Chapter 4. Forces and Mass. Classical Mechanics. Forces. Newton s First Law. Fundamental (Field) Forces. Contact and Field Forces

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1 Chapter 4 Classical Mechanics Forces and Mass does not apply for very tiny objects (< atomic sizes) objects moving near the speed of light Newton s First Law Forces If the net force!f exerted on an object is zero the object continues in its original state of motion. That is, if!f = 0, an object at rest remains at rest and an object moving with some velocity continues with the same velocity. Contrast with Aristotle! Usually a push or pull Vector Either contact or field force Contact and Field Forces Fundamental (Field) Forces Types Strong nuclear force Electromagnetic force Weak nuclear force Gravity

2 Strong Nuclear Force QCD (Quantum chromodynamics) confines quarks by exchaning gluons Nuclear force: binds protons and neutrons by exchanging pions Electromagnetic Forces Opposites attract, like-signs repel Electric forces bind electrons in atoms Magnetic forces arise from moving charges Weak Nuclear Force Gravity Involves exchange of heavy W or Z particle Responsible for decay of neutrons Attractive force between any two bodies Proportional to both masses Inversely proportional to square of distance F = G m1m 2 r 2 Inertia (Newton s First Law) Mass Tendency of an object to continue in its original motion A measure of the resistance of an object to changes in its motion due to a force Scalar SI units are kg

3 Newton s Second Law Acceleration is proportional to net force and inversely proportional to mass.!! F = m a! Units of Force SI unit is Newton (N) F = ma 1 N = 1 kg!m s 2 US Customary unit is pound (lb) 1 N = lb Weight Weight is magnitude of gravitational force Weight vs. Mass weight mass w = mg w = G M earthm r 2 g = GM earth 2 R earth Mass is inherent property Weight depends on location Newton s Third Law! F 12 =! F! 21 Single isolated force cannot exist For every action there is an equal and opposite reaction Force on 1 due to 2 Newton s Third Law cont. F 12 is action force F 21 is reaction force You can switch action <-> reaction Action & reaction forces act on different objects

4 Action-Reaction Pairs Define the OBJECT (free body)!! n =! n" ' F g =!F g Newton s Law uses the forces acting ON object n and F g act on object n and F g act on other objects Assumptions for F=ma Definition of Equilibrium! F! = 0 Objects behave as particles ignore rotational motion (for now) Consider only forces acting ON object neglect reaction forces Example 4.1a A Ford Pinto is parked in a parking lot There is no net force on the Pinto A) True B) False Example 4.1b A Ford Pinto is parked in a parking lot The contact force acting on the Pinto from the parking lot surface. A) Points upwards B) Is zero C) Points downward

5 Example 4.1c A Ford Pinto drives down a highway on the moon at constant velocity (where there is no air resistance) The Pinto s acceleration is A) Less than zero B) Equal to zero C) Greater than zero Example 4.1d A Ford Pinto drives down a highway on the moon at constant velocity (where there is no air resistance) The force acting on the Pinto from the contact with the highway is vertical. A) True B) False Mechanical Forces Some Rules for Ropes and Pulleys Strings, ropes and Pulleys Gravity Normal forces Friction Springs (later) Force from rope points AWAY from object Magnitude of the force is tension Tension does not change when going over frictionless pulley Example 4.2 Example 4.3a a) Find acceleration b) Find T, the tension above the bowling ball c) Find T 3, the tension in the rope between the pails d) Find force ceiling must exert on pulley a) a = g/6 = m/s 2 b) T = 57.2 N c) T 3 =24.5 N d) F pulley =2T = N 2) Which statements are correct? Assume the objects are static. T 1 is T 2 A) Less than B) Equal to C) Greater than cos(10 o )=0.985 sin(10 o )=0.173

6 Example 4.3b 2) Which statements are correct? Assume the objects are static. Example 4.3c 2) Which statements are correct? Assume the objects are static. T 2 is T 3 T 1 is Mg A) Less than B) Equal to C) Greater than A) Less than B) Equal to C) Greater than cos(10 o )=0.985 sin(10 o )=0.173 cos(10 o )=0.985 sin(10 o )=0.173 Example 4.3d 2) Which statements are correct? Assume the objects are static. Example 4.4 T 1 +T 2 is Mg A) Less than B) Equal to C) Greater than cos(10 o )=0.985 sin(10 o )=0.173 Given that M light = 25 kg, find all three tensions T 3 = N, T 1 = N, T 2 = N Cable Pull Demo Inclined Planes Choose x along the incline and y perpendicular to incline Replace force of gravity with its components F g,x = mgsin! F g,y = mgcos!

