Unit 3: Newton’s Laws Chapter 4 & 5

Unit 3 Objectives Describe and give examples of Newton's 1st Law. Newton's 1st Law: Objects at rest stay at rest, objects in motion stay in motion at constant speed in a straight line unless acted upon by unbalanced forces.  Understand and apply Newton’s 2nd Law Newton's 2nd Law: The acceleration of an object is directly proportional to the net force on an object and inversely proportional to the mass of the object (a = ΣF/m or ΣF = ma). Use Newton's 2nd Law to qualitatively describe the relationship between m and a, F and a, m and F. (For example, if you double the mass, the acceleration will . . ?) Understand and apply Newton's 3rd Law. Recognize that all forces come in pairs; paired forces are equal in magnitude, but opposite in direction. FAB = -FBA Newton's 3rd Law: For every force, there is an equal and opposite force. Another way of thinking about Newton's third law: You can't touch without being touched and you can only touch as hard as you are touched.

Unit 3 Objectives Given a diagram or a written description of the forces acting on an object: Draw and label a force diagram for the object Choose the simplest coordinate axis for analysis: horizontal – vertical or parallel – perpendicular Break forces in x and y components using trigonometry State whether the velocity of the object is constant or changing Solve quantitative problems involving forces, mass and acceleration using Newton's 2nd Law. use force diagram analysis in order to determine the equation for the forces acting on an object in a particular direction. Use Newton's second law to determine an object's acceleration and/or missing force. Use kinematics to determine the acceleration needed to be used in Newton’s second law. Use Newton’s second law to determine the acceleration needed in a kinematic calculation. Interpret graphs of position-time, velocity-time, acceleration-time and relate them to the net force acting on the object and vice-versa Use derivatives and integrals to for part c when the acceleration is not constant.

Unit 3 Objectives Distinguish between static and kinetic friction and qualitatively describe what factors affect it. Apply the model of static friction to an object at rest (or on the verge of moving) in order to determine the maximum static friction force or coefficient of static friction for two surfaces. Apply the model of kinetic friction to an object moving at constant speed or accelerating in order to determine the kinetic friction force or coefficient of kinetic friction of two surfaces. Distinguish between the mass of an object and the force of gravity acting on it, aka weight. Recognize that forces are classified as either contact and non-contact forces. Also, be able to distinguish which of the four fundamental forces a particular force is. For an object moving where drag is a factor: Draw the graphs of y vs. t, v vs. t, and a vs. t and understand the basic features of the graph Determine the terminal velocity of the object recognizing that the acceleration is zero Express Newton’s second law in differential form

Forces A push or a pull Forces must act on an object Pushes or pulls must be applied to an object Forces do not exist in isolation from the object Forces require agents: something to do the pushing or pulling Unbalanced forces cause an object to accelerate…. To speed up To slow down To change direction

Contact versus Field Forces Forces that exist during physical contact Tension Friction Applied Force Normal FIELD FORCES Forces that exist with NO physical contact Gravitational Electromagnetic

Sir Isaac Newton 1642-1727 Why do objects accelerate? Before Newton, people that studied motion believed that an internal property of objects is what caused this acceleration. Force was required to keep objects moving Newton, however, rejected this belief. The nature of objects is to continue moving unless some force acts on them. From Galileo’s Thought Experiment

Galileo’s Thought Experiment

Galileo’s Thought Experiment This thought experiment lead to Newton’s First Law.

Newton’s First Law Every body perseveres in its state of being at rest or of moving uniformly straight forward except insofar as it is compelled to change by forces impressed.

Newton’s First Law An object in motion remains in motion in a straight line and at a constant speed or an object at rest remains at rest, UNLESS acted upon by an EXTERNAL (unbalanced) Force. Condition #1 – the object CAN move but must be at a CONSTANT SPEED Condition #2 – The object is at REST Constraint – As long as the forces are BALANCED!!! All the forces are balanced SUM of all the forces are ZERO BOTTOM LINE: There is NO ACCELERATION in this case, and the object must be in equilibrium.

Forces & Equilibrium If the net force (ΣF) on a body is zero, then it is in equilibrium Forces are balanced No distinction between objects that have no forces acting on them or objects on which the sum of external forces are zero Dynamic Equilibrium An object in equilibrium may be moving relative to us Static Equilibrium An object in equilibrium may appear to be at rest

What if NOT in Equilibrium? If an object is NOT at rest nor is it moving at a constant velocity, then there must be UNBALANCED FORCES acting on the object. One force(s) in a certain direction overpowers the others THE OBJECT WILL ACCELERATE!!!

Newton’s First Law – Law of Inertia INERTIA – a quantity of matter, also called mass Italian for “lazy” Resistance to change MASS – same thing as inertia (to a physicist) Measured in kilograms

Free Body Diagrams (FBD) A pictorial representation of forces complete with labels!

Free body Diagrams Can choose to have the coordinate axis as horizontal-vertical or as parallel-perpendicular to the surface!!!

