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## Science Olympiad

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**Science Olympiad**Machines. Roger Demos**What do Machines do?**Do they allow one to do more work? Not really, at best they make completing a task easier. So then what do Machines do? • Multiply the force. • Multiply the distance. • Change the direction of the force.**Work = Force x Distance an object moves while the force is**applied. • W = F xd • In SI Units: • Force is measured in newtons (N) distance is measured in meters (m) • Work in N.m which is a joule (J). • Named after James Prescott Joule**What does work do?**• Work causes a change in Energy. In other words, it can do any of the following: • Make something move faster. • Lift something up. • Move something against friction. • A combination of the above.**Examples of Work:**A cart is pushed to the right as illustrated. 50.0 N distance cart is moved 4.00 m. How much work is done on the cart? W = F xd = (50.0 N)(4.00 m) = 200. J**Examples of Work:**A box is lifted as illustrated. How much work is done on the box? 80.0 N distance box is moved 20. m. W = F xd W = (80.0 N)(20. m) W = 1600 J**Now let’s apply this to some of our machines.**The simplest is most likely levers.**Class 1 Lever: load on one side of the fulcrum and the**effort on the other side. The Fulcrum is the pivot point. The Load is what we are trying to lift or the output of the machine. Effort The Effort is the force that is applied to lift the load or the input of the machine. Load Fulcrum**Class 1 Lever: Load on one side of the fulcrum and the**Effort on the other side. Effort Load Fulcrum**Class 1 Lever: More terminology**Note that in lifting the load the Effort moved much farther than the Load. Effort With a smaller Effort we could lift a Load that is heavier. Load Fulcrum**Class 1 Lever: More terminology**With an Effort of 300 N we were able to lift a Load of 900 N. We multiplied the input force by 3. Effort = 300 N The Effort moved 60 cm while the Load moved only 20 cm. We moved 3 times farther than the LOAD. Load = 900N Effort distance, dE = 60 cm Load distance, dL = 20 cm Fulcrum**Class 1 Lever: More terminology**Work, W = F xd WIN = E xdE = (300 N)(0.60 m) = 180 J WOUT = L xdL = (900 N)(0.20 m) = 180 J Effort = 300 N Note: WorkIN = WorkOUT We didn’t do more work, we just did it with less Effort than if I tried to lift it without the lever. Load = 900N Effort distance, dE = 60 cm Load distance, dL = 20 cm Fulcrum**Class 1 Lever: More terminology**We say that we have a Mechanical Advantage, MA. We can lift 3 times more than our input Effort. MA = Load/Effort MA = (900 N)/(300 N) MA = 3 Effort = 300 N Load = 900N MA = dE/dL MA = (60 cm)/(20 cm) MA = 3 Effort distance, dE = 60 cm Load distance, dL = 20 cm Fulcrum**Class 1 Lever: More terminology**We triple our Effort (input force) at the expense of moving the Load ⅓ as much. MA = Load/Effort MA = (900 N)/(300 N) MA = 3 Effort = 300 N Load = 900N MA = dE/dL MA = (60 cm)/(20 cm) MA = 3 Effort distance, dE = 60 cm Load distance, dL = 20 cm Fulcrum**Class 1 Lever: More terminology**We can also analyze the lever by measuring the distance from the Effort to the fulcrum (pivot point) and the distance from the Load to the fulcrum. This is called the lever arm or just arm and is often given the variable name “x.” Effort arm, xE = 3.0 m Load arm, xL = 1.0 m Fulcrum**Class 1 Lever: More terminology**This can also be used to calculate the Mechanical Advantage. MA = xE/xL = (3.00 m)/(1.00 m) = 3 Looks familiar doesn’t it. Load arm, xL = 1.0 m Effort arm, xE = 3.0 m Fulcrum**More terminology:**Often we use the terms, Ideal Mechanical Advantage, IMA and Actual Mechanical Advantage, AMA IMA = xE/xL or dE/dL AMA = L/E with the load being just what you ultimately wanted to move, excluding anything else that may have to be moved with it. This will become clearer when we look at a 2nd class lever.