Mousetrap Math

The Science of Mousetrap Powered Vehicles

Presenter: Erich LandstromPhysics Teacher & SECME School Coordinator

Seminole Ridge Community High School

Email: SeminoleSECME@gmail.com

SECME: rockets, robots, and raising your GPA

Warm-up

1. On your own paper, draw & label the force action-reaction pair interaction that makes a car move forward.

2. Define “Work” in your own words.

Physics REVIEW

Newton’s 0th law of motion– An object at rest tends to stay at rest– DEF. Inertia : tendency of an object to

resist change in motion

Physics REVIEW

Newton’s 1st law of motion– An object in motion tends to stay in

motion• In a straight line• At a constant speed(unless acted on by an outside net force!)

WITHOUT ACCELERATING!

Physics REVIEW

Newton’s 2nd Law of MotionThe amount an object (like a MTV) accelerates is inverse to its mass

– More MTV mass, less acceleration – Less MTV mass, more acceleration ☺

Physics REVIEW

FORCE– A force is a Push or a Pull– Measured in Newtons (N)– Newton’s 2nd Law of Motion: “Force is

equal to the mass of an object times its acceleration; F = m•a

Physics REVIEW

WORK– Work = Force • Distance = m•a•d

• So work makes you mad D:<– W = N•m = Joules– W = Measurement of Energy

Work Transfers Energy1. Open your mousetrap.2. Did you exert a force?

o How much force did you exert?3. Did you exert a force over a distance?4. Did you do WORK?5. Did it take ENERGY to do this work?6. Where is the energy now?

o STORED in the mousetrap!7. Can we use the stored energy for anything?

o Discuss with your shoulder partner & report back

How can we use the stored energy in a set mousetrap?

MOUSETRAP POWERED VEHICLES

Physics REVIEW

Newton’s 3rd Law of MotionEvery action has a reaction

– Equal in FORCE– Opposite in DIRECTION

Newton’s 3rd Law of Motion

Newton’s 3rd Law of Motion

Force of weight downward from gravity

Force of friction from floor

Force of drag from air resistance

Force of released spring tension

Normal Force upward from floor

Physics REVIEWMomentum

– Momentum = mass x speed = p = m•v– Force and momentum are related

• p = m•v• F = m•a = m•v/t

– Impulse = force x time = I = F•t– Impulse equals momentum because of Newton’s

2nd Law; F•t = m•v because F = m•v/t

The Spring Force powers the MTV

You can measure the force required to stretch the spring as a function of the displacement by hanging known weights from the "trap" end of the mousetrap and measuring how much the spring is wound up.

Physics REVIEW

Momentum– Energy and momentum are related– Both are conserved properties (not

created or destroyed, but transferred)• p = m•v• KE = 1/2 m•v2

FCAT Science Practice Problems

Please refer to FCAT Science Reference Sheet with formulas and conversions

FCAT Science Reference Sheet

Average SpeedAccelerationForceMomentumWorkEfficiency

2009 SECME National Engineering Design Scores Mousetrap Car High School Division

Mousetrap Vehicle Math

Take out your cell phone/calculatorSolve the practice problems

SSS Science BenchmarksSC.B.1.4.1 The student understands how knowledge of energy is fundamental to all the scientific disciplines (e.g., the energy required for biological processes in living organisms and the energy required for the building, erosion, and rebuilding of the Earth).SC.B.1.4.7 The student knows that the total amount of usable energy always decreases, even though the total amount of energy is conserved in any transfer

SSS Science Benchmarks

SC.C.1.4.1 The student knows that all motion is relative to whatever frame of reference is chosen and that there is no absolute frame of reference from which to observe all motion.SC.C.1.4.2 The student knows that any change in velocity is an acceleration.SC.C.2.4.6 The student explains that all forces come in pairs commonly called action and reaction.

NATURE OF SCIENCE BODY OF KNOWLEDGE Standard 3

SC.912.N.3.3 Explain that scientific laws are descriptions of specific relationships under given conditions in nature, but do not offer explanations for those relationships.

PHYSICAL SCIENCE BODY OF KNOWLEDGE Standard 10: Energy

SC.912.P.10.1 Differentiate among the various forms of energy and recognize that they can be transformed from one form to others.SC.912.P.10.2 Explore the Law of Conservation of Energy by differentiating among open, closed, and isolated systems and explain that the total energy in an isolated system is a conserved quantity.

PHYSICAL SCIENCE BODY OF KNOWLEDGE Standard 10: Energy

SC.912.P.10.3 Compare and contrast work and power qualitatively and quantitatively.

