PHY 101 1st Edition Lecture 10 Outline of Last Lecture I Why do things move II Aristotle vs Newton III 4 1 Forces IV 4 2 Newton s First Law Outline of Current Lecture V 4 3 Newton s Second Law VI Gravitational Force VII Gravitational Force Mass Weight Current Lecture 4 3 Newton s Second Law First law explains what happens to an object if there is not net force acting on it What happens if there is a net force acting on an oobject o The velocity of the object will change i e there will be acceleration o The greater the force the greater the acceleration o The greater the mass the smaller the acceleration Newton s second law of motion o The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass o A F m or F ma o F is the net external force acting on the object F vector sum of all external forces nd o 2 law in dimensions Fx max Fy may o The x and y components can be treated separately and independently o Units Newtons N 1N 1 kg m s2 Meaning when 1N of force acts on an object that has a mass of 1kg it produces an acceleration of 1 m s2 These notes represent a detailed interpretation of the professor s lecture GradeBuddy is best used as a supplement to your own notes not as a substitute Projectile motion a projectile only experiences the gravitational force which gives the acceleration of 9 8 m s 2 along the y direction Example 1D motion o Airboat mass 3 5 x 102 kg o Net horizontal force acting on it 7 0 x 102 N o A find acceleration A fnet m A 7 0 x 102 3 5 x 102 A 2 0 m s2 o B from rest how long does it take to reach a speed if 12 0 ms V at T v a 12 0 2 0 6s o Once it reaches 12 0 m s the pilot shuts off the engine and the boat drifts 50 0m until it stops Find the resistance force o Analysis to find the resistance force we need to find acceleration due to resistance force USE KINEMATICS 2a x v2 v2 v 0m s 2 2a 5 0 0 12 v0 12m s A 144 100 1 44m s2 Fresist ma 3 5 x 102kg 1 44m s2 504N Example horse pulling a barge o Mass of barge 2 0 x 103 kg o Each horse exerts a force of magnitude 6 0 x 102 N o Direction of forces Horse 1 30 Horse 2 45 Use 45 o Find the initial acceleration of the barge ignore water air etc resistance o Draw diagram coordinate system o Force and acceleration are vectors calculate x and y components separately then find magnitude and direction Horse 1 Fx1 Fcos 30 6 0 x 102 0 866 5 20 x 102N Horse 2 Fx2 Fcos 45 6 0 x 102 0 707 4 24 x 102N o X component Fx fx1 fx2 5 20 x 102N 4 24 x 102N 9 44 x 102N o Y component Horse 1 Fy1 Fsin 30 6 0 x 102 0 5 3 0 x 102N Horse 2 Fy2 Fsin 45 6 0 x 102 0 707 4 24 x 102N Fy Fy1 Fy2 3 0 x 102N 4 24 x 102N 1 24 x 102N Y component of the net force is along the negative y direction o Initial acceleration X a fx m 9 44 x 102N 2 0 x 102 kg 0 472 m s2 Y a fy m 1 24 x 102N 2 0 x 102 kg 0 062 m s2 o Magnitude A ax2 ay2 1 2 0 472 2 0 062 2 1 2 0 476 m s2 o Direction Tan ay ax 0 062 0 472 0 131 tan 1 0 131 7 46 Angle measured from the x axis Gravitational Force o Why do things always fall to the ground when released o Why does earth circle the sun o Gravitational force Mutual attraction between any two objects Things on earth obey the same laws as things in the heaven every particle in the universe attracts each other with a force that is directly proportional to the mass of the particles and inversely proportional to the square of the distance between them Gravitational Force Mass and Weight o Newton s law of universal gravitation Fg Gm1m2 r2 G 6 67 x 10 12 N m2kg2 the universal gravitation constant o Weight the magnitude of the gravitational force acting on an object of mass m is called the weight w of the object o Relation between g and the universal gravitational constant G Fg w GmEm r2 mg g GmE r2 o Example o It is known that the average radius of Earth is 6371 km calculate the mass of Earth g GmE r2 mE gr2 G g 9 8 6371 x 103 2 6 67 x 10 11 kg 6 0 x 1024 kg