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Engineering a Pinball Launch
Engineering a Pinball Launch
Imagine you are part of a design team tasked with engineering the plunger mechanism for a new, small-scale competitive pinball machine. Your goal is to design a launcher that can consistently send a steel ball (which acts like your cart) up a gently inclined ramp to a specific target zone.
To ensure fair play and predictable launch mechanics, you need to understand exactly how the spring's compression translates into the ball's launch speed, and how that speed, in turn, determines the maximum vertical height it will reach up the ramp.
Your engineering challenge is two-fold:
Calibration: Determine the precise relationship between the amount you pull the spring back (the compression distance, x) and the resulting initial velocity, v_0, of the ball. This will allow your team to know exactly how much energy is being delivered.
Performance Check: Verify the principle of energy conservation to predict the final height the ball will reach. Does the ball's initial kinetic energy perfectly convert into gravitational potential energy as it rolls uphill?
By performing this lab, you will be collecting the critical data necessary to write the software calibration tables for your pinball machine, ensuring that every launch is predictable and the machine operates exactly as designed. Friction must be minimized for your design to work, so your experiment will test how well the energy is conserved!
Pinball Action in Video Games -
Pinball Action in Video Games -
While few games explicitly show an x^2 versus v graph, many common mobile games rely on the energy conversion or projectile motion principles being studied.
1. Spring Energy to Kinetic Energy to Gravitational Potential Energy
1. Spring Energy to Kinetic Energy to Gravitational Potential Energy
The entire two-part lab is perfectly modeled by the physics of the "sling-shot" mechanic found in many games.
Angry Birds: This is the classic example.
Elastic Potential Energy (U_s): The bird is pulled back (like compressing the spring), storing elastic potential energy proportional to the square of the pullback distance (x).
Kinetic Energy (K): When released, this potential energy is converted into kinetic energy, giving the bird an initial velocity (v_0).
Projectile Motion/Gravitational Potential Energy (U_g): Once launched, the bird's kinetic energy is converted into gravitational potential energy as it flies upwards, following a parabolic path (projectile motion) governed by gravity. The player's success depends on intuitively understanding how the pullback distance (x) determines the flight path and height (∆)h.
Golf/Mini-Golf Games (with a Pullback Meter):
Many mobile golf games use a pull-and-release mechanic, often with a visual power meter. The distance you pull back the club (analogous to spring compression, x) directly determines the initial speed (v_0) and, consequently, the maximum height and distance the ball travels (analogous to ∆h).
2. Kinetic Energy to Gravitational Potential Energy
2. Kinetic Energy to Gravitational Potential Energy
This relationship is key to any game featuring jumping or trajectory.
Platformers (e.g., Super Mario Run, or endless runners with vertical jumps):
While not a spring, the jump is often simulated by giving the character an initial upward velocity (v_0).
The height the character reaches (∆h) is directly determined by that initial velocity, where v02∝h. Game designers must program the jump to be predictable based on this exact physics relationship.
Flappy Bird (and similar 'tap-to-fly' mechanics):
Each tap essentially applies a short impulse, boosting the kinetic energy and subsequent upward motion. The constant battle against gravity's pull (which converts K→Ug ) is the core challenge.
3. General Energy and Collision Games
3. General Energy and Collision Games
Pool/Billiards/Snooker Games:
The "launch" of the cue ball relies on the energy transfer from the cue stick (which can be modeled similarly to a spring or an impulse). The resulting speed (v_0) of the cue ball dictates how much kinetic energy is transferred during the subsequent elastic collisions with other balls. This kinetic energy transfer is governed by the conservation laws.
Potential energy can be stored in a variety of different systems. Typically potential energy is stored based on the relative position of one object to another or the change in an object's position. In this lab we will be storing energy in the compressed spring (EPE) and the gravitational field of the Earth (GPE). The energy will be transferred from the compression of the spring to the field of the Earth through the motion (Kinetic Energy) of the cart quantified by the cart's velocity.
∆x = 0 m ∴ F= 0 N
∆x = 0.10 m ∴ F= 3.4 N
In this case we can see that a force of 3.4 N was needed to extend a spring 0.10 m.
Work is being done on the system, W=FΔd, therefore energy is being put INTO the spring.
In this activity we would like to explore various springs and quantify the amount of energy stored in each spring when compressed.
