Newton s Third Law of Motion The first two laws deal with a single object and the net forces applied to it but not what is applying the force s The third law deals with how two objects interact with each other Whenever one object exerts a force on a second object the second object exerts a force of the same magnitude but opposite direction on the first object Astronaut ma Fs Fa Space station ms Third law says force astronaut applies to space station Fs must be equal but opposite to force the space station applies to astronaut Fa FBD Fs Fa F F a aa Fa ma aa aa Fa ma F ma Fs ms as as Fs ms F ms Since ma ms aa as The Tension Force rope Crate m n T T mg frictionless Frictionless pulley Assume rope is massless and taut FBD of rope T T T F x FBD of crate T T 0 m Crate at rest F T mg T mg 0 T mg y Like the normal force the friction and tension forces are all manifestations of the electromagnetic force They all are the result of attractive and repulsive forces of atoms and molecules within an object normal and tension or at the interface of two objects Applications of Newton s 2nd Law Equilibrium an object which has zero acceleration can be at rest or moving with constant velocity F 0 F x 0 Fy 0 Example book at rest on an incline with friction Non equilibrium the acceleration of the object s is non zero F ma Fx max Fy ma y Example Problem Three objects are connected by strings that pass over massless and frictionless pulleys The objects move and the coefficient of kinetic friction between the middle object and the surface of the table is 0 100 the other two being suspended by strings a What is the acceleration of the three objects b What is the tension in each of the two strings Given m1 10 0 kg m2 80 0 kg m3 25 0 kg k 0 100 m1 m2 m3 Find a1 a2 a3 T1 and T2 Solution 1 Draw free body diagrams T1 m1 T2 m3 N y T1 T2 fk m1g m3g m2g 2 Apply Newton s 2nd Law to each object x F y1 F m1a y1 y3 m3 a y 3 T1 m1 g m1a y1 T2 m3 g m3 a y 3 T1 m1 a y1 g T2 m3 a y 3 g F x2 m2 a x 2 F y2 0 T2 T1 f k m2 a x 2 N m2 g 0 Also ax1 0 ax3 0 ay2 0 N m2 g f k k N k m 2 g T2 T1 k m2 g m2 a x 2 T1 m1 a y1 g T2 m3 a y 3 g Three equations but five unknowns ay1 ay3 ax2 T1 and T2 But ay1 ax2 ay3 a Substitute 2nd and 3rd equations into the 1st equation m3 a g m1 a g k m2 g m2 a m3 a m3 g m1a m1 g k m2 g m2 a 0 a m3 m1 m2 g m3 m1 k m2 0 a m1 m2 m3 g m3 m1 k m2 m3 m1 k m2 a g m1 m2 m3 25 0 10 0 80 0 0 100 9 80 10 0 80 0 25 0 0 60 sm2 a y1 a x 2 a y 3 T1 m1 a g 10 0 0 60 9 80 104 N T2 m3 g a 25 0 9 80 0 60 230 N The Spring Consider a spring which we apply a force FA to either stretch it or compress it FA x unstretched FA x x 0 FA kx k is the spring constant units of N m different for different materials number of coils From Newton s 3rd Law the spring exerts a force that is equal in magnitude but opposite in direction Hooke s Law for the restoring force of an ideal spring It is s a conservative force F kx Example Problem 6 26 The equilibrium length of a certain spring with a force constant k 250 N m is 0 18 m a What is the magnitude of the force that is required to hold this spring at twice its equilibrium length b What is the magnitude of the force required to keep the spring compressed to half its equilibrium length
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