Topic: Kinematics; Forces; Conservation of Energy
Episode: The Thundermans, Restaurant Crashers; Season 1, Episode 12
Episode Summary: When the kids ruin Barb’s anniversary gift from Hank, a family friend helps them out with their request to fix it. (Source: imdb.com)
Video Source: Amazon.com, iTunes
- Apply the relationship between a particle’s displacement and its initial and final positions.
- Apply the relationship between a particle’s average velocity, its displacement and the time interval for that displacement.
- Apply the relationship between a particle’s average acceleration, its change in velocity and the time interval for that change.
- For constant acceleration, apply the relationships between position, displacement, velocity, acceleration and time.
- Identify that if a particle is in free fall, and if we can neglect the effects of air on its motion, the particle has a constant downward acceleration with magnitude g that we can take to be 9.8 m/sec2.
- Apply the constant acceleration equations to free-fall motion.
- Identify Newton’s first and second law of motion.
- Apply the relationship (Newton’s second law) between the net force on an object, the mass of the object and the acceleration produced by the net force.
- For an object that move vertically or on a horizontal or inclined plane, apply Newton’s second law to a free body diagram of the object.
- After first clearly defining which objects form a system, identify that the mechanical energy of the system is the sum of the kinetic and potential energies of those objects.
- For an isolated system in which only conservative forces act, apply the conservation of mechanical energy to relate initial potential and kinetic energies to the potential and kinetic energies at a later instant.
- 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.
(Source: The NSTA Quick-Reference Guide to the NGSS, High School, NSTA Press, 2015)
In the episode, a bowling ball sitting on a high shelf rolls of that shelf after a slowing car hits the support beam (that’s another activity for conservation of momentum). The ball then falls and dents the car.
The question: What is the acceleration needed to bring the ball to a stop? What force must the car hood exert on the ball for the ball to come to a stop?
Explore the Concepts
Understanding Kinematics (from a graphical perspective)
Understanding Free Fall Moton (Schoolhouse Rock – A Victim of Gravity)
Understanding Free Fall Motion
Understanding Conservation of Energy
Understanding Gravitational Potential Energy
Understanding Rocket Thrust
Vernier Video Physics
HSVPL Conservation of Energy Lab
The goal of the evaluation is to determine the acceleration required to bring the bowling to rest. The bowling ball is not in free fall since the hood of the car exerts an upward force on the ball. To complete this analysis, you may make several reasonable assumptions about the height of the shelf, the fall time and the contact time between the hood and the ball.
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. The standard diameter of a bowling ball is 21.8313 cm. Import your video into your video analysis program. By tracking the step-by-step motion of your bowling ball, you will produce a graphical analysis of the ball’s motion.
Using the graph’s of distance v time and velocity v time (in the x- and y-directions), you may calculate the acceleration of the ball at various parts of its motion (when it is in free fall and when it is in contact with the hood of the car). From this, using Newton’s Second Law, you can calculate the force required to bring the ball to a stop.
You can also answer this question conceptually. Consider the following physics concepts:
- Conservation of Energy
The bowling ball starts from rest and rolls a distance of 0.75 m before falling off the shelf. Describe a series of mathematical steps by which you could calculate the indentation of the car hood. List the concept you will use and the variable(s) you will solve for.