The video will provide background on determining the SPRING CONSTANT. It is this value that we will record for our two different springs.
Converting Elastic Potential Energy (US) to Gravitational Potential Energy (Ug) and Kinetic Energy (K)
Converting Elastic Potential Energy (US) to Gravitational Potential Energy (Ug) and Kinetic Energy (K)
Does doubling the compression of the spring double the height the cart reaches on the ramp?
Indicate the quantities to be measured and the equipment you are going to use to collect these measurements.
Draw a clearly labeled diagram, include where the measurements/variables are located on your diagram.
Describe how you would use the equipment to conduct the experiment.
A minimal number of steps in bulleted format.
Be sure to include how you will use each piece of equipment and how you will measure each of the variables defined in your table.
Define the terms you use in your experiment
Sketch a predicted graph of your data. Include the appropriate labels on your axis.
Sketch a diagram of your setup, labeling the significant variables on the diagram.
Indicate 3-5 positions on the sketch that will be significant in your experiments. (i.e. max height of the cart)
Data Sampling Set-up
Data Channels - Position and Force
Data Collection Rate - Determine the data collection rate that would be best for your experiment.
Zero Sensors -
With the cart resting on the stop, zero the position of the cart.
When the cart is NOT in contact with stop, zero the force sensor.
Conceptual understandings of the graphs.
Take a sample data set.
Match positions on the graph with the 3-5 positions on your sketch.
Determine the spring constant of your spring steel.
Five compression distances (∆x) and Force (N).
Determine slope/gradient of the trendline.
Determine height reached when spring is compressed to five different distances (∆x) and change in height of the cart (∆h).
How will you determine the change in height of the cart (not the distance traveled)?
Create a graph (manually or in Sheets) of height (y-axis) vs. compression (x-axis).
For each of the compressions, determine the maximum velocity when the cart is launched by the spring.
Create a graph (manually or in Sheets) of maximum velocity (y-axis) vs. compression (x-axis).
Typically for all of your data you should collect 5x3 data, however in the interest of time, we will only collect one trial.
Sample Data
Sample Data
Force vs. Compression of Spring Steel
Max Velocity vs. Compression of Spring Steel
Height vs. Compression of Spring Steel
Height vs. Compression of Spring Steel Distance Squared
Some Additional Resources:
Some Additional Resources:
Determining the Energy Stored in a Spring
Determining the Energy Stored in a Spring
Suppose each of the springs were to be used to launch six identical 0.050 kg steel marbles vertically into the air.
To test the system, initially the springs were compressed 0.050 m(x). Once the launching mechanism became fully operational the springs were compressed to 0.100 m (2x) and 0.150 m (3x).
Compare test heights v the fully operational heights reached by the 6 marbles.
You may find the information on 01.3b - Graphical Analysis useful.
Converting EPE to KE to GPE - Goal-less problem
Converting EPE to KE to GPE - Goal-less problem
Choose one of the Goal-less problems below or create your own. Both Pivot simulations have been assigned, you can explore both before making a decision as to which one you choose. OR go purely mental and choose Just a Ball, a Ramp and a Spring. OR if you are up for the challenge find your own spring and object and try one yourself. OR try your hand at being a Bungee Jump operator, (Goal #1 nobody hits their head)
This is a goal-less problem. You are to decide what models (types of energies) apply (state this explicitly and justify your choice), describe any assumptions you are making, and solve for as many unknowns as you can, making good use of written explanation, graphs, energy pie charts, and diagrams.
Prob #2: Einstein on a Joy Ride
Prob #2: Einstein on a Joy Ride
Prob #4: Bungee Jumping
Prob #4: Bungee Jumping
The study of energy has described three energy storage formats based on position, velocity and compression or extension. Be sure to include explanations of transfers amongst these different stores.
Diagrams should include
variables affecting the outcome of the trial.
energy pie charts of relative energy values at key points in the action.
motion maps showing relative velocities at key points.
Graphs should include:
key points that describe the relationship
analysis of the slope (units and values) - if applicable
area under the curve (units and values) - if applicable
The student’s job is to model the situation as best they can using the physics they know. First step: say which models apply and why. Second step: draw (and annotate) the graphs/diagrams that go with those models to represent the situation. Third step: use the diagrams to analyze the situation.
Kelly O'Shea - Goalless Problems
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