DEFINITION OF A MACHINE: Machines are designed to make your life _________. If they didn’t, there would be no point in using them. A machine is a device for either multiplying forces or changing the direction of forces. Machines cannot multiply work. If they did they would violate the ___________________ ___________________________. KINDS OF SIMPLE MACHINES: In the blanks provided, label the seven simple machines shown below. ________________ ________________ ________________ ________________ ________________ ________________ ________________ The following items are examples of which kinds of simple machines? ________ ________ ________ ________ THE MECHANICAL ADVANTAGE OF A MACHINE: In ideal conditions, all the work you put in on one side of a machine (Win) comes out the other side of the machine (Wout). In practice, however, some of the energy (work) you put in is “lost” as ____________ energy. Workin Workout This "loss" is a result of the presence of _______________________ between the parts of the machine. The MECHANICAL ADVANTAGE a machine gives to its user is the ratio of the Output Force (Fout) to the Input Force (Fin). OUTPUT FORCE : INPUT FORCE or Fout Fin *** REMEMBER: The Input Force is the force the USER applies. The Output Force is what results at the other end of the machine (what lifts, pulls, pushes the LOAD). The THEORETICAL MECHANICAL ADVANTAGE is the benefit the machine gives to a user in ideal conditions with no friction present. The ACTUAL MECHANICAL ADVANTAGE is the benefit the machine gives you in the real world (where friction exists). Obviously, the actual mechanical advantage is always __________________ than the theoretical mechanical advantage. PROBLEMS: If you were using a machine that required only an INPUT force of 80 N to obtain an OUTPUT force of 16,000 N, what would be that machine’s mechanical advantage? __________________ If a machine could lift 80 N of weight with only 20 N of human effort on the other end, what is the machine’s mechanical advantage? __________________ Fin = 10 N Fout = ? If a machine has a theoretical mechanical advantage of 4, and the INPUT FORCE is 10 N, what OUTPUT force is possible? __________________ If a machine has an actual mechanical advantage of 4, and the INPUT FORCE is 10 N, what OUTPUT force is possible? __________________ What is the ratio of OUTPUT distance to the INPUT distance if a machine has a mechanical advantage of 10? __________________ HINT: The mechanical advantage interestingly enough can also be expressed as the ratio of the INPUT DISTANCE TO THE OUTPUT DISTANCE (as opposed to the OUTPUT FORCE : INPUT FORCE). THE EFFICIENCY OF A MACHINE: The efficiency of a machine is the ratio of useful work output to total work input (or the actual mechanical advantage vs. theoretical mechanical advantage) Efficiency Wout MAactual Win MAtheor No machine is 100% efficient. Gasoline powered cars, for example, are at most 40% efficient. The rest of the energy is dissipated through heat losses due to friction, etc. PROBLEMS: What is the efficiency of a machine that gives 1.85 Joules of useful work out for every 3.25 J of work put in? __________________ If a machine is 60% efficient and has a theoretical mechanical advantage of 5:1, what is the actual mechanical advantage it gives a person using it? __________ Which is more efficient: a machine that has an actual mechanical advantage of 8 : 3 and a theoretical mechanical advantage of 12 : 3, or a machine that yields 220 J of useful work out for every 550 J of work put in ? _________________ THE LEVER There are three kinds of levers. Name them below and draw each in terms of the fulcrum’s location, the input force’s location, and the output force’s location. The DISTANCES used to calculate the WORK done using a lever are the arc lengths through which the lever arms move. BUT… If WORK is not necessary to solve the problem, using the distances from the forces to the fulcrum are more convenient for comparison purposes because they are simple straight-line distances so you don't have to mess with curves. dout din dout din EXAMPLE: If it requires 1000 N of input force to lift a load of 2550 N and the load is 2 m away from the fulcrum, how far away from the fulcrum should the input force be applied? Ans. The Force/distance relationship is proportional. d Fin 1000N 2m out so… Fout din 2550N din 1000din = 5100 din = 5.1 m but… the Work is NOT 1000 N X 5.1 m = 5100 Joules however, because the din is not in the same direction as the FORCEin!!! As mentioned earlier, to calculate the work, the arc lengths would have to be used for the distances. PROBLEMS: A. Andres wants to lift a 120,000 N car off the ground. The car is 0.2 meters from the fulcrum. If Andres can exert a force of 1320 N on his side of the lever, how far away from the fulcrum should he apply the force? ___________________ In each of the following lever arrangements, label the INPUT FORCE (Fin), the OUTPUT FORCE (Fout), the INPUT DISTANCE (din) and