CP Physics Chapter 4 Newton’s Laws

Force Force (F) is a push or a pull Measured in Newtons (N) for SI, pounds (lb) in US. (4.45 N = 1 lb) It has magnitude & direction, so it’s a vector

Force in general Name some forces How strong are they? Contact vs at-a- distance (or field)

Force in motion Forces act on things, or “bodies” Forces can require physical contact or be “at a distance” Forces are drawn as vectors and added as vectors To draw forces (vectors) acting on a body, isolate (or “free”) the body from everything—only the forces acting on the body are drawn. Called a Free Body Diagram (FBD)—see samples Force, acceleration, and mass (F, a, m) can be used to explain motion with Newton’s Laws of Motion

Newton’s First Law of Motion Law of Inertia Net Force (  F) a vector sum Constant velocity means  F = 0, or equilibrium, or a = 0..\My Videos\inertia\train-hurricane.mp4..\My Videos\inertia\planeland.mp4..\..\Videos\inertia\FirstSnowcarcrashfun.mp4 Bed of nails C:\Users\eanthony\Videos\CarCrashInSnow - StupidFunny.mp4

1 st Law: Inertia Old: A body at rest will stay at rest, A body in motion will stay in motion, Until acted on by an outside force New: A body at rest will stay at rest, A body with velocity will maintain its velocity, Until acted on by a Net Force

Example Net Force You place your book on a bathroom scale and you find that it weighs 50 N. A)What force does it exert on the scale? B)You now push down on the book with a force of 10 N, what is the force applied to the book by the Earth? What force is exerted on the scale? C)You now lift the book with a force of 20 N, what is the force exerted on the scale? packet examples

Newton’s Second Law of Motion Net Force = mass  acceleration or  F = m  a

Basic Example  F = m  a What is the net force required to accelerate a 1.5 kg box at 2.0 m/sec 2 ?

Basic Example 2 What is the net force exerted on a 1500 kg car if it is accelerated from 5 m/s to 10 m/s in 3 sec?

2 nd Law: Acceleration  F = m  a The most used equation in Physics Both sides of the equation can be a problem to solve The  F can be the difficult part because  F is a vector sum See the more advanced problems after 3 rd law

A use of 2 nd Law: What is... Mass, m (kg) Weight, F g (N), or force of gravity They are NOT the same thing! From 2 nd Law, when a is = g F g = m·g calculates weight

Examples How much does a 3 kg object weigh? What is the mass of a 900 N teacher?

Newton’s Third Law of Motion “Every action (force) has an equal & opposite reaction (force)” Forces are always in pairs When 2 objects interact, the forces they exert are an action-reaction pair Action-reaction forces are on different objects and are equal but opposite in direction

Newton’s Third Law Action-Reaction Pairs The hammer exerts a force on the nail to the right. The nail exerts an equal but opposite force on the hammer to the left. Action “hammer hits nail” Reaction “nail hits hammer”

Newton’s Third Law Action-Reaction Pairs The rocket exerts a downward force on the exhaust gases. The gases exert an equal but opposite upward force on the rocket. F fuel F Rocket

One more on Newton’s Third Law Action-Reaction Pairs The earth pulls down on you (weight)… You pull up on the earth with an equal and opposite force (same as your weight)

Common forces in Problems Weight (F g ), the force of gravity (= mg) Support Force; called Normal Force where “Normal” is perpendicular. This force is perpendicular to the supporting surface (F N ) Tension (F T ), when a rope, cable, spring, etc is pulled or stretched apart Friction (F f ), but not yet!

Normal Force, F N -Supporting force -Perpendicular to supporting surface -NOT always the same as weight FNFN

Problem solving-- Identify Forces, Knows, and Unknowns Sketch the problem –Choose your coordinate system (x & y) –Isolate the object –Draw external forces (free body diagram) Apply Newton’s Laws in x & y (  F x =ma x &  F y =ma y ). Know if a x or a y = 0 !! Solve for unknowns

Example A 52 N sled is pulled across a level cement sidewalk. A horizontal force of 36 N is exerted. A)What is the acceleration of the sled? B)What is the acceleration of the sled if the sled’s mass is 30 kg?

