KEEPING IT ALL IN BALANCE Torque is the tendency of a force to cause rotation. For an object to be balanced, not only must the net force acting on it be zero, but the net toque must also be zero. In other words, all the clockwise torques must balance the counterclockwise torques. INSTRUCTIONS: Imagine a bar that is clamped in the middle and placed on a stand. You will be given a series of problems. In each problem, you will be given the values of one or two forces, and their respective lever arms. Your objective is to calculate where a force of 1 Newton must be placed so that the bar remains balanced. You can check to see if you’re right by going to http://www.walter-fendt.de/ph14e/lever.htm. PROBLEMS: 1. 1 Nt, 0.6 meters left of pivot. 0.6 m Location of 1 Nt weight: 0.6 meters right of the pivot ? Total Clockwise Torque equals Total CounterClockwise Torque 1.0 N 1.0 N CW = CCW F×r = F×r = (1.0N) × (?) (1.0N) × (0.6m) ? = 0.6 meters right of the pivot . 2. 2 Nt, 0.4 meters left of pivot. 0.4 m Location of 1 Nt weight:_________0.8 m_____________ ? ܨଵ ݎଵ ൌ ܨଶ ݎଶ ሺʹܰሻሺͲǤͶ݉ሻ ൌ ሺͳܰሻݎଶ 2.0 N 3. 1.0 N 3 Nt, 0.2 meters right of pivot ? ݎଶ ൌ ͲǤͺܰ݉ ൌ ͲǤͺ݉ ͳܰ Location of 1 Nt weight:__________0.6 m____________ ܨଵ ݎଵ ൌ ܨଶ ݎଶ 0.2 m ሺͳܰሻݎଵ ൌ ሺ͵ܰሻሺͲǤʹ݉ሻ 1.0 N 3.0 N ݎଵ ൌ ͲǤܰ݉ ൌ ͲǤ݉ ͳܰ 82 4. 4 Nt, 0.2 meters left of pivot 0.2 m Location of 1 Nt weight:________ 0.8 m____________ ܨଵ ݎଵ ൌ ܨଶ ݎଶ ? ሺͶܰሻሺͲǤʹ݉ሻ ൌ ሺͳܰሻݎଶ 4.0 N 5. 1.0 N 2 Nt, 0.6 meters right of pivot. ? ݎଶ ൌ ͲǤͺܰ݉ ൌ ͲǤͺ݉ ͳܰ Location of 1 Nt weight:________ 1.2 m____________ 0.6 m ܨଵ ݎଵ ൌ ܨଶ ݎଶ ሺͳܰሻݎଵ ൌ ሺʹܰሻሺͲǤ݉ሻ 1.0 N 6. 2.0 N 3 Nt, 0.3 meters left of pivot. 0.3 m ? ݎଵ ൌ ͳǤʹܰ݉ ൌ ͳǤʹ݉ ͳܰ Location of 1 Nt weight:________ 0.9 m____________ ܨଵ ݎଵ ൌ ܨଶ ݎଶ ሺ͵ܰሻሺͲǤ͵݉ሻ ൌ ሺͳܰሻݎଶ 3.0 N 7. 1.0 N 1 Nt, 0.1 meters right of pivot 1 Nt, 0.4 meters right of pivot ? 0.1 m 0.4 m ݎଶ ൌ ͲǤͻܰ݉ ൌ ͲǤͻ݉ ͳܰ Location of 1 Nt weight:________ 0.5 m____________ ܨଵ ݎଵ ൌ ܨଶ ݎଶ ܨଷ ݎଷ ሺͳܰሻݎଵ ൌ ሺͳܰሻሺͲǤͳ݉ሻ ሺͳܰሻሺͲǤͶ݉ሻ ݎଵ ൌ 1.0 N 8. 1.0 N 1.0 N 2 Nt, 0.2 meters right of pivot; 1 Nt, 0.3 meters right of pivot ? 0.2 m 0.3 m Location of 1 Nt weight:________ 0.7 m____________ ܨଵ ݎଵ ൌ ܨଶ ݎଶ ܨଷ ݎଷ ሺͳܰሻݎଵ ൌ ሺʹܰሻሺͲǤʹ݉ሻ ሺͳܰሻሺͲǤ͵݉ሻ ݎଵ ൌ 1.0 N 2.0 N ͲǤͷܰ݉ ൌ ͲǤͷ݉ ͳܰ ͲǤܰ݉ ൌ ͲǤ݉ ͳܰ 1.0 N 83 LEVER EXAMPLES Classification of Levers x x x Class 1 - The fulcrum lies between the effort and the load Class 2 - The fulcrum is at one end, the effort at the other end and the load lies between the effort and the fulcrum Class 3 - The fulcrum is at one end, the load at the other end and the effort lies between the load and the fulcrum Class 1 Lever Class 2 Lever Class 3 Lever Examples in strength training x x x Class 1 - Seated dumbbell triceps extension Class 2 - Standing heel lift Class 3 - Seated biceps curl Class 1 Lever in the Body Class 2 Lever in the Body Class 3 Lever in the Body 84 85 CLASSIFYING LEVERS Instructions: Fill in the blanks with either – Fulcrum, effort force, or load! Identify Each Class of Lever and draw connecting lines from each picture to the appropriate oval! Class: