Subject: Force Probe + Mousetrap Torsion Spring Range of force from 0 - ~12 Newtons -- Subject: Galileo's Experiments Use with students: "Inclined Planes" and "Falling Objects" http://www.pbs.org/wgbh/nova/galileo/experiments.html Specifically, I'm thinking the kids might learn something from experimenting with the "Inclined Planes" Flash animations. Enjoy! -- Subject: Speed-racer Theme Song Google search: speedracer + "theme song" + MP3 Mike's Classic Cartoon Themes http://www.melaman2.com/cartoons/singles/speedracer.html -- Subject: Teacher's Guide Notes re: "Work Made Easy" Lab TEACHER INFORMATION (pp. T 75-76) Since work is the transfer of energy through motion, work, like energy, is measured in Joules. One Joule is equal to one Newton-meter. Machines make work easier by multiplying a force, changing the direction of the force, increasing the distance the object moves, or changing the speed of an object's movement. Most references list six types of simple machines: lever; pulley; wheel and axle; inclined plane; screw; and wedge. All of these machines are versions of [variations] the inclined plane or the lever. Two forces are involved when a machine is used to do work. The force applied to the machine is called the effort force, F(e). The force applied by the machine to overcome resistance is called the resistance force, F(r). The mechanical advantage of a machine is calculated by dividing the resistance force by the effort force, MA = F(r) / F(e). The MA tells the number of times the machine multiplies the effort force. Any machine that multiplies force does so at the expense of distance. Efficiency is a measure of how much of the work put into a machine is changed to useful work put out by the machine: efficiency (%) = W(out) / W(in) x 100 Many machines can be made more efficient by reducing friction since friction opposes the motion of the effort force. TEACHING TIPS (p. T 76) 3. ... calculated answers cannot be more accurately described than the measurements from which they were derived. ESSENTIAL LEARNINGS (p. T 77) A machine is never 100% efficient. The work input is always greater than the work output due to friction. GOING FURTHER (p. T 77) * Use the MiniLAB, Glencoe, p. 190, to investigate how pulleys make work easier. [Useless lab that doesn't actually use pulleys!] [Note: Spring scales must be "zeroed" in the direction it is used, e.g., upside-down when used with levers or pulleys.] * Challenge advanced classes with problems like those below: 2. Calculate the mechanical advantage of the lever you used in Part 1. 3. How could the mechanical advantage of this lever be increased? -- Subject: Torque Google search: door + lever + physics What do you call the force that is applied to a lever? Torque Torque and rotational inertia http://physics.bu.edu/py105/notes/Torque.html Torque is a rotational force. -- Subject: Hovercraft Hockey One-man hovercraft hockey - a game of balanced & unbalanced forces. NHHL - The National Hovercraft Hockey League (superimpose one "H" on top of other to resemble "NHL") Two teams; one two-minute "POWER" play per team. Winner = most goals scored during 2-min. period. Stick is T-shaped; puck is styrofoam disk. Set up four-object obstacle course (to simulate 4-man power play advantage). Return to face-off circle after goal scored or out-of-bounds. Clocks stops until puck is dropped. Face-off circle ("x" = small circle); entire diagram w/in larger circle: _| |_ x _ _ | | -- Subject: Misc. Notes (from Glencoe _Physical Science_) re: MPVs p. 181 The force applied to the machine is called the EFFORT FORCE, F(e). The force applied by the machine to overcome the resistance is called the resistance force, F(r). Work done ON the machine: work input, W(in) W(in) = F(e) x d(e) Work done BY the machine: work output, W(out) W(out) = F(r) x d(r) IDEAL MACHINE W(in) = W(out) F(e) x d(e) = F(r) x d(r) p. 182 In most cases, a machine multiplies the force applied to it -- F(r) is greater than F(e). So, in order for W(in) to equal W(out), the effort force must travel farther than the resistance force -- d(e) must be greater than d(r). MECHANICAL