AP Torque Practice Calculations

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Mechanical Engineering

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Apr 3, 2024

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' .. L ____________ ___ Name: A b.lh l~frf'l~(J{ Period: 7 AP Torque Practice Calculations Torque is a measurement of the tendency of a force to produce a rotation about an axis; Torque= perpendicular force x lever arm or t = F x d The lever arm, d, is the distance from the-pivot point, or fulcrum, to the point where the component of the force perpendicular to the lever arm is being exerted. The longer the lever arm, the larger the torque. This is why it is easier to loosen a tight screw with a long wrench than with your hand or a short pair of tweezers. . If a torque causes a counterclockwise rotation of an object around the fulcrum, it is positive. If the torque causes a clockwise rotation_ of an object around the fulcrum, it is negative. This convention works even if the object remains balances and the torques just attempt to cause a rotation. Example 1: Ned tightens a bold in his car engine by exerting 12-N of force on his wrench at a _distance of 0.40-m form the fulcrum. How much torque must Ned produce to turn the bolt? Given: F = 12- N Unkonwn: r = ? d =0.40-m Original Equation: r = Fx d Solve: r = F x d = (12-N}(0.40-m} = 4.,8-Nm Keep in mind that when an object is balanced, all the toques must also balance. Therefore, the total torque, t, is zero. For example, if two people are sitting on either side of a seesaw and they want to remain level, they can position themselves so that all the torques on one side of the seesaw equal all the torques on the other side. The total torque on ' a system equals the sum of all the individual torques, or: \ 1 • t = (F1 X d1 ) + (Fz x dz) + .... Example 2: Mabel and Maude are seesawing on the school playground and decide to see if they can move to the correct location to make the seesaw balance. Mable weighs 400-N and she sits 2-m form the fulcrum of the seesaw. Where should 450-N Mau.de sit to balance the seesaw? Given: Fi= 400-N F2 = 450-N d1 = 2-m Unkonwn: d2 = ? Original Equation r = {F1 x di} + (F2 x d2} + .... Solve: If Mable makes the seesaw turn in a counterclockwise direction, then Maude makes the seesaw turn clockwise. Therefore, r = {F 1 x d 1 ) + -(F2 x d2}. If the seesaw is balances then r = 0 and the equation becomes r = {F1 x d1) + -{F2 x d2) = 0, or (F1 x d1 ) = (F2 x d2). Therefore, d 2 = {F1 x di} /F2 = {400-N}{2-m} I {450-N} = 1.78 m from the fulcrum Problem 1: A water Faucet is turned on when a force of 2-N ix exerted on the handle, at a distance of 0.060-m form the pivot point. How much torque.must be produces to turn the handle? {
Problem 2: Nancy, whose mass is 60-kg, is working at a construction site and she sits down for a bite to eat at noon. If Nancy sits on the very end of a 3-m long plank pivoted in the middle of a saw horse, how much torque must her co- worker provide on the other end of the plank in order to keep Nancy from falling to the ground? 7 : r i d /~ . (. 1 , r c : [fto,q{h 1/ '(la'J/ I I I Problem 3: Barry carries his tray of food to his favorite cafeteria table for lunch. The 0.50-m long tray has a mass of 0.20-kg and holds a 0.40-kg plate of food 0.20-m form the right edge. Barry holds the tray by the left edge with one hand, using his thumb as the fulcrum, and pushes up 0.10-m form the fulcrum with his finger tips. (a) How much upward force must his finger tips exert to keep the tray level? (b) How might Barry make the tray easier to carry if he still chooses to use only one hand? Problem 4: Sylvia is b.uilding a mobile to hang over her baby's crib. She hangs a 0.020-kg toy sailboat 0.010-m from the .... -::::Z left edge and a 0.015-kg toy truck 0.20-~ from the right end of a bar 0.50-m long. If the lever arm itself had a negligible mass, where must the support string be placed so that the arm balances? r r,d--M I / 1- "'} ,,· i l t r ( / 1 , 11"1 -, ( ,, i \ I,: I { ~----~----; (')."1Z ,,,,.~flt ...-,lt_vt L . / ' / ___,_,.-- I I ~---=--1 (--{ -, )l ., . 1--j I 1[ I •cl, I / 2-- (11) C. 0 I < ._, J ' / , ol NJ \J ,91pr; C •qffK<j L~ 0 l7t, •. z11-,-1(.,01~JJ1J ./ I 2f 5 ' (94/'lu)?d t ,,,,. ,, . r J ( -:: ,(20 ii 1 -~ ,{)(() ; O.[ 50 (v\ tVotf/' 1 frf Problem 5: Aaron and Anita, two paramedics, rush a 60-kg man from the scene of an-accident to a waiting ambulance, carrying him on a uniform 3-kg stretcher held by both ends. The stretcher is 2.6-m long and the man's center of mass is 1-m from Anita. How much force must Aaron and Anita each exert to keep the man horizontal? t I) ( 1"1 f G n q ' I) C I , G 9 7-t (-7i 'i, I ') C I' a )-1 ( o_, (/ ') 0 r = 5 7 ,, q 31) A vol] c G 9 • 1. , ) n J + c ~. 1 J c 1 ~ 0 J i r c--- 1 /pg J o r : 24 r loct1ee
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