Effort Force Load oad The fulcrum is between the effort and the load oad Effort Force Class: Class Load The load is between the fulcrum and the effort ffortt Effort Force Class: Load The effort is between the fulcrum and the load 86 SIMPLE MACHINCES PRACTICE QUESTIONS 1. A worker uses a pulley system to raise a 210 Nt weight through a height of 3.00 meters. The worker pulls on the rope a distance of 9.00 meters. a) Calculate the IMA of the system (3.00) ࡵࡹ ൌ b) The worker pulls with a force of 100 Nt. Calculate the AMA of the system (2.10) ࡹ ൌ c) ࡲ࢘ ൌ ൌ Ǥ ࡲࢋ Calculate the efficiency of the system (70%) ࢋࢌࢌǤ ൌ d) ࢊࢋ ૢ ൌ ൌ Ǥ ࢊ࢘ ࡹ Ǥ ൌ ൌ Ǥ ૠ ՜ ૠΨ ࡵࡹ Ǥ What force would be needed if there was no friction? (70 Nt) ࢋࢌࢌࢌ࢘ࢉ࢚ ൌ Ǥ ࢋࢌࢌǤ ൌ 2. ࡲ࢘ ࢊ࢘ ࡲ࢘ ࢊ࢘ כ ՜ ࡲࢋ ൌ ሺࢋࢌࢌǤ ሻ ൬ ൰ൌ ൌ ૠࡺ ࡲࢋ ࢊࢋ ࢊࢋ ૢ `Calculate the theoretical mechanical advantage of each machine shown in the diagram: (3.0, 3.0) ࢚ࢎࢋ࢘ࢋ࢚ࢉࢇ ൌ ࢊ ࢊ࢛࢚ ࢛ࢋ࢟ െ ࢘ࢇ െ ሺ࢚࢟ሻ 87 3. a) Calculate the theoretical mechanical advantage (IMA) of each machine shown in the diagram: (2.0, 4.0) ࢚ࢎࢋ࢘ࢋ࢚ࢉࢇ ൌ ࢊ ࢊ࢛࢚ ࢛ࢋ࢟ െ ࢘ࢇ െ b) What are the AMA and efficiency of the inclined plane? (4.0, 2.5, 62.5%) ࡵࡹ ൌ ࡹ ൌ ࢋࢌࢌǤ ൌ c) ൌ Ǥ ࢊࢋ ൌ ൌ ࢊ࢘ Ǥ ࡲ࢘ ൌ ൌ Ǥ ࡲࢋ ࡹ Ǥ ൌ ൌ Ǥ Ψሺ࢚࢟ሻ ࡵࡹ If the AMA of the pulley system is actually 1.75, what is the efficiency of this machine? (87.5%) ࢋࢌࢌǤ ൌ ࡹ Ǥ ૠ ൌ ൌ Ǥ ૡૠૡૠǤ Ψ ࡵࡹ 88 SIMPLE MACHINE BOOK PRACTICE 89 Lever Problems 1.A lever used to lift a heavy box has an input arm of 4 meter and an output arm of .8 meters. What is the mechanical advantage of the lever? ࡹ ൌ ࡸ ൌ ൌ ࡸ࢛࢚ Ǥ ૡ 2.What is the mechanical advantage of a lever that has an input arm of 3 meters and na output arm of 2 meters? ࡹ ൌ ࡸ ൌ ൌ Ǥ ࡸ࢛࢚ 3.A lever with an input arm of 2 meters has a mechanical advantage of 4. What is the output arm’s length? ࡹ ൌ ࡸ ՜ ࡸ࢛࢚ ൌ ൌ Ǥ ࡸ࢛࢚ 4.A lever with an output arm of .8m has a mechanical advantage of 6. What is the length of the input arm? ࡹ ൌ ࡸ ՜ ࡸ ൌ ሺǤ ૡሻ ൌ Ǥ ૡ ࡸ࢛࢚ 5.A rake is held so that its input arm is .4meters and its output arm is 1 meters. What is the mechanical advantage of the rake? ࡹ ൌ ࡸ Ǥ ൌ ൌ Ǥ ࡸ࢛࢚ 6.A broom with an input arm length of .4m has a mechanical advantage of .5. What is the length of the output arm? ࡹ ൌ ࡸ Ǥ ՜ ࡸ࢛࢚ ൌ ൌ Ǥ ૡ Ǥ ࡸ࢛࢚ 90 Ramp Problems 1.A 5-meter ramp lifts objects to a height of .75meters. What is the mechanical advantage of the ramp? ࡹ ൌ ࡸࢋࢍ࢚ࢎ ൌ ൌ Ǥ ૠ ࡴࢋࢍࢎ࢚ Ǥ ૠ 2. A 10-meter-long ramp has a mechanical advantage of 5. What is the height of the ramp? ࡹ ൌ ࡸࢋࢍ࢚ࢎ ՜ ࡴ ൌ ൌ ࡴࢋࢍࢎ࢚ 3.A ramp with a mechanical advantage of 8 lifts objects to a height of 1.5meters. How long is the ramp? ࡹ ൌ ࡸࢋࢍ࢚ࢎ ՜ ࡸ ൌ ૡሺǤ ሻ ൌ ࡴࢋࢍࢎ࢚ 4.A child makes a ramp to push his toy dump truck up to his sandbox. If he uses 5 Newtons of force to push the 12-Newton truck up the ramp, what is the mechanical advantage of his ramp? ࡹ ൌ ࡲ࢛࢚ ࡺ ൌ ൌ Ǥ ࡲ ࡺ 5.A ramp with a mechanical advantage of 6 is used to move a 36-Newton load. What input force is needed to push the load up the ramp? ࡹ ൌ ࡲ࢛࢚ ࡺ ՜ ࡲ ൌ ൌ ࡺ ࡲ 91
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