ADVANTAGE The number of times a machine multiplies the effort force is the mechanical advantage (MA) of the machine. MA = resistance force/effort force = F(r)/F(e) p. 183 Other machines, such as third-class levers, have mechanical advantages that are less than one (1). Such machines are used to increase the distance an object moves or the speed at which it moves. p. 186 THE SIMPLE MACHINES The fixed point of a lever is called the FULCRUM. The part of the lever on which the effort force is applied is called the EFFORT ARM. The part of the lever that exerts the resistance force is called the RESISTANCE ARM. p. 187 FINDING THE IDEAL MECHANICAL ADVANTAGE (IMA) You can also use the lengths of the arms of a lever to find the IMA of the lever. The length of the effort arm is the distance from the fulcrum to the point where the effort force is applied. The length of the resistance arm is the distance from the fulcrum to the point where the resistance force is applied. The following equation, which assumes no friction, can be used to find the IMA of any lever. IMA = length of effort arm/length of resistance arm = L(e)/L(r) Demo 1 - Lab Set-Up: 50 cm/50 cm = 1x Demo 2 - Modified Lab Set-Up: 75 cm/25 cm = 3x Third-Class: The effort force is located between the resistance force and the fulcrum in 3rd-class levers. The effort arm is always shorter than the resistance arm, so it cannot multiply force and its MA is always less than one. effort | F E R <-- resistance ^ | fulcrum p. 200 EFFICIENCY efficiency = W(out)/W(in) x 100% = F(r) x d(r)/F(e) x d(e) x 100% p. 201 POWER power = work/time or P = W/t A watt is pretty small--about equal to the power used to raise a glass of H2O from your knees to your mouth in one second. -- Subject: Physical Science with Computers Physical Science with Computers by Donald Volz & Sandy Sapatka Vernier (refer to electronic versions on CD-ROM) Experiments Using a Motion Detector 35 Graphing Your Motion 36 Velocity 37 It's Race Day 38 Momentum: A Crash Lesson 39 Newton's Second Law 40 Falling Objects Experiments Using a Force Sensor 19 Frictional Forces 20 First-Class Levers 21 Pulleys 22 An Inclined Plane -- Subject: Red Lab Guide Review Grade 8 Science Investigating Motion, Forces, and Energy Student Lab Guide ISD, FCPS > Overview > Investigations *** Graphing Your Motion - Interpreting Distance-Time Graphs What is motion? Frames of reference. Motion graphs: a graph of distance (m) vs. time (sec) actually shows speed (dist/time); a graph of speed vs. time actually shows acceleration (m/sec/sec). *** Need explanation: How is "m per sec/sec" mathematically equivalent to "m per sec-squared?" Ask Burghardt. *** *** Keep on Truckin' - Analyzing Motion Vocab: motion, speed, instantaneous speed, constant speed, acceleration (positive & negative) average speed (s) [or velocity] = total distance (d) / total time (t) acceleration = delta-velocity (or delta-speed) / time a = delta-v / t momentum: p = m x v *** The Force of Friction - Designing Your Own Experiment *** Laws of Motion: Activities - Applying Newton's Three Laws Law 1: inertia Law 2: force = mass x acceleration F = m x A p = m x kg-m/s(2) A = F / m "magic motion triangle" F m A [need to double-check units in the following equations ...] F (N) = m (g) x A (kg-m/s2) m (g) = F (N) / A (kg-m/s2) A (kg-m/s2) = F (N) / m (g) [A Newton is equal to 1 kg-m/sec(2)] http://en.wikipedia.org/wiki/Newton "In physics, a derived SI unit, the newton (symbol: N) is the unit of force, named after Sir Isaac Newton in recognition of his work on classical mechanics. It was adopted by the General Conference on Weights and Measures (CGPM) in 1960. It is defined as the amount of force required to accelerate a one-kilogram mass at a rate of one meter per second per second. Its dimensions in SI base units are m x kg/s(2). It is also the unit of weight, as weight is the force acting between two objects due to gravity. A mass of one kilogram near the Earth's surface has a weight of approximately 9.81 newtons, although this figure varies by a few tenths of one per cent over the Earth's surface. Conversely, an object with a mass of 