Copyright © 2012 Pearson Education Inc. PowerPoint ® Lectures for University Physics, Thirteenth Edition – Hugh D. Young and Roger A. Freedman Chapter 5 Applying Newton’s Laws

Copyright © 2012 Pearson Education Inc. Congratulations!

Copyright © 2012 Pearson Education Inc. Congratulations!

Copyright © 2012 Pearson Education Inc. Congratulations!

Copyright © 2012 Pearson Education Inc. Congratulations!

Copyright © 2012 Pearson Education Inc. Congratulations! On the first try…. Thursday! Ahmed, Christian, Nick, Fern Troy, Ali, Russell, Moses, Andrew Dolly, Samuel, Ray, Hye Friday!  Hairu, Guohao, Dan, Quinlan On the second try…. Robert, Saminder, Jaikar, Kelsi Joshua, Rex, Steven, Shean, Hesham Jordan, Camille, Andrew, Bryan David, Omar, Sugei, Louis, Eduardo Roger, Sue, Becky, Adolfo, Jasmine

Copyright © 2012 Pearson Education Inc. Goals for Chapter 5 Use Newton’s 1st law for bodies in equilibrium (statics) Use Newton’s 2nd law for accelerating bodies (dynamics) Study types of friction & fluid resistance Solve circular motion problems

Copyright © 2012 Pearson Education Inc. Using Newton’s First Law when forces are in equilibrium A body is in equilibrium when it is at rest or moving with constant velocity in an inertial frame of reference. Follow Problem-Solving Strategy 5.1.

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Using Newton’s First Law when forces are in equilibrium VISUALIZE (create a coordinate system; decide what is happening?) SKETCH FREE-BODY DIAGRAM Isolate one point/body/object Show all forces in that coordinate system ON that body (not acting by that body!) LABEL all forces clearly, consistently Normal forces from surfaces Friction forces from surfaces Tension Forces from ropes Contact forces from other objects Weight from gravity

Copyright © 2012 Pearson Education Inc. Using Newton’s First Law when forces are in equilibrium BREAK ALL applied forces into components based on your coordinate system. Apply Newton’s Laws to like components ONLY  F x = ma x ;  F y = ma y

Copyright © 2012 Pearson Education Inc. One-dimensional equilibrium: Tension in a massless rope A gymnast hangs from the end of a massless rope. Example 5.1 (mg = 50 kg; what is weight & force on rope?)

Copyright © 2012 Pearson Education Inc. One-dimensional equilibrium: Tension in a massless rope A gymnast hangs from the end of a massless rope. Example (mg = 50 kg; what is weight & force on rope?)

Copyright © 2012 Pearson Education Inc. One-dimensional equilibrium: Tension in a massless rope A gymnast hangs from the end of a massless rope. Example (mg = 50 kg; what is weight & force on rope?) Tension of Rope on Gymnast

Copyright © 2012 Pearson Education Inc. One-dimensional equilibrium: Tension in a rope with mass What is the tension in the previous example if the rope has mass? (Example 5.2 weight of rope = 120 N)

Copyright © 2012 Pearson Education Inc. Two-dimensional equilibrium A car engine hangs from several chains. Weight of car engine = w; ignore chain weights

Copyright © 2012 Pearson Education Inc. A car on an inclined plane An car rests on a slanted ramp (car of weight w)

Copyright © 2012 Pearson Education Inc. A car on an inclined plane Coordinate system choice #1: –(y) parallel to slope & – (x) perpendicular to slope x y  

Copyright © 2012 Pearson Education Inc. A car on an inclined plane Coordinate system choice #1: –(y) parallel to slope & – (x) perpendicular to slope x y   N (in y) T (in x) W (in x & y)

Copyright © 2012 Pearson Education Inc. A car on an inclined plane Coordinate system choice #2: –(y) perpendicular to ground – (x) parallel to ground x y   N in both x & y! W (in y only) T (in x & y!)

Copyright © 2012 Pearson Education Inc. A car on an inclined plane Coordinate system choice #2: –(y) perpendicular to ground – (x) parallel to ground x y   N W T   NxNx NyNy TxTx TxTx

Copyright © 2012 Pearson Education Inc. Example 5.5: Bodies connected by a cable and pulley Cart connected to bucket by cable passing over pulley. Initially, assume pulley is massless and frictionless! Pulleys REDIRECT force – they don’t amplify or reduce. Tension in rope pulls upwards along slope SAME tension in rope pulls upwards on bucket

Copyright © 2012 Pearson Education Inc. Example 5.5: Bodies connected by a cable and pulley Draw separate free-body diagrams for the bucket and the cart.