**More terminology:**Often we use the terms, Ideal Mechanical Advantage, IMA and Actual Mechanical Advantage, AMA We want to find out how well the particular machine does its work. This is called Efficiency, Eff. Efficiency, Eff = (AMA/IMA) x 100%**2nd class lever:**Notice that the Effort and the Load are on the same side of the Fulcrum and the Load is between the Effort and the Fulcrum. Effort Load Fulcrum**2nd class lever:**Again the Effort moves much farther than the Load. We are getting more force out than what we put in, but the load only moves a short distance. We are also lifting the lever along with the load. Effort Effort Load Load Fulcrum**2nd class lever:**IMA = xE/xL = (2.8 m)/(0.35 m) = 8 The load is 900 N and since the Effort has to lift the Load and the lever, let’s say that the Effort is 150 N. Load arm, xL = 0.35 m Effort Load Effort arm, xE = 2.8 m Fulcrum**2nd class lever:**IMA = xE/xL = (2.8 m)/(0.35 m) = 8 AMA = L/E = (900 N)/(150 N) = 6 Eff = AMA/IMA = 6/8 x 100% = 75% E = 150N L = 900 N Effort arm, xE = 2.8 m Load arm, xL = 0.35 m Fulcrum**3rd class lever:**Notice that the Effort and the Load are on the same side of the Fulcrum and the Effort is between the Load and the Fulcrum. Effort Load Fulcrum**3rd class lever:**IMA = xE/xL = (0.50 m)/(2.0 m) = ¼ = 0.25 AMA = L/E = (200 N)/(1000 N) = ⅕ = 0.2 Eff = AMA/IMA = (0.2/0.25) x 100% = 80% E = 1000 N L = 200 N xL = 2.0 m xE = 50. cm Fulcrum**There is a lab part of the competition. Let’s look at some**of the basic concepts for a lever that is in static equilibrium.**The easiest lever to analyze is the first class lever**(seesaw), that is balanced by itself. The center of gravity of the lever is on the fulcrum. c.g.**If a lever is not moving (rotating) then it is said to be at**static equilibrium. When an object is at static equilibrium the following is true: ΣF = 0, that is netF = 0, no unbalanced forces. Στ = 0, that is there are no unbalanced torques. If you place a seesaw so that its center of gravity is on the fulcrum, it will balance. That is, the left side balances the right side.**Torque is the tendency of a force to cause an object to**rotate around an axis. In the case of a lever, the axis is the fulcrum. Force In this case the force would make the left side of the lever go down or rotate the lever counterclockwise, ccw.**Torque is the tendency of a force to cause an object to**rotate around an axis. In the case of a lever, the axis is the fulcrum. In this case the force would make the left side of the lever go down or rotate the lever counterclockwise, CCW. Force**What if the force is 24 N, what torque is applied?**Earlier we talked about the lever arm or arm being the distance from the fulcrum (axis) to the force. We will use the letter “x” as the symbol for lever arm. The symbol for torque is the Greek letter tau, τ F = 24 N τ = (F)(x) = (24 N)(1.2 m) τ = 28.8 N.m = 29 N.m x = 1.2 m A torque of 29 N.m will rotate the lever CCW.**The weight of the seesaw on the left creates a torque that**tries to rotate the seesaw counter-clockwise, CCW, so that the left side would go down. The weight of the seesaw on the right creates a torque that tries to make it rotate clockwise,CW, so that the right side would go down. F F The two balance each other and it does not rotate.**Another way to look at this is that we can place all the**weight of the seesaw ( FL ) at its center of gravity. The center of gravity of the seesaw is at the axis of rotation (fulcrum) so the value of the lever arm is zero and the force creates no torque. c.g. Note: The center of gravity may not be at the geometric center. Especially when using wooden meter sticks! FL**Sample problem: Two identical 40.0 kg twin girls are sitting**on opposite ends of a seesaw that is 4.0 m long and weighs 700 N, so that the center of gravity of the seesaw is on the fulcrum. How do we analyze this situation? c.g.