Topic: Springs, Hooke’s Law
Episode: Henry Danger, Birthday Girl Down, Season 1, Episode 9.
Episode Summary: An accusation prevents Henry from being invited to a birthday party.
Video Source: Amazon Instant Video ($1.99)
- Apply the relationship (Hooke’s Law) between the force on an object due to a spring, the stretch or compression of the spring and the spring constant of the spring.
- Identify that the spring force is a variable force.
- Identify that the spring force is a restoring force.
- Calculate the work done on an object by the spring force by graphically integrating on a graph of force versus position of the object.
- Apply the work-kinetic energy theorem to situations in which an object is moved by a spring force.
- Calculate the elastic potential energy of a block-spring system.
- Source: Walker, Fundamental of Physics, 10th edition
Disciplinary Code Ideas (DCIs)
PS2.A Forces and Motion: Newton’s Second Law predicts changes in the motion of macroscopic objects.
PS3.A Definitions of Energy: Energy is a quantitative property of a system that depends on the motion and interaction of matter and radiation within the system. That there is a single quantity called energy is due to the fact that a system’s total energy is conserved, even as, within a system, energy is continually transferred from one object to another and between its various possible forms. (HS-PS3-2)
PS3.B Conservation of Energy and Energy Transfer: Conservation of Energy means that the total change of energy in any system is always equal to the total energy transferred into or out of the system.
Energy cannot be created or destroyed, but it can be transported from one place to another and transferred between systems. (HS-PS3-4)
Mathematical expressions, which quantify how the stored energy in a system depends on its configuration and how kinetic energy depends on mass and speed, allow the concept of conservation of energy to be used to predict and describe system behavior.
The availability of energy limits what can occur in any system.
PS3.C. Relationship Between Energy and Forces
When two objects interacting through a field change relative position, the energy stored in the field is change.
(Source: The NSTA Quick-Reference Guide to the NGSS, High School, NSTA Press, 2015)
In the episode, Henry is not invited to a girl’s birthday party after seriously injuring her (and her cat) at a previous party. During one scene, Henry jumps up and down on a trampoline.
The question: What is the effective spring constant of the trampoline?
Explore the Concepts
Introduction to Springs and Hooke’s Law
How It’s Made: Springs
Potential Energy Stored in a Spring
Conservation of Energy with a Spring
Vernier Video Physics
HSVPL Conservation of Energy Lab
HSVPL Hooke’s Law Lab
- Use these Apps to further develop your understanding of the motion of springs.
- Use Vernier Video Physics to record the motion of a spring. What data and information can you obtain and what data can you calculate based on the data you collected.
The goal of the evaluation is to determine the spring constant of the trampoline. Springs are elastic, which means after they are deformed (when they are being stressed or compressed), they return to their original shape. Ideal springs obey Hooke’s Law: F = -kx. The spring constant is representative of how stiff the spring is. Stiffer (more difficult to stretch) springs have higher spring constants. (Source: http://www.education.com/science-fair/article/springs-pulling-harder/)
Do you think the trampoline has a high spring constant or a low spring consnat.
Import the video of the scene into Vernier Video Analysis on your iPad or into Logger Pro on your laptop.
You will need to set a scale. Jace Norman’s height is 1.57 m and his mass is approximately 50 kg.. Import your video into your video analysis program. By tracking the step-by-step motion of Henry compressing the trampoline, you will produce a graphical analysis of the Henry’s motion.
You can use the graphs to determine the maximum compression of the trampoline. Using this information, along with Hooke’s Law and Newton’s Second Law of Motion, you can calculate the spring constant of the trampoline.
You can also apply what you have learned in this activity. You now know the spring constant of the trampoline, along with a force – displacement pair.
- Who would compress the trampoline more? Jasper or Charlotte?
- Design an experiment to verify your prediction in (a).
- Assume that the trampoline is replaced with a trampoline with a lower spring constant?
- Would the maximum compression of the trampoline increase, decrease or stay the same?
- Would Henry’s return bounce be higher, lower or remain the same.
- Design an experiment to verify your predictions in (c).
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