Copyright © 2012 Pearson Education Inc. A note on free-body diagrams Only the force of gravity acts on the falling apple. ma does not belong in a free-body diagram! It is the SUM of all the forces you find! 

Copyright © 2012 Pearson Education Inc. Ex 5.6 Straight-line motion with constant force Wind exerts a constant horizontal force on the boat. 4.0 s after release, v = 6.0 m/s; mass = 200 kg.

Copyright © 2012 Pearson Education Inc. Ex 5.6 Straight-line motion with constant force Wind exerts a constant horizontal force on the boat. 4.0 s after release, v = 6.0 m/s; mass = 200 kg. Find W, the force of the wind!

Copyright © 2012 Pearson Education Inc. Example 5.7: Straight-line motion with friction For the ice boat in the previous example, a constant horizontal friction force of 100 N opposes its motion What constant force needed by wind to create the same acceleration (a = m/s/s)?

Copyright © 2012 Pearson Education Inc. Example 5.7: Straight-line motion with friction For the ice boat in the previous example, a constant horizontal friction force now opposes its motion (100N); what constant force needed by wind to create the same acceleration (a = m/s/s)?

Copyright © 2012 Pearson Education Inc. Example 5.8: Tension in an elevator cable Elevator (800 kg) is moving 10 m/s but slowing to a stop over 25.0 m. What is the tension in the supporting cable?

Copyright © 2012 Pearson Education Inc. Example 5.8: Tension in an elevator cable Elevator (800 kg) is moving 10 m/s but slowing to a stop over 25.0 m. What is the tension in the supporting cable?

Copyright © 2012 Pearson Education Inc. Example 5.8: Tension in an elevator cable Compare Tension to Weight while elevator slows?

Copyright © 2012 Pearson Education Inc. Example 5.8: Tension in an elevator cable Compare Tension to Weight while elevator slows? What if elevator was accelerating upwards at same rate?

Copyright © 2012 Pearson Education Inc. Example 5.8: Tension in an elevator cable What if elevator was accelerating upwards at same rate? Same Free Body Diagram! Same result!

Copyright © 2012 Pearson Education Inc. Ex 5.9 Apparent weight in an accelerating elevator A woman inside the elevator of the previous example is standing on a scale. How will the acceleration of the elevator affect the scale reading?

Copyright © 2012 Pearson Education Inc. Ex 5.9 Apparent weight in an accelerating elevator A woman inside the elevator of the previous example is standing on a scale. How will the acceleration of the elevator affect the scale reading?

Copyright © 2012 Pearson Education Inc. Ex 5.9 Apparent weight in an accelerating elevator What if she was accelerating downward, rather than slowing? Increasing speed down?

Copyright © 2012 Pearson Education Inc. Acceleration down a hill What is the acceleration of a toboggan sliding down a friction-free slope?

Copyright © 2012 Pearson Education Inc. Acceleration down a hill What is the acceleration of a toboggan sliding down a friction-free slope? Follow Example 5.10.

Copyright © 2012 Pearson Education Inc. Two common free-body diagram errors The normal force must be perpendicular to the surface. There is no separate “ma force.” 

Copyright © 2012 Pearson Education Inc. Two bodies with the same acceleration We can treat the milk carton and tray as separate bodies, or we can treat them as a single composite body.

Copyright © 2012 Pearson Education Inc. Two bodies with the same acceleration Push a 1.00 kg food tray with constant 9 N force, no friction. What is acceleration of tray and force of tray on the carton of milk?

Copyright © 2012 Pearson Education Inc. Two bodies with the same magnitude of acceleration The glider on the air track and the falling weight move in different directions, but their accelerations have the same magnitude and relative direction (both increasing, or both decreasing)

Copyright © 2012 Pearson Education Inc. Two bodies with the same magnitude of acceleration What is the tension T, and the acceleration a, of the system?

Copyright © 2012 Pearson Education Inc. Frictional forces When a body rests or slides on a surface, the friction force is parallel to the surface. Friction between two surfaces arises from interactions between molecules on the surfaces.

Copyright © 2012 Pearson Education Inc. Kinetic and static friction Kinetic friction acts when a body slides over a surface. The kinetic friction force is f k = µ k n. Static friction acts when there is no relative motion between bodies. The static friction force can vary between zero and its maximum value: f s ≤ µ s n.

Copyright © 2012 Pearson Education Inc. Static friction followed by kinetic friction Before the box slides, static friction acts. But once it starts to slide, kinetic friction acts.