7 Example 4.5 Example 4.6 (Skip) M Find the acceleration and the tension a = 4.43 m/s 2, T= 53.7 N Find M such that the box slides at constant v M=15.6 kg Forces of Friction RESISTIVE force between object and neighbors or the medium Examples: Sliding a box Air resistance Rolling resistance Sliding Friction f! µ s N f = µ k N µ s > µ k Parallel to surface, opposite to other forces ~ independent of the area of contact Depends on the surfaces in contact Coefficients of Friction f! µ s N f = µ k N Static Friction, ƒ s f s! µ s N µ s > µ k µ s is coefficient of static friction N is the normal force f F

8 Kinetic Friction, ƒ k Friction Demo f = µ k n µ k is coefficient of kinetic friction Friction force opposes F n is the normal force F f Example 4.7 Example 4.8 The man pushes/pulls with a force of 200 N. The child and sled combo has a mass of 30 kg and the coefficient of kinetic friction is For each case: What is the frictional force opposing his efforts? What is the acceleration of the child? f=59 N, a=3.80 m/s 2 / f=29.1 N, a=4.8 m/s 2 Given m 1 = 10 kg and m 2 = 5 kg: a) What value of µ s would stop the block from sliding? b) If the box is sliding and µ k = 0.2, what is the acceleration? c) What is the tension of the rope? a) µ s = 0.5 b) a=1.96 m/s 2 c) N Example 4.9 Other kinds of friction Air resistance, F ~ Area " v 2 Rolling resistance, F ~ v Terminal velocity: What is the minimum µ s required to prevent a sled from slipping down a hill of slope 30 degrees? F resistance = CAv 2 = mg at terminal velocity µ s = 0.577

9 Coffee Filter Demo Example 4.9 An elevator falls with acceleration a = 8.0 m/s 2. If a 100-kg person stood on a bathroom scale during the fall, what would the scale read? kg Accelerating Reference Frames Fictitious Force: Derivation Equivalent to Fictitious gravitational force g fictitious =!a frame x = v 0 t at 2 = v 0 t F m t 2 x 0 (t) = 1 2 a f t 2 Eq. of motion in fixed frame x! x 0 (t) = v 0 t + 1 (F! ma f ) 2 m F-ma f looks like force in new frame, ma f acts like fake gravitational force! t 2 Example 4.10 You are calibrating an accelerometer so that you can measure the steady horizontal acceleration of a car by measuring the angle a ball swings backwards. If M = 2.5 kg and the acceleration, a = 3.0 m/s 2 : a) At what angle does the ball swing backwards? b) What is the tension in the string? Example 4.11a A fisherman catches a 20 lb trout (mass=9.072 kg), and takes the trout in an elevator to the 78th floor to impress his girl friend, who is the CEO of a large accounting firm. The fish is hanging on a scale, which reads 20 lb.s while the fisherman is stationary. Later, he returns via the elevator to the ground floor with the fish still hanging from the scale. # # = 17 deg T= 25.6 N In the instant just after the elevator begins to move upward, the reading on the scale will be 20 lbs. a) Greater than b) Less than c) Equal to

10 Example 4.11b A fisherman catches a 20 lb trout (mass=9.072 kg), and takes the trout in an elevator to the 78th floor to impress his girl friend, who is the CEO of a large accounting firm. The fish is hanging on a scale, which reads 20 lb.s while the fisherman is stationary. Later, he returns via the elevator to the ground floor with the fish still hanging from the scale. Example 4.11c A fisherman catches a 20 lb trout (mass=9.072 kg), and takes the trout in an elevator to the 78th floor to impress his girl friend, who is the CEO of a large accounting firm. The fish is hanging on a scale, which reads 20 lb.s while the fisherman is stationary. Later, he returns via the elevator to the ground floor with the fish still hanging from the scale. On the way back down, while descending at constant velocity, the reading on the scale will be 20 lbs. a) Greater than b) Less than c) Equal to In the instant just before the elevator comes to a stop on the 78th floor, the mass of the fish will be kg. a) Greater than b) Less than c) Equal to

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