102 grams weighs roughly one newton [1,000 g/9.81 N = 101.94]. Rather fittingly, given the story about Newton's discovery of gravity, this is about the mass of a small apple." (or ~7 fig newtons!) Law 3: action-reaction Gravity & falling objects: objects of different mass accelerate at the same rate of 9.8 m/s(2). Terminal velocity: objects no longer accelerate. *** Work Made Easy - Using Simple Machines Vocab: simple machine, work, mechanical advantage, efficiency Simple machine: A device that does work with only one movement. A machine makes it easier to do work. Work: When a force moves an object through a distance. Work, like energy, is measured in Joules (J); one Newton-meter equals one Joule. W (N-m) = F (N) x d (m) If you lift a 500 g mass (a.k.a., the resistance) to a height of 20 cm, then you do 1 Joule of work: W (N-m) = 5 N x .2 m W = 1 N-m or 1 Joule A Newton is the force required to accelerate 1 kg (of mass) 1 m/sec(2). [1 meter per sec per sec.] This can be expressed mathematically: 1 N = 1 kg x m/sec(2) How many [fig] newtons is a Newton? W = F x d; F = m x a; F = .5 kg x 9.8 m/s(2); F = 4.9 kg-m/s(2) or 4.9 N Part 2: What Difference Does a Machine Make? - effort force: the force applied to a machine (Fe) - effort distance: the distance the effort force moves using the machine (d-sub-e) - resistance force (Fr): The force applied by a machine to overcome the resistance; this is the same as the force which would have to be applied w/o the machine. - resistance distance (d-sub-r) is the distance the resistance moves; it is the same distance the resistance would move w/o the machine. - mechanical advantage (MA): the advantage of using a machine; it tells the number of times the machine multiplies the force. MA = Fr / Fe - efficiency = Wo/Wi x 100 work output vs work input "magic work triangle" W F d W (N-m) = F (N) x d (m) F (N) = W (N-m) / d (m) d (m) = W (N-m) / F (N) *** Power to Do Work - Calculating Power - power: the rate at which work is done, calculated by dividing the amount of work done by the time it takes to do the work. The unit of power is the watt (W). One watt is equal to one Joule of work done in one second. Work (J) = Force (N) x distance (m) Power (W) = work (J)/time (sec) *** Moving On - Transforming Energy mechanical energy, electricity & magnetism *** A Follow-Up Demonstration: The Generator -- Subject: Generating Electrical Power Demos You can generate electrical energy by converting mechanical energy to electrical energy. If you turn a magnet inside a wire coil (or vice-versa), then you stimulate the flow of electrons along the wire -- the flow of electrons along a wire is what we call electricity! Magnetism & electricity are inseparbly interrelated. Demos: > Hand-cranked generator (wire coil turning inside BIG magnets) > Electric motor as a generator (and vice-versa): Mount small electric motor in test tube clamp on ring stand. Connect to motor shaft an adaptor/nail with string & paper clip; connect motor to small light bulb using wire leads w. alligator clips. Add five (5) 1 oz. (28 g) lead [fishing] sinkers to paper clip; use gravity to spin motor. Light bulb will light up briefly. Use "D" cell to rewind motor/string. Changing the wire leads changes the direction the motor turns. -- Subject: Misc. Resources: Pulleys; Block & Tackle Misc. reflections from field-test, Fri., 23 April 2004: Title: "Oh Pulleys, MA!" Pre-lab: Read/highlight p. 26, No. 4: "Simple machines have different purposes: A simple machine may ... - multiply the effort force; - ***change the direction of the effort force***; - change the speed at which the object (resistance) moves." Revisit p. 25: Do the same work (lift 500 g mass to a height of 20 cm) three different ways: 1) "Dead lift" [5 N x .2 m = 1 N-m or 1 Joule]; 2) ramp (inclined plane); 3) lever ["The fulcrum of the lever should be exactly in the middle of the meter stick (50 cm)."] When using the ramp, what's the necessary trade-off in order to reduce the effort force (Fe)? A. Must pull the mass a greater distance, i.e., the length of the ramp (~1.2 m). Since there are only two variables in the equation