the OUTPUT DISTANCE (dout). Be sure that as the fulcrum’s position changes, the size of the arrows you use to represent the forces change accordingly. Label the fulcrum and the location of the input and output forces in the simple machines shown at right. What kind of levers (Type I, Type II, or Type III) are they? __________________ _______________ dout din BillyBoBob wants to get a load of fertilizer up to a height where he can load it on his pickup. _____________ a. Through what arc length should BillyBoBob apply a force of 2400 N if he wishes to raise a 5000 N load through an arc length of 0.4 m? _____________ b. If the lever arm from the fulcrum to BillyBoBob is 5 m, what part of the circle is the arc through which he must apply the force of 2400 N? _____________ c. If the distance from the fulcrum to BillyBoBob is 3 m, through what angle did he apply the force? (Hint: s = r) THE INCLINED PLANE An inclined plane is a simple machine that connects a higher level to a lower level. The inclined plane, as with all machines, makes it “easier” to move things at the expense of the distance through which they must be moved. Label the illustration above with the INPUT FORCE (Fin), the OUTPUT FORCE (Fout), the INPUT DISTANCE (din) and the OUTPUT DISTANCE (dout). PROBLEMS: If in the figure above, the large force (F) was 300 N, the small distance (d) was 2 m, and the “small” force (f) was 80 N, how long would the ramp have to be? _________. The total work done in raising a box through a vertical distance of three meters is 4000 J. With how much force would a person have to push the same box, if he/she used a ramp that was 12 meters long? _____________________ It requires 4000 J of work to lift a box from the ground to the top of the ramp shown. If the weight of the box is 500 N and the ramp is 15 meters long, what is wrong with this problem? ________________________________ _______________________________. A 35° inclined plane that is 3 meters long leads to the incinerator. If it requires 400 N of force to move a crate full of fake CD's up the inclined plane, 15 m 500 N 3m 400 N _____________ a. how high is the incinerator off the ground? = 35 _____________ b. how heavy is the box? An inclined plane that is 2.5 meters long and 1 meter high leads to the incinerator. If it requires 800 N of force to move a box full of trash picked up by JQM up the plane, _____________ a. what is the angle of the inclined plane? 2.5 m 1m 800 N =? _____________ b. how heavy is the box? An inclined plane that is 4 meters long and has a base of length 2.2 meters leads to the incinerator. If it requires 200 N of force to lift a crate full of used disciplinary action forms to 200 N 4m the height of the incinerator, _____________ a. how high is the incinerator off the ground? 2.2 m _____________ b. how much force would it take to move the crate to the incinerator up the inclined plane? THE WEDGE The wedge is simply a moving ________________________. Normally an inclined plane is stationary and objects (such as boxes) are moved up its slope. A wedge, on the other hand, is jammed under, between, or into objects. As with every machine, the wedge works to minimize the effort put in by the user so as to maximize the output force on the other end but always at the expense of _____________. In the illustration of a wedge used as a door jamb at right, draw and label the input and output distances and forces f (small force), F (big force), d (small distance), D (big distance). In the illustration of a wedge used as an axe in the picture at left, draw and label the input and output forces f (small force), F (big force). Make sure you draw the input and output arrows to scale with each other. PROBLEMS: If a wedge is jammed under a door a distance of 0.1 m by a force of 200 N, how far up will the door move considering that the upwards force is 980 N? _______________ . ? 0.1 m Which of the wedges shown at right are "easier" (require less input force) to use (they are drawn to scale with each other)? Why? __________________________________________ __________________________________________ __________________________________________ __________________________________________ __________________________________________ THE PULLEY The pulley is just a modified lever. It is a very useful for two reasons. It can be used to: a. ______________________________________ b. ______________________________________ a. Change the direction of the force. TYPE I LEVER output The single pulley in the following illustration behaves as a type I lever. The axis of the pulley acts as the fulcrum of the lever and both lever distances (the radii of the pulley are equal in length, so the pulley does not magnify force, it simply changes its direction (the person can pull down to get the load to go up). Note that the input distance and output distance will be the same (the amount of rope that the person pulls down will be the same as the amount of distance the load rises) input