Activity Title – Teachers NotesScience Activity

Next Generation Science Standards (Middle School Physical Science):MS-PS2-2. Plan an investigation to provide evidence that the change in an object’s motion depends on the sum of the forces on the object and the mass of the object. MS-PS2-2. Plan an investigation to provide evidence that the change in an object’s motion depends on the sum of the forces on the object and the mass of the object. MS-PS3-5. Construct, use, and present arguments to support the claim that when the kinetic energy of an object changes, energy is transferred to or from the object.Engineering Extension:MS-ETS1-2. Evaluate competing design solutions using a systematic process to determine how well they meet the criteria and constraints of the problem. MS-ETS1-3. Analyze data from tests to determine similarities and differences among several design solutions to identify the best characteristics of each that can be combined into a new solution to better meet the criteria for success. MS-ETS1-4. Develop a model to generate data for iterative testing and modification of a proposed object, tool, or process such that an optimal design can be achieved.

All NGSSHS-PS3-1. Create a computational model to calculate the change in the energy of one component in a system when the change in energy of the other component(s) and energy flows in and out of the system are known.

Science Standards (Natural Science & Physical Science):

Arkansas Physical Science Standards P.6.PS.10 Calculate force, mass, and acceleration using Newton’s second law of motion:

F = ma, where F =force, m=mass, a =acceleration P.6.PS.14 Solve problems by using formulas for gravitational potential and kinetic

energy, *KE=1/2mv2 *PE=mgh, Where KE= kinetic energy, PE= potential energy, m= mass, v=velocity

P.6.PS.12 Compare and contrast the effects of forces on fluids: o Archimedes’ principleo Pascal’s principleo Bernoulli’s principle

NS.10.PS.1 Develop and explain the appropriate procedure, controls, and variables (dependent and independent) in scientific experimentation

NS.10.PS.4 Gather and analyze data using appropriate summary statistics NS.10.PS.6 Communicate experimental results using appropriate reports, figures, and

tables NS.12.PS.1 Use appropriate equipment and technology as tools for solving problems

(e.g., balances, scales, calculators, probes, glassware, burners, computer software and hardware)  

NS.12.PS.2 Collect and analyze scientific data using appropriate mathematical calculations, figures, and tablesArkansas 8th Grade Science Standards

NS.1.8.1 Justify conclusions based on appropriate and unbiased observations NS.1.8.3 Formulate a testable problem using experimental design NS.1.8.6 Formulate inferences based on scientific data   NS.1.8.7 Communicate results and conclusions from scientific inquiry following peer

review

Arkansas 7th Grade Science Standards NS.1.7.1 -Interpret evidence based on observations NS.1.7.4 - Construct and interpret scientific data using

• histograms • circle graphs • scatter plots • double line graphs • line graphs by approximating line of best fit  

NS.1.7.5 - Communicate results and conclusions from scientific inquiry PS.6.7.3 - Demonstrate Newton’s second law of motion PS.6.7.5 - Explain how Newton’s three laws of motion apply to real world situations (e.g.,

sports, transportation)

Math Standards:

Common Core 8th Grade Standards CCSS.MATH.CONTENT.8.EE.A.3 - Use numbers expressed in the form of a single digit

times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 times 108 and the population of the world as 7 times 109, and determine that the world population is more than 20 times larger.

CCSS.MATH.CONTENT.8.EE.A.4 - Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology

CCSS.MATH.CONTENT.8.EE.B.5 - Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

CCSS.MATH.CONTENT.8.EE.C.7 - Solve linear equations in one variable.o CCSS.MATH.CONTENT.8.EE.C.7.A - Give examples of linear equations in one

variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).

o CCSS.MATH.CONTENT.8.EE.C.7.B - Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

CCSS.MATH.CONTENT.8.F.A.1 - Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.1

CCSS.MATH.CONTENT.8.F.B.4 - Construct a function to model a linear relationship between two quantities. Determine the rate of change  and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

CCSS.MATH.CONTENT.8.F.B.5 - Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

CCSS.MATH.CONTENT.8.SP.A.1 - Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.

CCSS.MATH.CONTENT.8.SP.A.2 - Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.

