Lecture 4 First Law Second Law Third Law Everybody continues in its state of rest or of uniform motion in a right line unless it is compelled to change that state by forces impressed upon it The change of motion is proportional to the motive force impresses and is made in the direction of the right line in which that force is impressed To every action there is always opposed an equal reaction or the mutual action of two bodies upon each other are always equal and directed to contrary parts Description of motion Vector Coordinate system with coordinate functions Physical forces Vectors Tool Free body diagrams and force diagrams Vector decomposition Examples of forces Gravity Electric and magnetic forces Elastic forces Hooke s law Frictional forces static and kinetic friction uid resistance Constant forces normal forces and static friction Tension and compression Universal law of gravity Gravitational Force near the surface of the Earth Near the surface of the earth the gravitational interaction between a body and the earth is mutually attractive and has a magnitude of where m is the gravitational mass of the body R os the radius of the earth and M is the mass of the earth Tension Force A rope is attached to a block B on one end and pulled by an applied force from the other end The force of the rope F on the block is called a tension force When the rope is virtually massless the magnitude of the tension force is equal to the magnitude of the applied pulling force A cart is placed on a nearly ctionless surface A force sensor on the cart is attached via a string to a hanging weight The cart is initially held When the cart is released and in motion does the tension in the string Concept question Tension a increase b stay the same c decrease d cannot determine Force Law Hooke s Law Newtonian Induction Consider a mass m attached to a spring Stretch or compress spring by different amounts produces different accelerations Direction restoring the spring to equilibrium De nition of force has no predicative content Need to measure the acceleration and the mass in order to de ne the force Force law discover experimental relation between force exerted on object and change in properties of object Induction Extend force law from nite measurements to all cases within some range creating a model Second law can now be used to predict motion If prediction disagrees with measurement adjust model Contact forces between surfaces The constant force on the hand between hand and surface is denoted by Normal Force component of the constant for on hand perpendicular to the surface and is denoted by Friction Force component of the contact force on hand tangent to the surface and is denoted by The contact force on hand can be modeled as a vector sum Sliding Object Concept Question Concept Question f kinetic friction opposes motion f N a the two forces form a third law interaction pair b the net force on the car is zero c neither of the above d unsure a larger than the downward force of gravity on the person b identical to the downward force of gravity on the person c smaller than the downward force of gravity on the person Pulley and Inclined Plane Consider a car at rest We can conclude that the downward gravitational pull of Earth on the car and the upward contact force of the Earth on it are equal and opposite Consider a person standing in an elevator that is accelerating upward The upward normal force N exerted by the elevator oor on the person is
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