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Transcript
Four Types (review) • weight: Non-contact (“action at a distance” means no contact required) An Introduction to Forces Part 2 PHYS& 114: Eyres – Pulling – Between 2 objects with mass • Tension: contact required – Pulling – Must have a rope or string or spring attached • normal: contact required – Pushing – Due to contact with a surface • friction: contact required – Opposite direction to motion or the direction of potential motion – Rubbing (kinetic friction) or “Stickyness” associated with “trying to move it” (static friciton) Testing possible relationships between force and motion Testing the relationship between the sum of forces and the motion of the system object • Two possible relationships: – The sum of forces is in the same direction as the velocity. – The sum of forces is in the same direction as the change in velocity. 1. Use each relationship to predict the outcome of testing experiments. 2. Perform the experiments and compare the outcomes with the predictions. 3. From this comparison, decide whether we can reject one or both of the relationships. © 2014 Pearson Education, Inc. © 2014 Pearson Education, Inc. Newton’s 2nd Law Inertial reference frame • An inertial reference frame is one in which an observer: Sees no change in the velocity if the sum of all forces exerted on the system object is zero • The equation we deduced for Newton's second law is: The force diagram and the motion diagram match. • In non-inertial reference frames, the velocity of the system object can change even though the sum of forces exerted on it is zero. The force diagram and the motion diagram do not match. • Another way to write this equation is: Σ = 1 Mass and Weight • Mass ( in kg) is a fundamental quantity • Weight is the attractive force between 2 objects that have mass. ( in N) F= Mass and Weight Gm1m2 F= r2 Gm1m2 r2 F= Gmearth (mobject ) r2 F = 9.8 Gravitational force N (mobject ) kg Newton's third law of motion • When two objects interact, object 1 exerts a force on object 2. Object 2 in turn exerts an equal-magnitude, oppositely directed force on object 1. • These forces are exerted on different objects and cannot be added to find the sum of the forces exerted on one object. © 2014 Pearson Education, Inc. © 2014 Pearson Education, Inc. Newton’s Laws • Newton’s 3rd Law If Object 1 pushes on Object 2 then Object 2 pushes on Object 1 Free-Body Diagrams • Circle the object of interest • Choose a coordinate system On 2 By 1 N1on2 Is the object moving horizontal or vertical? Pick a standard system On 1 By 2 N2on1 Is the object moving up or down a slope? Pick a slanted system or • This can help to identify forces 2 Free-Body Diagrams Free-Body Diagrams • Identify your vectors • Draw coordinate system • Add vectors (don’t worry about length) On and By and Direction of Forces Table By On B Normal Ground B normal Dad On Weight Earth By Weight Earth B NGB B Normal Ground B normal Dad Use FBD to Solve • Add component information to the vector table. • Put in values if you know them. + Use FBD to Solve x Weight 0 Normal 0 y -wy + Ny NGB nDB 1. Sketch and translate. – Sketch the process, choose the system object and coordinate system, and label the sketch with everything you know about the situation. y -wy + Ny Normal + nx 0 ΣFx = max Skills for applying Newton's second law for one-dimensional processes © 2014 Pearson Education, Inc. • Write Newton’s 2nd Law x Equations in Component Weight 0 Form Normal 0 Normal + nx 0 + WEB nDB WEB B + nDB = max ΣFy = may − WEB + N GB = may Skills for applying Newton's second law for one-dimensional processes (Cont'd) 2. Simplify and diagram. – Make appropriate simplifying assumptions and represent the process with a motion diagram and/or a force diagram. © 2014 Pearson Education, Inc. 3 Skills for applying Newton's second law for onedimensional processes (Cont'd) Practice Problem 3. Represent mathematically. – Convert the representations into quantitative mathematical descriptions using kinematics and Newton's second law. 4. Solve and evaluate. – Substitute the known values and solve, and then evaluate your work to see if it is reasonable. Check whether all representations are consistent. • • • • • • Physics Principles Circle the Object Draw Coordinate Identify Forces, On & By Make Component Table Write Newton’s Law in Component Form • List other information • Solve • Evaluate A 7.0-kg bucket of tools is raised from the ground by a rope. If the upward acceleration of the bucket is 4.0 m/s2, find the force exerted by the rope on the bucket. © 2014 Pearson Education, Inc. Practice Problem • • • • • • Physics Principles Circle the Object Draw Coordinate Identify Forces, On & By Make Component Table Write Newton’s Law in Component Form • List other information • Solve • Evaluate The parachute on a race car of weight 8 500 N opens at the end of a race when the car is traveling at 40 m/s. What force must be supplied by the parachute to stop the car in a distance of 1 000 m? Practice Problem • • • • • • Physics Principles Circle the Object Draw Coordinate Identify Forces, On & By Make Component Table Write Newton’s Law in Component Form • List other information • Solve • Evaluate A 50.0-kg wagon is towed up a hill inclined at 20° above the horizontal. The tow rope is parallel to the incline and has a tension of 150 N. Assume that the wagon starts from rest at the bottom of the hill, and neglect friction. How fast is the wagon going after moving 60.0 m up the hill? Other Force Information • • • • Weight: w=mg Friction: f=µn T is the same all along a taught rope/string Springs: nbyspring=-ksp∆x or Tbyspring=-ksp∆x – Springs push (n) when they are constricted – Springs pull (T) when they are extended – You can also simply use Fsp for spring force. Note: Why the minus sign? Because ∆x is in the opposite direction to Fsp 4