PHYSICAL SCIENCE BODY OF KNOWLEDGE Standard 12: Motion

SC.912.P.12.2 Analyze the motion of an object in terms of its position, velocity, and acceleration (with respect to a frame of reference) as functions of time.SC.912.P.12.3 Interpret and apply Newton's three laws of motion.

PHYSICAL SCIENCE BODY OF KNOWLEDGE Standard 12: Motion

SC.912.P.12.5 Apply the law of conservation of linear momentum to interactions, such as collisions between objects.SC.912.P.12.6 Qualitatively apply the concept of angular momentum

Average speed

In the 2009 SECME National competition, The Crusaders mousetrap vehicle was 0.083 meters long, had a mass of 0.0292 kilograms, and it crossed a distance of 24.625 meters. Suppose the mousetrap vehicle operated for 16 seconds. What speed, in meters per second, did the Crusaders mousetrap achieve?

Average Speed ANSWER

Average speed = distance/time24.625 m/16 s = 1.54 m/s

Acceleration

In the 2009 SECME National competition, the Blue Devils mousetrap vehicle was 0.152 meters long, had a mass of 0.0572 kilograms, and it crossed a distance of 18.286 meters. Suppose the mousetrap vehicle started from rest and operated for 18 seconds. What acceleration, in meters per second squared, did the Blue Devils mousetrap achieve?

Acceleration ANSWER

Acceleration = change in velocity/time v = d/t = 18.286 m/18 s = 1.02 m/s

a = v/t = 1.02 m/s /18 s = 0.056 m/s2

Force (Newton’s 2nd Law of Motion)

In the 2009 SECME National competition, The Anomalies mousetrap vehicle was 0.108 meters long, had a mass of 0.0506 kilograms, and it crossed a distance of 24.765 meters. Suppose the mousetrap vehicle started from rest and operated for 17 seconds. How much horizontal force, in newtons, did the Anomalies vehicle apply during its total movement?

Force ANSWER

Force = mass x acceleration = m x v/tForce = (0.0506 kg x 24.765 m/17 s)/17 s

Force = 0.004 Newtons

Force of Gravity vertical

Force of weight = mass x gravitational acceleration

Force = 0.0506 kg x 9.8 m/s2

Force = 4.96 Newtons

Momentum

In the 2009 SECME National competition, The Hybrid Kids mousetrap vehicle was 0.368 meters long, had a mass of 0.0911 kilograms, and it crossed a distance of 12.828 meters. Suppose the mousetrap vehicle started from rest and operated for 20 seconds. How much momentum, in kilogram-meters per second, did the Anomalies vehicle create during its total movement?

Momentum ANSWER

progress = mass x velocityp = 0.0911 kg x 12.828 m/20 sp = 0.058 kg-m/s

Work

In the 2009 SECME National competition, the Lightening mousetrap vehicle was 0.184 meters long, had a mass of 0.0813 kilograms, and it crossed a distance of 13.720 centimeters. Suppose the mousetrap vehicle started from rest and operated for 18 seconds. How much work, in Joules, did the Lightening vehicle achieve during its total movement?

Work ANSWER

Work = force x distance = madW = 0.0813 kg x (13.72 m/17 s)/17 s x 13.72 mW = 0.047 Joules

More Work

An extended Victor mousetrap bail arm is 12.5 centimeters. What is the longest pull string through which it can work to apply force to the axle?

More Work ANSWERC = 2πrC = 2 x 3.14 x 12.5 cm = 78.5 cmArc = ½ C = 39.25 cmYour longest pull string will be 40 cm!

Graphing Ideas for MTVs

distance vs. timevelocity vs. timeacceleration vs. timework vs. time 0

5

10

15

2s 4s 6s 8s 10s

Trial 1Trial 2Trial 3

BUT WAIT! THERE’S MORE!

Centripetal forceCentripetal accelerationTorqueGear Ratios

Simple MachinesPotential EnergyKinetic EnergySpring constant

APPENDIX

SC.912.P.10.6 Create and interpret potential energy diagrams, for example: chemical reactions, orbits around a central body, motion of a pendulum.SC.912.P.10.8 Explain entropy's role in determining the efficiency of processes that convert energy to work.

Coefficent of Friction

Your mousetrap vehicle is 0.100 kg. It gives a forward force of 5 Newtons. If the μ between the MTV and the floor is 0.4, what is the net force on the MTV?What is its acceleration?