Inertial Reference Frames The part of the world that we use to measure motion of moving objects Since the world around us seems to be at rest (uniform), then any motion we measure relative to our surroundings is correctly observed If motion appears uniform, it must truly be uniform, and if the motion appears nonuniform, then it must truly be nonuniform. What if instead of using the world around us (uniform motion), we used a moving car (non-uniform motion)?

Inertial Reference Frames EXAMPLE: You are a passenger riding in a car. Brakes are applied, and the book on the seat next to you slides forward. No apparent force on the book, yet it moved Violates Newton’s First Law Your friend standing on the side of the road, sees you, the car, and the book moving together Follows Newton’s First Law

Inertial Reference Frames Galileo in all frames of reference which are moving uniformly relative to each other, the laws of nature must be the same Reference frames are not accelerating !!! Classical mechanics only hold true in inertial reference frames!!!

Mass & Weight MASS - A property of an object that determines how much it will resist a change in velocity Measured in kilograms WEIGHT – a force due to gravity How your mass is affected by gravity NOTE: MASS and WEIGHT are NOT the same thing. Mass never changes while weight does as gravity changes.

Newton’s Second Law “A change in motion is proportional to the motive force impressed and takes place along the straight line in which that force is impressed.” A body acted on by an external force will accelerate acceleration is directly proportional to the net force on an object and inversely proportional to its mass.

Newton’s Second Law Slope = mass Acceleration is directly proportional to Force. Thus the resulting acceleration-force graph is linear with y-intercept at the origin.

Newton’s Second Law Acceleration is inversely proportional to mass. Thus the resulting acceleration-mass graph is a inverse (hyperbola).

Example: Rocket Guy Rocket Guy weighs 905 N and his jet pack provides 1250 N of thrust, straight up. What is his acceleration? ΣF = ma Fthrust – Fg = ma – 905 = 92.3 a a = 3.74 m/s2 Fg = mg 905 N = m (9.8m/s2) m = 92.3 kg Fg FThrust

Practice: Helicopter Lift A helicopter of mass 3770 kg can create an upward lift force F. When empty, it can accelerate straight upward at a maximum of 1.37 m/s2.  A careless crewman overloads the helicopter so that it is just unable to lift off.  What is the mass of the cargo?

Example Problem A 10 kg box is being pulled across the table to the right at a constant speed with a force of 50 N. Calculate the Force of Friction Calculate the Normal Force

Example Problem Continued Suppose the same box is now pulled at an angle of 30 degrees above the horizontal at constant speed. Calculate the new Frictional force Calculate the new Normal Force

Newton’s Second Law: Systems Instead of treating the problem as two separate objects, treat as one system. Draw a FBD for each object in the system. Only forces parallel to the acceleration of the individual object affect the motion Forces perpendicular to motion do not affect it Internal forces do not affect motion (only external) Forces that point in the direction of motion are positive Forces that point away from direction of motion are negative a

Example: Systems A mass, m1 = 3.00 kg, is resting on a frictionless horizontal table is connected to a cable that passes over a pulley and then is fastened to a hanging mass, m2 = 11.00 kg as shown below. Find the acceleration of each mass and the tension in the cable.

Newton’s Third Law “To any action there is always an opposite and equal reaction; in other words, the actions of two bodies upon each other are always equal and always opposite in direction”. For every action, there is an EQUAL and OPPOSITE reaction!! Action-Reaction Pairs 1.5 N

Newton’s Third Law Examples This law focuses on action/reaction pairs (forces) They NEVER cancel out Action: Earth pulls on YOU Reaction: YOU pull on the earth Action: HAMMER HITS NAIL Reaction: NAIL HITS HAMMER

Friction A force that resists the motion of one object sliding past another Always parallel to the surface Note: Friction ONLY depends on the MATERIALS sliding against each other, NOT on surface area.

Friction: Two Types Static Kinetic Friction that keeps an object at rest and prevents it from moving Kinetic Friction that acts during motion The coefficient of friction is a unitless constant that is specific to the material type and usually less than one.

Static Friction A force that resists the sliding motion of two objects that are stationary relative to one another. Frictional force must be calculated by applying Newton’s 2nd Law Equation for static friction is for the maximum value Coefficients of friction have been determined for different material surfaces

Kinetic Friction Friction when an object slides along another.

Friction: Example A 1500 N crate is being pushed across a level floor at a constant speed by a force F of 600 N at an angle of 20°below the horizontal as shown in the figure. a) What is the coefficient of kinetic friction between the crate and the floor?

Inclines Rotate axis to make it parallel and perpendicular to the surface Break weight into components Write equations of motion or equilibrium Solve

Inclines: Example Masses m1 = 4.00 kg and m2 = 9.00 kg are connected by a light string that passes over a frictionless pulley. As shown in the diagram, m1 is held at rest on the floor and m2 rests on a fixed incline of angle 40 degrees. The masses are released from rest, and m2 slides1.00 m down the incline in 4 seconds. Determine (a) The acceleration of each mass (b) The coefficient of kinetic friction (c) The tension in the string.