Chapter 5 Force and Motion I I Newton s first law II Newton s second law III Particular forces Gravitational Weight Normal Friction Tension IV Newton s third law Newton mechanics laws cannot be applied when 1 The speed of the interacting bodies are a fraction of the speed of light Einstein s special theory of relativity 2 The interacting bodies are on the scale of the atomic structure Quantum mechanics I Newton s first law If no net force acts on a body then the body s velocity cannot change the body cannot accelerate v constant in magnitude and direction Principle of superposition when two or more forces act on a body the net force can be obtained by adding the individual forces vectorially Inertial reference frame where Newton s laws hold 1 II Newton s second law The net force on a body is equal to the product of the body s mass and its acceleration Fnet ma 5 1 Fnet x ma x Fnet y ma y Fnet z ma z 5 2 The acceleration component along a given axis is caused only by the sum of the force components along the same axis and not by force components along any other axis System collection of bodies External force any force on the bodies inside the system III Particular forces Gravitational pull directed towards a second body normally the Earth Fg mg 5 3 Weight magnitude of the upward force needed to balance the gravitational force on the body due to an astronomical body W mg 5 4 Normal force perpendicular force on a body from a surface against which the body presses N mg 5 5 Frictional force force on a body when the body attempts to slide along a surface It is parallel to the surface and opposite to the motion Tension pull on a body directed away from the body along a massless cord 2 IV Newton s third law FBC FCB When two bodies interact the forces on the bodies from each other are always equal in magnitude and opposite in direction 5 6 QUESTIONS Q2 Two horizontal forces F1 F2 pull a banana split across a frictionless counter Without using a calculator determine which of the vectors in the free body diagram below best represent a F1 b F2 What is the net force component along c the x axis d the y axis Into which quadrant do e the net force vector and f the split s acceleration vector point F1 3 N i 4 N j F2 1N i 2 N j Fnet F1 F2 2N i 6N j Same quadrant 4 F1 F2 I Frictional force Counter force that appears when an external force tends to slide a body along a surface It is directed parallel to the surface and opposite to the sliding motion Static fs compensates the applied force the body does not move f s F No motion Kinetic fk appears after a large enough external force is applied and the body loses its intimate contact with the surface sliding along it Acceleration F applied force Constant velocity 3 f s max s N f k f s max 6 1 Friction coefficients If F f s max body slides fk k N 6 2 After the body starts sliding fk decreases Q1 The figure below shows overhead views of four situations in which forces act on a block that lies on a frictionless floor If the force magnitudes are chosen properly in which situation it is possible that the block is a stationary and b moving with constant velocity a 0 ay 0 a 0 ay 0 Q5 In which situations does the object acceleration have a an x component b a y component c give the direction of a Fnet Fnet 4 Q A body suspended by a rope has a weigh of 75N Is T equal to greater than or less than 75N when the body is moving downward at a increasing speed and b decreasing speed Fnet Fg T ma T m g a Movement a Increasing speed vf v0 a 0 T Fg b Decreasing speed vf v0 a 0 T Fg Fg T1 Q8 The figure below shows a train of four blocks being pulled across a frictionless floor by force F What total mass is accelerated to the right by a F b cord 3 c cord 1 d Rank the blocks according to their accelerations greatest first e Rank the cords according to their tension greatest first T2 T3 a F pulls mtotal 10 3 5 2 kg 20kg c Cord 1 T1 m 10kg b Cord 3 T3 m 10 3 5 kg 18kg d F ma All tie same acceleration e F T3 2a T3 T2 5a T2 T1 3a T1 10a F T3 2a F 18a 2a 20a T3 13a 5a T3 18a T2 10a 3a T2 13a T1 10a Q A toy box is on top of a heavier dog house which sits on a wood floor These objects are represented by dots at the corresponding heights and six vertical vectors not to scale are shown Which of the vectors best represents a the gravitational force on the dog house b on the toy box c the force on the toy box from the dog house d the force on the dog house from the toy box e force on the dog house from the floor f the force on the floor from the dog house g Which of the forces are equal in magnitude Which are h greatest and i least in magnitude a Fg on dog house 4 or 5 h Greatest 6 3 b Fg on toy box 2 i Smallest 1 2 5 c Ftoy from dog house 1 d Fdog house from toy box 4 or 5 e Fdog house from floor 3 f Ffloor from dog house 6 g Equal 1 2 1 5 3 6 5 5 There are two forces on the 2 kg box in the overhead view of the figure below but only one is shown The figure also shows the acceleration of the box Find the second force a in unit vector notation and as b magnitude and c direction F2 a 12 cos 240 i 12 sin 240 j m s 2 6i 10 39 j m s 2 FT ma 2kg 6i 10 39 j m s 2 12i 20 78 j N FT F1 F2 20i F2 FTx 12 N F2 x 20 N F2 x 32 N FTy 20 78 N F2 y F2 32i 20 78 j N F2 322 212 38 27 N tan 20 78 33 or 180 33 213 32 Rules to solve Dynamic problems Select a reference system Make a drawing of the particle system Isolate the particles within the system Draw the forces that act on each of the isolated bodies Find the components of the forces present Apply Newton s second law F ma to each isolated particle 6 9 a A 11kg salami is supported by a cord that runs to a spring scale which is supported by another cord from …