Classes of Forces Contact forces involve physical contact between two objects Field forces act through empty space Examples of Forces Spring force contact force Gravitational force between objects field force Tension force contact force Direction of tension always along the rope Normal force contact force Directed perpendicular to the surface Friction due to surface roughness atoms on surface run into each other Kinetic friction contact force acts on object in motion opposes direction of motion Static friction contact force acts on object at rest In direction that prevents slipping Drag force Resistive force that opposes motion Thrust propelling force engine expels gas molecules at high speed Measuring the strength of a force a spring can be used to measure the magnitude of a force Forces are vectors use rules for vector addition to find net force Magnitude F F12 F22 1 2 2 24 Direction tan q F1 F2 26 6 Motion with constant acceleration in 2D break the motion into two simpler motions in two orthogonal axes chapters 1 to 4 y x axis 1 2 x x0 v0 xt a x t 2 vx v0 x a x t vx v0 x 2a x x x0 2 2 1 2 v y v0 y 2a y y y0 2 2 3 y Ax A cos q Ay A sin q Ay tan q Ax ax vx and x are positive if their vectors point toward positive axis y axis 1 2 y y0 v0 y t a y t 2 v y v0 y a y t A Ay Ax A Ax Ay 2 2 x x 1 2 3 What makes an object change its velocity or gain an acceleration Newton s laws of motion in the inertial frame of reference F1 F1 x x F1 y y F2 F2 x x F2 y y F3 F3 x x F3 y y F1 m F2 F4 F3 Fnet F1 F2 F3 F F1 x F2 x F3 x x F1 y F2 y F3 y y Fx x Fy y How does the object move Newton s first law Newton s second law F5 If Fnet 0 v constant Fnet x ax m Fnet a Fnet y m ay m Free body diagram we can consider an sizable object as a point Question Fnet x in the left figure is a 241 5N c 241 5N and b 80 5N d 80 5N Motion with constant acceleration in 2D break the motion into two simpler motions in two orthogonal axes chapters 1 to 4 y x axis 1 2 x x0 v0 xt a x t 2 vx v0 x a x t vx v0 x 2a x x x0 2 2 1 2 v y v0 y 2a y y y0 2 2 3 y Ax A cos q Ay A sin q Ay tan q Ax ax vx and x are positive if their vectors point toward positive axis y axis 1 2 y y0 v0 y t a y t 2 v y v0 y a y t A Ay Ax A Ax Ay 2 2 x x 1 2 3 What makes an object change its velocity or gain an acceleration Without getting the absolute values of the accelerations choose the correct answer a a1 a2 b a1 a2 c a1 a2 d Can not evaluate Where a1 and a2 is the magnitude acceleration of the first boat and the second boat respectively F1 is the force object 2 acts on object 1 F2 is the force object 1 acts on object 2 Newton s laws of motion in the inertial frame of reference F1 m Free body diagram F2 F4 F5 F3 F1 F1 x x F1 y y F2 F2 x x F2 y y F3 F3 x x F3 y y F1 Fnet F1 F2 F3 F Newton s first law If Fnet 0 v constant Newton s third law x F1 x F2 x F3 x x F1 y F2 y F3 y y Fx x Fy y Fnet a m F2 1 F1 2 ax ay Fnet x m Fnet y m F4 F5 y How does the object move Newton s second law F2 F3 Weighing scale By a balance By normal force N By tension or sprint balance Look at the apparent weight of the person when the elevator is going upward Start to go up Feel heavier During the movement Feel normal Slow down Feel lighter Angle 30o m 40kg g 9 81m s2 Problem 7 a What is the tension of the rope b What is the tension of the cable Frictional forces We did not consider friction in the previous chapter For example in the projectile motion and freely fall motion the fictional forces caused by air resistance has been ignored Friction is caused by the random microscopic irregularities of a surface Therefore there is no law of nature for friction There are rules of thumb that gives quite accurate for calculating the frictional forces The frictional forces can appear i when two surfaces move relative to each other kinetic friction OR ii to prevent two surfaces moving relative to each other static friction Roughness of the Si wafe measured by an atomic force microscopy AFM Kinetic friction f k k N Where k is coefficient of kinetic friction that depends on the properties of two surfaces N is the normal force which is not strictly equal to the weight in general Static friction appears to cancel the kinetic forces 0 f s s N Where s is coefficient of kinetic friction that also depends on the properties of two surfaces s is normally larger than k N is the normal force m1 1kg and m2 2kg Pulley Egyptian pyramids Carnival ride You are driving your car with mass m over a circular shaped bridge in the road that has a radius of curvature r When you pass over the top of the bump the normal force of the car is a Larger than m g b smaller than m g and c equal to m g Circular motions To keep an object moving in a circular path we must provide a centripetal force net force to the object Magnitude of the force acting on an object with constant circular speed Fnet Fc m v2 r N Fc Fnet W roller coaster Egyptian pyramids Pulley F Work done by a constant force Work done by F W Fd cos Fx d F d m 1550 kg d 20 4m Fair 15 0N 5 00 o The second exam It will cover from chapter 5 to chapter 8 and HW 4 5 6 I will have freedom to ask you the three equations of motion The same format as the first exam will be given to the second exam Would you like to postpone the exam to March 16 2015 a Yes b no I can not delay the exam further since March 19 2015 is the last day for dropping the course a Wnc 0 870J b Wnc 0 870J c Wnc 0J
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