for work, increased distance is ALWAYS the trade-off for reduced effort! Revisit equal-arm lever (50/50 cm). Distance is the same; machine simply changes the direction of the force. Demo an unequal-arm lever (75/25 cm); distance is greater so Fe is much less (~2-3 N). Segue to pulleys and block & tackle. Use two ring stands/test tube clamps + dowel rod to create "trapeze." Ring stands may require a couple of textbooks for counterweight. Materials: 500 g mass; spring scale; string (~5-6 ft long); large paperclips; 1 single pulley (w. hooks); 1 single pulley (w/o hooks); 1 double pulley. Using laptop plus large-screen projector, show graphics (in order of increasing complexity) from "HowStuffWorks" Web page, "How a Block and Tackle Works." Draw set-up; record effort force (Fe). After assembling/testing each set-up, discuss the relationship between the number of ropes and the mechanical advantage (1:1). -- *pulley (no pictures; good text) http://www.bartleby.com/65/pu/pulley.html Google Search: "rigging pulleys" http://store7.yimg.com/I/yhst-77492104710481_1791_1266380 Google Search: "block and tackle" ***How a Block and Tackle Works http://www.howstuffworks.com/pulley.htm Use either Netscape or Mozilla to right-click/"View Image"; demo/experiment set-ups shown in four graphics: bt1.gif thru bt4.gif (plus bt7.gif). Printable Version (see section entitled, "Other Force/Distance Tradeoffs" re: levers (bt5.gif) -- key concept is to change the position of the fulcrum! http://www.howstuffworks.com/pulley.htm/printable block and tackle. http://www.bartleby.com/61/imagepages/A4blotac.html block and tackle http://www.britannica.com/eb/article?eu=15887 Block and Tackle (Java animation) http://www.jimloy.com/cindy/block.htm Block and tackle http://encyclopedia.thefreedictionary.com/Block%20and%20tackle pulley http://encyclopedia.thefreedictionary.com/pulley Block and Tackle http://discover.edventures.com/functions/termlib.php?action=&termid= 1669&alpha=b&searchString= Pulley http://discover.edventures.com/functions/termlib.php?action=&single=&word= pulley *A Simple Block and Tackle Pulley Demonstration http://www.flinnsci.com/Documents/demoPDFs/PhysicalSci/PS10409.pdf The Mechanical Advantage Of A Simple Machine With the Ropes and Pulleys http://www.cpo.com/CPOCatalog/RP/rp_b1.htm http://www.peter-thomson.co.uk/coralcastle/coralcastle.html "Simple block and tackle has been used for centuries to lift heavy weights, but above a mechanical advantage of 8:1 the friction in the pulley blocks prevents any increase in mechanical efficiency." Block and Tackle http://www.physics.lsa.umich.edu/demolab/demo.asp?id=471 *http://www.physics.lsa.umich.edu/demolab/graphics2/1m20_u1a.gif -- Subject: Simple Machines - Bill Nye In "Simple Machines," Bill careens around on a roller coaster and furiously pedals his bike on the "Tour de Science" to show that simple machines doing complicated things can be found everywhere. Edition Details Release Date: 2003 Running Time: 26 minutes Sequencing: Show video during "Work Made Easy" lab, between Part 1 & Part 2 (immediately after post-lab discussion of Part 1). Video does a great job of reinforcing the concept that a ramp requires less effort force (Fe) in contrast with resistance force (Fr). Also good reinforcement of example of how a 10-speed bike makes pedalling up a hill easier: the effort to pedal the bike is easier, but you turn the pedals more times (greater distance). -- Subject: Re: Galileo's Experiments It's there because the acceleration function measures instantaneous speed, but the distance measurement is going to be dependent on average speed. Since you're starting from speed zero and accelerating at a uniform rate, a quick way to calculate average speed is to to simply divide the final speed by two. Here's a concrete example. Drop a weight from a starting position (0). It accelerates uniformly at a rate dictated by the gravitational constant (9.8 meters per second per second). At the end of one second, it's moving at a speed of 9.8 meters/second, but has only traveled 4.9 meters (because it wasn't going that fast for the whole time). Phil --