9/11/13 1 Concept of Force and Newton’s Laws of Motion 8.01 W02D2 Chapter 7 Newton’s Laws of Motion, Sections 7.1-7.4 Chapter 8 Applications of Newton’s Second Law, Sections 8.1-8.4.1 Announcements W02D3 Reading Assignment Chapter 8 Applications of Newton’s Second Law, Section 8.6: Example 8.6-8.9 Exam 1: Thursday Sept 19 7:30 pm - 9:30 pm Newton’s Laws of Motion: Review First Law: Every body 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. Second Law: 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, Third Law: 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. .m=F a F1,2= −F2,1 F1,2≡ force on 2 due to interaction between 1 and 29/11/13 2 Newton’s Second Law: Physics and Mathematics F = maphysics ⇔ geometrycause of motion (why)⇔description of motion (how)dynamics ⇔ kinematicsExamples of Forces • Gravity • Electric and magnetic forces • Elastic forces (Hooke’s Law) • Frictional forces: static and kinetic friction, fluid resistance • Contact forces: normal forces and static friction • Tension and compression Force Law: Universal Law of Gravity Gravitational force: gravitational force on body 2 due to the interaction between bodies 1 and 2 Magnitude: Direction: Attractive F1,2 F1,2= Gm1m2r122G = 6.67 × 10−11N ⋅ m2⋅ kg-29/11/13 3 Force Law: 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, RE is the radius of the earth, and ME is the mass of the earth. Fearth,object= m g =GmEmRE2⇒g =GmERE2= 9.81 m ⋅ s−2Tension 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 on the block is called a tension force. Denote magnitude of tension force by When rope is very light (massless) magnitude of tension force equal magnitude of the applied pulling force. FR,B T ≡FR,BConcept Question: Tension A cart is placed on a nearly frictionless 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 1. increase? 2. stay the same? 3. decrease? 4. cannot determine. Need more information.9/11/13 4 Force Law: Hooke’s Law Consider a mass m attached to a spring Stretch or compress spring by different amounts produces different accelerations Hooke’s law: Direction: restoring spring to equilibrium Hooke’s law holds within some reasonable range of extension or compression | | k l= ΔFWorked Example: Spring Equation of Motion For the spring force law: Newton’s Second Law in the positive -direction (equation of motion) Solution: (later in course) −k(x − xeq) = md2xdt2 Fs= −Fsˆi = −k(x − xeq)ˆiˆi x(t) = xeq+ Acoskmt +φ⎛⎝⎜⎞⎠⎟Force Law: Newtonian Induction • Definition of force has no predictive content. • Need to measure the acceleration and the mass in order to define the force. • Force Law: Discover experimental relation between force exerted on object and change in properties of object. • Induction: Extend force law from finite 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.9/11/13 5 Force Laws: Contact Forces Between Surfaces The contact force on the hand between hand and surface is denoted by Normal Force: Component of the contact force on hand perpendicular to surface and is denoted by Friction Force: Component of the contact force on hand tangent to the surface and is denoted by Therefore the contact force on hand can be modeled as a vector sum ,normalsurface hand≡F N ,tangentsurface hand≡F f C ≡N +f Fsurface,handtotal≡CConcept Question: Car-Earth Interaction Consider a car at rest. We can conclude that the downward gravitational pull of Earth on the car and the upward contact force of Earth on it are equal and opposite because 1. the two forces form a third law interaction pair. 2. the net force on the car is zero. 3. neither of the above. 4. unsure Concept Question: Normal Force Consider a person standing in an elevator that is accelerating upward. The upward normal force N exerted by the elevator floor on the person is 1. larger than 2. identical to 3. smaller than the downward force of gravity on the person.9/11/13 6 Kinetic Friction The kinetic frictional force fk is proportional to the normal force, but independent of surface area of contact and the velocity. The magnitude of fk is where µk is the coefficients of friction. Direction of fk: opposes motion fk=µkNStatic Friction Varies in direction and magnitude depending on applied forces: Static friction is equal to it’s maximum value 0 ≤ fs≤ fs,max=µsN fs,max=µsN Tug of War Contest Each table forms a team of two students (one male and one female) and competes against the other tables in a tug of war until one table wins an elimination competition. The other students at the table figure out what forces are acting on their team and identify all interaction pairs of forces.9/11/13 7 Tug of War Force Diagrams Each table forms a team of two students (one male and one female) and competes against the other tables in a tug of war until one table wins an elimination competition. The other students at the table figure out what forces are acting on their team and identify all interaction pairs of forces. Free Body Diagram • Represent each force that is acting on the object by an arrow on a free body force diagram that indicates the direction of the force • Choose set of independent unit vectors and draw them on free body diagram. • Decompose each force in terms of vector components. • Add vector components to find
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