Example A) A 24 N fish hangs from a scale in an elevator. The elevator accelerates upward at 3 m/sec 2. What does the scale read? B) Again; this time the car accelerates downward at 1.8 m/sec 2. So, when is the elevator cable most likely to break?

Example An 800 N student stands in an elevator. The elevator accelerates upward at 2.5 m/sec 2. What is the tension in the cables if the elevator car’s mass is 1000 kg? When the car accelerates downward at 2 m/sec 2 ?

Example What is the acceleration of an Atwood machine if the two masses hanging on it is 3 kg and 4 kg? What is the tension in the cable?

CP Physics Chapter 4 Newton’s Laws with friction

Study two types of Friction Static (s) stopped Kinetic (k) moving Drag is fluid friction, which works differently

What Affects the Force of Friction (F f ) on a sliding object? Speed? (assuming v > 0) Area in contact? Weight of object? Materials in contact (surface roughness)?

What if... ? F push F f, max F f is NOT an “applied” force

F s   s F N so F s,max   s F N F k =  k F N FYI:  s >  k  (mu) is the coefficient of friction  is a property of the materials, which depends on their surface roughness and contact force, F N General: F f =  F N s=static k=kinetic

Example #1 What is the acceleration of a 30 kg crate if the coefficient of friction is and the object has a 15 N horizontal pulling force applied to it? Try this problem again but the crate weighs 30 N.

Example #2A A 52 N sled is pulled across a cement sidewalk at constant speed. A horizontal force of 36 N is exerted. What is the coefficient of friction between the metal runners and the cement?

Example #2B Now the sled runs on packed snow where the coefficient of friction is If a 650 N person sits on the sled: A)What is the applied force needed to move it at constant speed? B)How much force is needed to accelerate the sled at 2 m/s 2 ?

Example #3A What coefficient of friction is needed to keep the system at equilibrium?  =? m 2 =3 kg m 1 =4 kg

m 2 =3 kg Example #3B What is the acceleration of the system shown below? What is the tension in the cable?  =0.2 m 1 =4 kg

1) What is the minimum mass of the fish needed to just cause the Spam to move?  s = 0.5 m spam = 20 kg m fish = ? 2) What is  if the fish was 12.5 kg causing acceleration of 1.2 m/s 2 ?

Example #4 A penguin slides across the ice 15 m to a stop. The coefficient of friction between the penguin and the ice is What was the acceleration and how fast was the penguin going initially?

CP Physics Chapter 4 Newton’s Laws if any Angles SOH CAH TOA !

Calculate x & y components of all vectors. Add all components for x, and all for y direction to find the total in the x (  F x ) and y (  F y ). Knowing  F x and  F y, calculate Resultant Force with Pythagorean Thm: Vector Addition

Example A 80 kg skier starts from rest and accelerates down a hill which is angled 35  above horizontal. The coefficient of friction between the skis and snow is Draw the forces acting on the skier What direction is the acceleration in?

Problem solving-- Identify Forces, Knows, and Unknowns Sketch the problem –Choose your coordinate system –Isolate the object(s) –RESOLVE any Forces at angles into x & y –Draw external forces Apply Newton’s Laws in x & y (  F x =ma x &  F y =ma y ) Solve for unknowns

Example A sled of mass 30 kg is pulled with a force of 50 N at a 25 degree angle. If the coefficient of friction between the runners and the snow is 0.1, what is the acceleration of the sled?

Example A 50 kg boy is inside a 20 kg crate that is pushed with a 200 N force at 20 degrees below the horizontal. a)What coefficient of friction would keep the crate from accelerating? b)What coefficient of friction would keep the crate accelerating at 1.5 m/sec 2 ? F = 200 N

Review You are standing on a scale while riding an elevator and your mass is 35 kg. Determine how much the Normal force is when: The elevator is coming down at a constant speed of 2.3 m/s The elevator is accelerating down at 1.35 m/s 2 The elevator is accelerating up at 2.25 m/s 2