**First, we need to draw a torque diagram of the seesaw. This**is a free body diagram which includes the lever arms. Next, we define the axis of rotation (circle with a dot in the middle) and the lever arms. We place all the forces at their proper location. x2 = 2.0 m x1 = 2.0 m c.g. . FN = 1500 N FL = 700 N F1 = 400 N F2 = 400 N**FL and FN both act through the axis of rotation, so their**lever arm is zero, making their torque 0. Στ = 0 or ΣτCCW = ΣτCW F1x1 = F2x2 (400 N)(2.0 m) = (400 N)(2.0 m) The torques balance so the seesaw can be in static equilibrium. 800 Nm = 800 Nm x2 = 2.0 m x1 = 2.0 m c.g. . FN = 1500 N FL = 700 N F1 = 400 N F2 = 400 N**It is important that the seesaw be level, so that the force**applied by each of the girls is acting downward and is perpendicular to the lever arm. If the Force and the Lever Arm are not perpendicular, then the equation for the torque becomes complex. It is better that we avoid that situation.**So, what do you do to balance the seesaw if the two people**are not the same weight (mass)? One 400 N girl sits on one end of a seesaw that is centered on the fulcrum, is 4.0 m long, and weighs 700 N. Where must her 650 N brother sit in order for the seesaw to be in static equilibrium? ? c.g. Option #1, move the heavier person closer to the fulcrum.**FL and FN both act through the axis of rotation, so their**lever arms are zero. Στ = 0 or ΣτCCW = ΣτCW FGxG = FBxB xB = (800 Nm)/(650 N) xB = 1.23 m (400 N)(2.0 m) = (650 N)xB 800 = 650xB xG = 2.0 m xB = ?? m c.g. . FN = 1750 N FL = 700 N FG = 400 N FB = 650 N**Option #2, move the center of gravity of the seesaw so that**more of the seesaw is on the side of the lighter person, One 400 N girl sits on one end of a 4.0 m long seesaw weighing 700 N That has moved the center of gravity of the lever 0.2 meters towards her. Where must her 650 N brother sit in order for the seesaw to be in static equilibrium? ? c.g. Now the weight of the seesaw creates a torque helping the girl.**FN acts through the axis of rotation, so its lever arm is**zero. Στ = 0 or ΣτCCW = ΣτCW FGxG + FLxL = FBxB (400)(2.2) + (700)(0.2) = (650 N)xB xB = (1020 Nm)/(650 N) xB = 1.57 m 880 + 140 = 650xB xG = 2.2 m xB = ?? m c.g. . xL = 0.2 m FN = 1750 N FL = 700 N FG = 400 N FB = 650 N**For the Middle School (Division B) Competition, you will**need to build a simple first class lever system. The lever may not be longer than 1.00 meter.**Simple Machines. (Simple case.)**Given small mass placed on one side. Given unknown large mass on the other. Unless the values are too extreme, you may be able to move the large mass close enough to the fulcrum. c.g. If this is the setup, you don’t have to worry about the weight of the lever.**Simple Machines. (Simple case.)**Big Mass Small Mass FN xS xB c.g. c.g. . FS FB FL**Simple Machines. (Simple case.)**In this case the torque equation is: τCCW = τCW (FS)(xS) = (FB)(xB) and you can solve for any value. FN xS xB c.g. . FS FB FL**So far we have been dealing with the force applied by the**hanging mass. This force is known as the weight of the object or the force of gravity (Fg) acting on the object. The force of gravity acting on an object is the product of the mass of the object multiplied by the gravity constant on the planet Earth (9.8 N/kg). Fg = mg = m(9.8 N/kg) so, mass, m = Fg/(9.8 N/kg) This gets quite confusing because weight is measured in newtons and mass is measured in grams or kilograms (kg). You may have been told to weigh something but you actually measured its mass in grams.**Simple Machines. (Simple case.)**Knowing that Fg = mg (FS)(xS) = (FB)(xB) This equation can be written: (msg)(xS) = (mBg)(xB) Dividing by g we get: FN (msg)(xS)/g = (mBg)(xB)/g (ms)(xS) = (mB)(xB) xS xB c.g. . FS = mSg FB = mBg FL**Simple Machines. (Simple case.)**We can now solve for a mass using this equation and modify our torque diagram as shown: (ms)(xS) = (mB)(xB) FN xS xB c.g. . mS mB FL**Simple Machines. (Simple case.)**Suppose that you were given a small mass of 125 grams and an unknown large mass. You set up your lever so it balances as shown: FN xB = 10.0 cm xS = 47.6 cm c.g. . mS = 125 g mB = ?? FL**Simple Machines. (Simple case.)**(ms)(xS) = (mB)(xB) (125 g)(47.6 cm) = (mB)(10.0 cm) mB = (125 g)(47.6 cm)/(10.0 cm) = 595 grams FN xB = 10.0 cm xS = 47.6 cm c.g. . mS = 125 g mB = ?? FL