Classical Mechanics does not apply for very tiny objects (< atomic sizes) objects moving near the speed of light
Newton’s First Law 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!
Forces Usually a push or pull Vector Either contact or field force
Define the OBJECT (free body) 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 Objects behave as particles ignore rotational motion (for now) Consider only forces acting ON object neglect reaction forces
Problem Solving Strategy Identify object (free body) Label all forces acting on object Resolve forces into x- and y-components, using convenient coordinate system Apply equations, keep track of signs!
Mechanical Forces Strings, ropes and Pulleys Gravity Normal forces Friction Springs (later in the book)
Some Rules for Ropes and Pulleys Force from rope points AWAY from object Magnitude of the force is called tension Tension does not change when going over a pulley (if frictionless)
Example 4.1 Given that M light = 25 kg, find all three tensions T 3 = 245.3 N, T 1 = 147.4 N, T 2 = 195.7 N
Example 4.2 2) Which statements are correct? Assume the objects are static. A) T 1 must = T 2 B) T 2 must = T 3 C) T 1 must be < Mg D) T 1 +T 2 must be > Mg cos(10 o )=0.985 sin(10 o )=0.173 A) T B) T C) T D) T
Example 4.3 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 = 1.635 m/s 2 b) T = 57.2 N c) T 3 =24.5 N d) F pulley =2T = 114.5 N
Inclined Planes Choose x along the incline and y perpendicular to incline Replace force of gravity with its components
Example 4.4 Find the acceleration and the tension a = 4.43 m/s 2, T= 53.7 N
Example 4.5 Find M such that the box slides at constant v M=15.6 kg M
Forces of Friction Resistive force between object and neighbors or the medium Examples: Sliding a box Air resistance Rolling resistance
Sliding Friction Direction parallel to surface, opposite to other forces Nearly independent of the area of contact The coefficient of friction (µ) depends on the surfaces in contact
Example 4.6 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 0.15. 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
Example 4.7 Given m 1 = 10 kg and m 2 = 5 kg: a) What value of s would stop the block from sliding? b) If the box is sliding and k = 0.2, what is the acceleration? c) What is the tension of the rope? a) s = 0.5 b) a=1.96 m/s 2 c) 39.25 N
Example 4.8 What is the minimum s required to prevent a sled from slipping down a hill of slope 30 degrees? s = 0.577
Other kinds of friction Air resistance, F ~ Area v 2 Rolling resistance, F ~ v Terminal velocity:
Accelerating Reference Frames Equivalent to “Fictitious” gravitational force
Fictitious Force: Derivation Eq. of motion in fixed frame F-ma f looks like force in new frame, ma f acts like fake gravitational force!
Example 4.9 An elevator falls with acceleration a = 8.0 m/s 2. If a 200-lb person stood on a bathroom scale during the fall, what would the scale read? 36.9 lbs
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? = 17 deg T= 25.6 N