axis or fulcrum output input b. Multiply or Magnify the Force. In the illustration to the right, the single pulley acts as a type II lever. The fulcrum in this case is the left edge of the lever (where the rope that is tied to the ceiling makes contact with the pulley wheel). The load (which is where the output force is being applied) is suspended half way between the fulcrum and the input force (the input force is located where the rope that the user is holding makes contact with the pulley wheel). By conservation of output input input TYPE II LEVER output axis or fulcrum energy and the principles we learned earlier about the lever, one need only apply half as much force as input when the input force is applied twice as far from the fulcrum as the output force (fD = Fd). The pay-off is that one will have to apply this smaller force through twice the distance. How a pulley multiplies a force can also be interpreted in terms of the tension in a string and equilibrium of forces. In the illustration of a pulley system at right, the system is at rest. In order for this to be true, what must be true about the sum of the forces upward and the sum of the forces downward? _____________________________ In the illustration at right, draw the arrows that represent where these forces are acting (to scale with each other). The multiplication of force (the same thing as mechanical advantage) available to a user of a pulley is easy to obtain. The user needs only to count the number of ropes/rope segments that are holding up the load. So, as in the above illustration, the ratio of the output force to the input force, is 2: 1 because the user can lift 2 N of weight with only 1 N of applied force. The catch is of course, that the user apply this 1 N of force over twice the distance that the load moves… PROBLEMS: In the illustration shown at right, although there are three rope segments present, only two actually support weight. Which are they and what is the third rope doing in this pulley arrangement? A B C _________________________________________ _________________________________________ _________________________________________ In the illustration at right, draw the arrows that represent where the forces are acting (to scale with each other). _______ What is the mechanical advantage of the pulley shown? THE WHEEL AND AXLE The wheel and axle can be thought of as a circular lever. The fulcrum is the center of the axle. The input force is applied to the wheel’s outer rim. The output force is applied to the axle’s outer rim… The distances in a wheel and axle machine are the distances through which the wheel turn (input distance) and the distance through which the axle turns (output distance). NOTE: Once again, as with the lengths of the lever arms in the lever, although the radius of the axle and dout the radius of the wheel cannot be used to calculate the WORK done, they can be used to compare the din input and output forces!!! Example: If the outer radius is twice as large as the inner radius then the output force will be twice as large as the input force. As mentioned before, to calculate work, the arc lengths should be used for distance. Din dout axle is fulcrum PROBLEMS: . output FORCE input force A screwdriver applies a force of 2978 N to the head of a screw and turns a distance of 0.25 m. _______________ a. Through what distance must the screwdriver handle have turned if the input force is 168 N? _______________ b. How many rotations of the screwdriver does that distance correspond to if the screwdriver handle has a radius of 0.04 m? THE SCREW The screw is simply an _____________ wrapped around a shaft or cylinder. The screw just allows the user to apply the forces in a circular motion rather than in a linear one. As with all machines, the input force is smaller, but consequently, the screw must be turned many times (through many revolutions and hence, a lot of distance) to produce a considerable output force over just a short distance on the other end (the distance into the wood that the screw penetrates). In the illustration of a screw shown at right, label the screw with an F (BIG FORCE), D (BIG DISTANCE), f (small force), d (small distance). PITCH Another way of comparing the amount of input force that you have to apply to the screw is the PITCH of the threads of the screw. The PITCH is the distance between adjacent threads on a screw (as shown in the illustration). If we compare how far a screw with a large pitch goes into a piece of wood and how far a screw of the same size, length, and shape but with a small pitch goes into a wood, we will find that the larger pitched screw will penetrate _____________ into the wood after “x” number of turns of the screw head are applied to both. But if what was just mentioned is true then what must be true of the input force applied to a large-pitched screw vs. the input force applied to a small pitched screw? ______________________________. Compare hammering a nail into a piece of wood and screwing in a screw of the same mass, size, and shape into the same piece of wood the same distance. Which of the two machines requires greater input distance? greater input force? Explain. _______________________________ ____________________________________ _______________________________ _______________________________ _______________________________ _______________________________ Which of the two machines has the greater mechanical advantage (all other things being equal)?