative terms, situations involving work, gravitational potential energy, kinetic energy, thermal energy, and elastic potential energy, in one and two dimensions (e.g., a block sliding along an inclined plane with friction; a cart rising and falling on a roller coaster track; an object, such as a mass attached to a spring pendulum, that undergoes simple harmonic motion), and use the law of conservation of energy to solve related problems.
C3.1 Describe and explain Hooke’s law, and explain the relationships between that law, work, and elastic potential energy in a system of objects.
C3.2 Describe and explain the simple harmonic motion (SHM) of an object, and explain the relationship between SHM, Hooke’s law, and uniform circular motion.
Success Criteria:
- Why the spring force considered a restorative force?
- How to determine the direction of the restorative force acting on a spring?
- What is the equation for Hooke's law? And what factor does, k, the spring constant depend on?
- Is the spring force exerted on the spring or by the spring on whatever stretches it?
- Relative to what coordinate is the displacement in Hooke's law measured from?
- What is an ideal spring?
- In what kind of objects is elastic potential energy present?
- Like gravitational potential energy, does elastic potential energy depend on an object's elevation?
- Describe the motion of a block when it is connected to a spring and both are resting on a friction-less surface. Make sure to include forces and energy in your discussion.
- What is Simple Harmonic Motion (SHM)?
Time Allocation: 2 hours
Learning Activities:
Read pages 192 - 199 from Nelson 4.6.
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Masses and Springs
A realistic mass and spring laboratory. Hang masses from springs and adjust the spring stiffness and damping. You can even slow time. Transport the lab to different planets. A chart shows the kinetic, potential, and thermal energy for each spring. |
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Hooke's law: the magnitude of the force exerted by a spring is directly proportional to the distance the spring has moved from equilibrium.
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Simple harmonic motion (at left) is a projection of the uniform circular motion (at right).
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Acceleration vector, graphs of position, velocity and acceleration vs time for a body suspended to a spring.
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In the playlist below, video:
- Will show you how to find the potential energy gained when pushing against a spring. (The advanced mathematics is just showing completeness of derivation, the main idea is that you need to take the area under the curve to calculate the work done).
- Will show you how to develop the equation of work done by a spring.
- Will introduce and develop the velocity and acceleration using energy equations.
- Will introduce and develop the distance, velocity and acceleration using the x as a function of time.
Practice questions 1 and 2 on page 195.
Practice question 2 on page 196.
Practice questions 1 on page 199.
Practice question 2 on page 196.
Practice questions 1 on page 199.
Task:
Solve questions 2, 4, 7, and 8 from Nelson 4.6 Review on page 200.
Optional Extension:
Optional Extension:
- Solve questions 6, 9, and 10 on page 200.
Reflect:
A car mounted on the springs in its suspension acts like a mass on a spring. How will the frequency of oscillations change if passengers are added to the car? Will the frequency increase, decrease, or stay the same? Explain your answer.
