PHYSICS 231 PH 2 1 Lecture 9 More on forces PHY 231 1 For Mid Term Exam PHY 231 2 For Mid Term Exam PHY 231 3 For Mid Term Exam PHY 231 4 Newton s Laws First Law If the net force exerted on an object is zero the object continues in its original state of motion ti if it was att rest t it remains i att rest t If it was moving with a certain velocity it will keep on moving g with the same velocity y Second Law The acceleration of an object is proportional to the net force acting on it and inversely proportional to its mass F ma If two objects interact the force exerted by the first object j on the second is equal q but opposite pp in direction to the force exerted by the second object on the first F12 F21 PHY 231 5 General strategy If not given make a drawing of the problem Put all the relevant forces in the drawing object by object object Think about the axis Think about the signs Decompose the forces in direction parallel to the motion and perpendicular to it Write down Newton s Newton s 2nd law for forces in the parallel direction and perpendicular direction Solve for the unknowns use in further equations if necessary Check whether your answer makes sense PHY 231 6 Review Inclined Plane Step 1 pick coordinate system such that x axis x axis is along plane Step 2 y component has no acceleration determines normal force Fy 0 N mg cos Step 3 Use Newton s Second Law to determine accelerationin x direction N Fx max ax g sin mg sin y Please note that the mass of the object has canceled out of this equation All objects accelerate att the th same rate t on this thi plane l independent of their mass We can write down the equation for the acceleration vector mg cos a g sin ex Fg x Limiting case acceleration approaches 0 as angle approaches 0 Expected PHY 231 7 Determining Static Friction Coefficients We can determine coefficient of static friction by using an inclined plane with variable angle Slowly raise plane form horizontal toward vertical Record angle at which object just starts slipping Right before slipping acceleration was 0 and static friction force was at maximum maximum just balancing component of weight along plane F xi x i i 0 mg ssin s mg cos Solve for coefficient of static friction mg sin s mg cos sin s cos s tan PHY 231 8 Determining Kinetic Friction Coefficient Review Slide object across horizontal surface with constant velocity and measure force F Also measure weight of object normal force N mg Top p view F Coefficient of kinetic friction PHY 231 F k mg 9 Inclined Plane Friction Now add friction force note blue arrow Direction opposite to motion i e up p the hill Magnitude use kinetic friction the skier is moving fk k N k mg cos Newton s Newton s Second Law in x direction F x i mg sin i k mg cos max i Final results ax g sin k cos PHY 231 10 Two Blocks Review Free body diagrams m1a T T m2 g m2 a m2 a g m1 m2 PHY 231 11 Two Blocks Friction Free body diagram for m2 stays the same New free body diagram for m1 also contains friction T m2 g m2 a m1a T f m2 g f a m1 m2 PHY 231 12 quiz A homogeneous block of 10 kg is hanging with 2 ropes from a ceiling The tension in each of the ropes is a 0 N b 49 N c 98 N d 196 N e don t d k know PHY 231 13 T 900 T 1kg A mass of 1 kg is hanging from a rope as shown in the figure figure If the angle between the 2 supporting wires is 90 degrees what is the tension in each rope TVerL h horizontal l Verticall TVerR 0 45 0 left rope Tsin 45 Tcos 45 45 right g rope p Tsin 45 Tcos 45 gravity 0 1 9 81 Sum 0 2Tcos 45 9 81 ThorR ThorL O Object j ct iss stationary stat onary so so 2Tcos 45 9 81 0 so T 6 9 N Fg 14 PHY 231 Problem n FgL A If s 1 0 what is the angle g for which the block just starts to slide F mgsin g FgL mgcos B The block starts moving Given that k 0 5 0 5 what is the acceleration of the block Fg mg Fs k A Parallel P ll l direction di ti mgsin i sn 0 0 F ma F Perpendicular direction mgcos n 0 so n mgcos Combine mgsin g smgcos g 0 s sin cos tan 1 so 45o B Parallel direction mgsin 45o kmgcos 45o ma F ma g 2 2 2 a 2 so s a g 2 PHY 231 15 All the forces come together n T T If a 3 30 m s2 the 12kg block is moving g downward what is the value of k Fg For the 7 kg block parallel to the slope T mgsin kmgcos ma For the 12 kg block Mg T Ma Fk Fg Solve for k k M g a mg sin ma 0 25 mg cos PHY 231 16 puck on ice After being hit by a hockey player a puck is moving over a sheet of ice frictionless The forces working g on the puck are a No force whatsoever b the normal force only c the normal force and the gravitational force d the force that keeps the puck moving e the th normall f force th the gravitational it ti lf force and d th the f force that keeps the puck moving PHY 231 17 example A 1000 kg g car is pulling p g a 300 kg g trailer Their acceleration is 2 15 m s2 Ignoring friction find a the net force on the car b the net force on the trailer c the net force exerted by the trailer on the car Fengine 1000 Ftc Fct 300 Fengine mtotala 1300 2 15 2795 N Fct mtrailer 2 15 645 N so Ftc 645 N a Fcar 2795 645 2150 Fcar mcar 2 15 2150 b Ftrailer Ftc 645 N c Ftc 645 645 N PHY 231 18 elevator blues T a b c d An object of 1 kg is hanging from a spring scale in an elevator What is the weight read from the scale if the elevator a moves with constant velocity b accelerates upward with 3 m s2 c accelerates l downward d d with i h 3 m s 2 d decelerates with 3 m s2 while moving up Before B f starting t ti thi this 1 Imagine standing in an elevator yourself 2 the scale reading g is equal q to the tension T F ma so T mg ma and thus T m a g a 0 T …
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