Copyright © 2012 Pearson Education Inc. Some approximate coefficients of friction

Copyright © 2012 Pearson Education Inc. Friction in horizontal motion – example 5.13 Move a 500-N crate across a floor with friction by pulling with a force of 230 N. Initially, pull harder to get it going; later pull easier (at 200N once it is going). What are  s ?  k ?

Copyright © 2012 Pearson Education Inc. Friction in horizontal motion Before the crate moves, static friction acts on it.

Copyright © 2012 Pearson Education Inc. Friction in horizontal motion After it starts to move, kinetic friction acts.

Copyright © 2012 Pearson Education Inc. Static friction can be less than the maximum Static friction only has its maximum value just before the box “breaks loose” and starts to slide. Force Time Force builds in time to maximum value, then object starts moving & slipping

Copyright © 2012 Pearson Education Inc. Pulling a crate at an angle The angle of the pull affects the normal force, which in turn affects the friction force. Follow Example 5.15.

Copyright © 2012 Pearson Education Inc. Motion on a slope having friction – ex 5.16 Consider a toboggan going down a slope at constant speed. What is  ? Now consider same toboggan on steeper hill, so it is now accelerating. What is a?

Copyright © 2012 Pearson Education Inc. Fluid resistance and terminal speed Fluid resistance on a body depends on the speed of the body. Resistance can depend upon v or v 2 and upon the shape moving through the fluid. F resistance = -kv or - Dv 2 These will result in different terminal speeds

Copyright © 2012 Pearson Education Inc. Fluid resistance and terminal speed A falling body reaches its terminal speed when resisting force equals weight of the body. If F = -kv for a falling body, v terminal = mg/k If F = - Dv 2 for a falling body, v terminal = (mg/D) ½

Copyright © 2012 Pearson Education Inc. Dynamics of circular motion If something is in uniform circular motion, both its acceleration and net force on it are directed toward center of circle. The net force on the particle is F net = mv 2 /R, always towards the center.

Copyright © 2012 Pearson Education Inc. Using Newton’s First Law when forces are in equilibrium IF you see uniform circular motion… v r

Copyright © 2012 Pearson Education Inc. Using Newton’s First Law when forces are in equilibrium IF you see uniform circular motion… THEN remember centripetal force is NOT another force – it is the SUM of one or more forces already present!  F x = mv 2 /R NOT mv 2 /R + T – mg = ma v r

Copyright © 2012 Pearson Education Inc. Avoid using “centrifugal force” Figure (a) shows the correct free-body diagram for a body in uniform circular motion. Figure (b) shows a common error. In an inertial frame of reference, there is no such thing as “centrifugal force.”

Copyright © 2012 Pearson Education Inc. Force in uniform circular motion A 25 kg sled on frictionless ice is kept in uniform circular motion by a 5.00 m rope at 5 rev/minute. What is the force?

Copyright © 2012 Pearson Education Inc. Force in uniform circular motion A 25 kg sled on frictionless ice is kept in uniform circular motion by a 5.00 m rope at 5 rev/minute. What is the force?

Copyright © 2012 Pearson Education Inc. What if the string breaks? If the string breaks, no net force acts on the ball, so it obeys Newton’s first law and moves in a straight line.

Copyright © 2012 Pearson Education Inc. A conical pendulum – Ex 5.20 A bob at the end of a wire moves in a horizontal circle with constant speed.

Copyright © 2012 Pearson Education Inc. A car rounds a flat curve A car rounds a flat unbanked curve. What is its maximum speed?

Copyright © 2012 Pearson Education Inc. A car rounds a flat curve A car rounds a flat unbanked curve. What is its maximum speed?

Copyright © 2012 Pearson Education Inc. A car rounds a banked curve At what angle should a curve be banked so a car can make the turn even with no friction?

Copyright © 2012 Pearson Education Inc. A car rounds a banked curve At what angle should a curve be banked so a car can make the turn even with no friction?

Copyright © 2012 Pearson Education Inc. Uniform motion in a vertical circle – Ex A person on a Ferris wheel moves in a vertical circle at constant speed. What are forces on person at top and bottom?

Copyright © 2012 Pearson Education Inc. Uniform motion in a vertical circle – Ex A person on a Ferris wheel moves in a vertical circle.

Copyright © 2012 Pearson Education Inc. The fundamental forces of nature According to current understanding, all forces are expressions of four distinct fundamental forces: gravitational interactions electromagnetic interactions strong interaction weak interaction Physicists have taken steps to unify all interactions into a theory of everything.