_______________ The spiral staircase is an example of the screw applied on a large scale. What is the advantage of the spiral staircase in the following comparison of two ladies climbing a tower? ___________________________________________ ________________________________________________________________ What is the disadvantage of the spiral staircase? ________________________ ________________________________________________________________ Can you identify the PITCH in the illustration of the spiral staircase (draw it in)? Would it be easier or harder if the staircase had a smaller “PITCH”? ________ _______________________________________________________________. THE GEAR Gears are pairs on interlocking toothed wheels that transmit force and motion in machines. Gears can do any one of the following three things: a. _____________________________________________________ b. _____________________________________________________ c. _____________________________________________________ a. Gears change the direction of the applied (input) force. In a gear train (a system of at least two gears), one gear is the driving gear or driver. One gear is the driven gear. The driver is associated with which force? _____________The driven gear is associated with which force? ____________ Label the driver and the driven gear in the illustration to the right. If the driving gear in the illustration is spinning clockwise, in what direction will the driven gear spin? ___________________ Draw arrows on the illustration above indicating the direction of motion of each gear. In the following gear trains draw arrows indicating the direction of motion of the gears given that the driven gear is moving… a. Clockwise b. Counter-clockwise c. Clockwise Driven Gear Driven Gear b. Multiplying force The gear is subject to the same relationship that the other machines follow. The distance through which a gear train turns can be interpreted several ways for comparison purposes: drivers i. in terms of the number of times the driver turns compared to the number of times the driven gear turns ii. by comparing the number of teeth that each gear has. iii. by comparing the radii of the gears. If the driver gear has twice as many teeth as the driven gear, then it will also have twice the radius of the driven gear and will only turn once for every two times the driven gear turns… In the following illustrations a mark has been painted at the bottom point of each gear. Draw the gears and label the new position of the marks after the driver has gone through…a. …¼ turns, b. …½ turns, c. …¾ turn, d. …one full turn Do the above for the following two cases. I. The driver has twice as many teeth as the driven gear a. b. c. d. driver II. The driver has half as many teeth as the driven gear a. b. c. d. driver As you can see, from the above examples, the larger the gear size (however you may interpret that…”fewer turns,” “more teeth,” or “larger radius”), the less distance the gear turns compared to a gear of smaller size (i. e. “smaller radius”, “more turns”, “fewer teeth”). If f D = Fd is to hold true, then the larger gear (which travels less distance) must offer up ____________________ force. Label the following illustrations correctly with f (small force), F (large force), d (small distance), and D (large distance). a. b. driver driver c. A real-life example of using gears. The bicycle employs a gear train to adjust how much force the rider can transfer from the front sprocket (the chain ring to which the pedal is attached) to the rear wheel sprocket (which applies the force to the wheel for motion) A chain is used to transfer the force between the gears (driver and driven gears) and ideally does not affect the force transfer. c If you wanted to go down a hill on a multi.b speed bicycle, which front chain ring would a. you want your chain to be on? Why? _________________________________ . __________________________________ ___________________________________ _____________________________________ d. Do the following gear problems: 1. The driver gear has 14 teeth and provides a force of 300 N to the driven gear. If the driven gear delivers 1200 N to a shaft attached to it, how many teeth does it have? 2. A driven gear has a radius of 0.5 m and the driver gear has a radius of 2 m. What is the mechanical advantage of this gear train? 3. What is the output force of a gear train if the input force is 220 N and the driver gear turns ½ a turn for every turn of the driven gear?