CCSS.MATH.CONTENT.8.SP.A.3 - Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.Common Core Algebra 1 Standards

N.Q.1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.

N.Q.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

A.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

A.CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R.

A.REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

A.REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

F.IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.

F.IF.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

Common Core 7th Grade StandardsCCSS.MATH.CONTENT.7.RP.A.2Recognize and represent proportional relationships between quantities.CCSS.MATH.CONTENT.7.RP.A.2.ADecide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.CCSS.MATH.CONTENT.7.RP.A.2.BIdentify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.CCSS.MATH.CONTENT.7.RP.A.2.CRepresent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.CCSS.MATH.CONTENT.7.RP.A.2.DExplain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.CCSS.MATH.CONTENT.7.G.B.4

Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.CCSS.MATH.CONTENT.7.G.B.6Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.CCSS.MATH.CONTENT.7.EE.B.4Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.CCSS.MATH.CONTENT.7.EE.B.4.ASolve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

**Teacher NOTEs**This activity is written for Physical Science and Algebra I, but can be modified with ease to many levels. Simple machines in the extension can be built with ease for 6th grade standards, with a light focus on ratios and proportions of the movement of the syringes and mechanical advantage. A Google search for “hydraulic machines using syringes” will bring up many examples of what can be achieved. In 7th and 8th grade, the nature of science standards are primarily what can be achieved, but the extension of building machines will address many NGSS Engineering standards, while many 8th grade math standards are covered. Removing part 2 of the investigation will eliminate the more advanced physical science concepts. If both investigations are done, another extension would involve plotting the results of part 1 and part 2 against each other, and see how close the slope is to 1, to find the level of correlation between the sets of results that should be equal. Part 1 & the use of scientific notation may be too much for 7th grade, thus Part 2 and the simple step one problem solving is a better fit for 7th grade math and provides 7th grade science teachers the opportunity to tie in Newton’s Law.

M.A.S.T Activity - Prairie Grove Middle School8th Grade Math and Integrated Science8th Grade Algebra I and Physical Science

Hydraulics, Pascal’s Principle and Work

Purpose:  Investigate the relationship between Force, Area and Pressure in Pascal’s Principle and the relationship between Force, Height, and Work.

Learning Goals: Students will discover the relationships between Force, Area and Pressure as

well as the relationship between Force, Height, and Work.

Equipment and Supplies: Variety of syringe sizes (60 mL, 35 mL, 20 mL, 12 mL, 6mL, and  3mL) Standard Vinyl Aquarium Tubing 1 kg mass Lab Stand with right angle clamp and large clamp Cup of Water Set of digital calipers or a ruler Calculator

Part I - Pascal’s Principle

Form a hypothesis first - With which piston/syringe would it be easier to move 1 kg of mass placed on the large (60 mL) piston/syringe, if both syringes and the tubing contain water?  (See the picture below and /or teacher demonstration at the front of the room) The 3 mL?  The 6 mL?  The 12 mL?  The 20 mL?  or the 35 mL?  Why do you believe this piston or syringe will move the mass more easily?

To determine which size of piston/syringe will move the mass with the most ease, we are going to collect some data and use something called Pascal’s Principle, which states:

Pressure1 = Pressure2, or P1 = P2

&

Pressure = Force x Area, or P = FA

Before we begin using Pascal’s Principle, we will need to find the area of the plungers in each of our different syringes.  Using the digital calipers and your calculator, complete the following table.

Diameter of the plunger

(mm)

Radius of the plunger (mm)

Radius of the plunger (m)

Area of the plunger

(m2)

60 mL piston/syringe

3 mL piston/ syringe

6 mL piston/syringe

12 mL piston/syringe

20 mL piston/syringe

35 mL piston/syringe

Now, since we know that P1 = P2, and P = FA, we can create a proportion to compare the pressure of the large piston/syringe to each of the other pistons/syringes.

