PHYSICS 231 INTRODUCTORY PHYSICS I Lecture 5 Main points of last lecture vi2 Range yi yf R sin2 g Relative velocity vbe vbr vre Newton s Laws 1 If r F r 0 velocity doesn t change F 2 r mra 3 F12 F21 Newton s Third Law r r F12 F21 Force on 1 due to 2 Single isolated force cannot exist For every action there is an equal and opposite reaction Action and Reaction Forces act on different objects Free body Diagram Draw arrows for all forcesr acting ON object F 0 If the object is in equilibrium at rest or constant r r v F ma Otherwise find acceleration by Ignore rotational motion for now Treat object as a particle Example 4 1 blocks sit on a frictionless table The masses are 2 kg and M2 3 Kg A horizontal force F 5 N applied to Block 1 What is the acceleration of the blocks What is the force of block 1 on block 2 F M1 M2 1 a 1 m s2 2 F21 3 N Mechanical Forces Gravity w mg down Normal forces Strings ropes and Pulleys Friction Springs later Rules for Ropes and Pulleys Force from rope points AWAY from object Rope can only pull Magnitude of the force is Tension Tension is same everywhere in the rope Tension does not change when going over pulley Approximations Neglect mass of rope and pulley neglect friction in pulley Example 4 2 I pull a 5 kg mass up with a rope so that it accelerates 2 m s2 What is the tension in the rope T 59 N Example 4 3 Atwood Machine a Find acceleration b Find T the tension in the string c Find force ceiling must exert on pulley 5 kg a a g 6 1 635 m s2 b T 57 2 N c Fpulley 2T 114 5 N 7 kg Example 4 4a Which statements are correct Assume the objects are in static equilibrium T1 is T2 A Less than B Equal to C Greater than cos 10o 0 985 sin 10o 0 173 Example 4 4b ich statements are correct sume the objects are static T2 is T3 A Less than B Equal to C Greater than cos 10o 0 985 sin 10o 0 173 Example 4 4c ich statements are correct sume the objects are static T3 is Mg A Less than B Equal to C Greater than cos 10o 0 985 sin 10o 0 173 Example 4 4d ich statements are correct sume the objects are static T1 T2 is Mg A Less than B Equal to C Greater than cos 10o 0 985 sin 10o 0 173 Example 4 4 ven that Mlight 25 kg find all three tensions T3 245 3 N T1 147 4 N T2 195 7 N Cable Pull Demo Inclined Planes Choose x along the incline and y perpendicular to incline Replace force of gravity with its components F mgsin g x Fg y mgcos 30 0 Example 4 5 ind the acceleration and the tension a 4 43 m s2 T 53 7 N Example 4 6 M nd M such that the box slides at constant v M 15 6 kg Frictional Forces RESISTIVE force between object and neighbors or the medium Examples Sliding a box Air resistance Rolling resistance Sliding Friction Parallel to surface opposing direction of motion independent of the area of contact Depends on the surfaces in contact Object at rest Static friction Object in motion Kinetic friction Static Friction s fs sN Just enough force to keep object at rest s is coefficient of static friction N is the normal force f F Kinetic Friction k f k k N k is coefficient of kinetic friction Friction force opposes direction of motion N is the normal force f F Coefficients of Friction f sN f kN s k Example 4 7 The man pushes pulls with a force of 200 N The child and sled combo has a mass of 30 kg and the coefficient of kinetic friction is 0 15 For each case What is the frictional force opposing his efforts What the acceleration child 59 N is a 3 80 m s2 of the f 29 1 N a 4 8 m s2 Example 4 8 Given m1 10 kg and m2 5 kg a What value of s would stop the block from sliding b If the box is sliding and k 0 2 what is the acceleration is the tension of the rope 2 a c What 0 5 b a 1 96 m s c 39 25 N s Example 4 9 What is the minimum s required to prevent a sled from slipping down a hill of slope 30 degrees s 0 577 Other kinds of friction Air resistance F Area v2 Rolling resistance F v Terminal velocity Fresistance CAv2 mg at terminal velocity Coffee Filter Demo Example 4 9 An elevator falls with acceleration a 8 0 m s2 If a 200 lb person stood on a bathroom scale during the fall what would the scale read 36 9 lbs Accelerating Reference Frames Equivalent to Fictitious gravitational force g fictitious aframe Fictitious Force Derivation 1 2 x v0t at 2 1 F 2 Eq of motion in fixed frame v0t t 2m 1 2 x0 t af t 2 1 F maf 2 x x0 t v0t t 2 m F maf looks like force in new frame maf acts like fake gravitational force Example 4 10 You are calibrating an accelerometer so that you can measure the steady horizontal acceleration of a car by measuring the angle a ball swings backwards If M 2 5 kg and the acceleration a 3 0 m s2 a At what angle does the ball swing backwards b What is the tension in the string 17 deg T 25 6 N Example 4 11a A fisherman catches a 20 lb trout mass 9 072 kg and takes the trout in an elevator to the 78th floor to impress his girl friend who is the CEO of a large accounting firm The fish is hanging on a scale which reads 20 lb s while the fisherman is stationary Later he returns via the elevator to the ground floor with the fish still hanging from the scale In the instant just after the elevator begins to move upward the reading on the scale will be 20 lbs a Greater than b Less than c Equal to Example 4 11b A fisherman catches a 20 lb trout mass 9 072 kg and takes the trout in an elevator to the 78th floor to impress his girl friend who is the CEO of a large accounting firm The fish is hanging on a scale which reads 20 lb s while the fisherman is stationary Later he returns via the elevator to the ground floor with the fish still hanging from the scale On the way back down while descending at constant velocity the reading on the scale will be 20 lbs a Greater than b Less than c Equal to Example 4 11c A fisherman …
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