F1

A1=F2

A2

A1 and A2 are already known, they are the area of our large piston/syringe and the area of one of the other piston/syringes.  We can find the Force being applied to the large piston/syringe using the Force Equation,

Force = mass x acceleration, or F = ma

Calculate: To keep our 1 kg mass moving upward after we overcome the initial friction, we must supply an upward force through the tubing that exactly matches the downward force on the big piston due to gravity.  Knowing that acceleration due to gravity is 9.81 m/s2, Calculate the force being applied to your large piston/syringe. Show your work.

Now that you have calculated the force on your large piston, use it to determine the force you need to apply to each of the smaller pistons/syringes to lift that 1 kg of mass and record it in the table below.  

Piston/Syringe Size

Area of the plunger (m2)

Force required to lift 1kg of mass on the Large Piston /Syringe (Newtons)

3 mL

6 mL

12 mL

20 mL

35 mL

Plot the Force required to lift 1 kg of mass on the large piston/syringe (in Newtons) versus the area (in m2) of each of the smaller piston/syringes on the graph below.  

Questions:

1.  What does your graph suggest about the relationship between the surface area of the plunger and the force needed to move 1 kg of mass on the large piston/syringe?

2.  How does this compare to what you predicted in your hypothesis at the beginning of the activity?

3.  Create an equation which represents the function that is modeled on your graph.

4.  A 90 mL syringe requires a force of 15.21 N to move the 1 kg mass on the large piston/syringe.  What is the area of the 90 mL syringe’s plunger?  What is its radius?

Part II - WorkWork is a measure of the energy expended moving an object in the same direction as the applied force.  Work is measured in Joules.    You find work done by multiplying Mass (kg) times the force we apply to overcome gravity, times the height we raised the mass (m). This tells us how much potential energy we added to the object by raising it higher.

w = mgh

Or, if your force is not due to gravity, work = force x distance.  Force is measured in Newtons, kg m/s2. This means one Newton of force will accelerate one kilogram from rest to a speed of one meter per second.

Question: If a 60 kg student runs up a flight of stairs 3 meters higher than his starting point, how much work did he do?

Calculate: Look closely at the units, and work out what combination of units a Joule represents.

In our hydraulic pistons/syringes, work raises the mass up, giving it more potential energy, so work equals the change in potential energy. We can measure the change in the height of the mass to find the change in potential energy. Since energy is conserved, the work we do on one piston (pushing in) will have to be done by the other piston (pushing out). Finally, the change in potential energy equals the work you did on the small syringe!

so, WS = WL, or WS = mLghL

Also remember that work = force distance, so mgh=fd

Using your lab stand and clamps, set up a hydraulic lift using your large (60 mL) piston/syringe and each of the smaller syringes, one at a time.  When setting up your hydraulic system, make sure to remove all air from the lines.  Place 1 kg of mass on your large piston/syringe.  Apply force to the small piston/syringe to lift the mass on the large piston/syringe as far as you can.

In the table below, record the distance you pressed in the small piston/syringe, and the distance the large piston/syringe rises (you can use your digital calipers for this, or a ruler).  Then, calculate the work done by the large piston lifting the mass. Finally, use the fact that  Work = Work, and mgh = fd to find the force (in Newtons) you applied to the small piston to raise the mass.  

Piston/Syringe Size

Small piston/syringe push distance (m)

Large piston/syringe

risedistance

(m)

Mass Lifted (kg)

Force of Gravity (m/s2)

Work done by Large piston

(J)

W = mgh

Force applied to small piston (N)

3mL 1

6mL 1

12mL 1

20 mL 1

35 mL 1

Questions:1. How do the forces you applied to the small piston/syringe you calculated above compare to the forces you calculated in Part 1 for the same syringes?

2. Explain why you observed these similarities or differences?

3.  Do the results of Part 1 and Part 2 support your initial hypothesis?  Why or Why not?

4. In what kind of situation or device would you need to apply force to a piston with a very large plunger area to move one with a much smaller plunger area?

Extension of Hydraulics:Design a device using two pairs of syringes that will be able to move the mass from one side of the challenge course to the other.  Test your device extensively BEFORE the challenge! Try to make it fail, find out how it fails, and change your design to make it better! Engineering a good design takes several rounds of trial and error!

Modern Marvels Episode - Hydraulicshttps://www.youtube.com/watch?v=nthi0EyQdUQ