Isaac Newton (1642-1727) 1687 Published Principia Invented Calculus 3 Laws of Motion Universal Law of Gravity
Newton s First Law (Law of Inertia) An object will remain at rest or in a constant state of motion unless acted upon by external net forces.
Inertia The resistance of an object to change its state of motion. A measure of mass or how much stuff an object has.
Newton s First Law If F = 0 => No Change in Motion Dynamic Equilibrium Static Equilibrium
Static Equilibrium Forces up equal the forces down. Forces sideways cancel too. F = y 0 F = x 0 T 1 T 2 W
Dynamic Equilibrium F = 0 If the Net Force is zero, then the object moves at a constant speed in dynamic equilibrium. W
Net Forces cause Acceleration
Newton s 2nd Law F = ma a = F net m The acceleration of object is directly related to the net forces acting on it and inversely proportional to its mass.
Newton s 2nd Law Units F = ma [ ] m kg 2 = = s N
Net Force Direction of applied forces matters!!! Opposite forces cancel!
Force Components F = ma F = ma F = ma x x y y Newton s Second Law is a Vector equation that can be broken down into scalar components. Since x and y directions are independent, Newton s Second Law can be expressed as independent x and y equations.
Problem Starting from rest, Sally pulls Billy on the sled (total mass = 60kg) with a total force of 100 N at an angle of 40 degrees above the horizontal, as shown. After 5 seconds, how fast is the sled moving and how far has it traveled from where it started? F x = ma x Fcos θ = ma x F cosθ ax = vf = v0 + at m Fcosθ 100Ncos 40 vf = v0 + at = t = 5 s= 6.38 m / s m 60kg
Support Forces-Normal Forces Support force is a reaction force and will balance the applied force until the material breaks.
Tension Forces Tension forces are transmitted undiminished through the rope. Different T Same T
Ropes and Pulleys are Massless until Chapter 11 & 12!
Frictional Forces Friction always opposes the applied force and is in the opposite direction of motion. The greater the normal force the greater the frictional force. f k = μ N k
Frictional Forces f k = μ N k Fig. 5.16, p.131
Air Resistance Air resistance is proportional to the size and speed of an object. WHY? The greater the cross sectional area of an object, the greater amount of air pushed out of the way the air pushes back! The faster an object falls, the faster it has to push the air out of the way the air pushes back! This is air resistance.
a Terminal Velocity When the air resistance balances the weight, the object stops accelerating and it falls with constant velocity called F Terminal Velocity. Net + = = W m m R R = W W m W = 0
Problem What is the acceleration of a sky diver when the air resistance equals ½ the total weight? a F Net = m W R = m W W /2 = m mg mg /2 = = g /2 m R + W
Newton s 3rd Law F hand on wall = F wall on hand To every force there is an equal but opposite reaction force.
Newton s 3rd Law F hand on wall = F wall on hand You can t TOUCH without being TOUCHED back!!
Newton s 3rd Law F hand on wall = F wall on hand This is an INTERACTIVE Universe.
Gravity is an Interaction F Earth on Rock = F Rock on Earth
Newton s 3 Laws of Motion 1. If F = 0 No change in motion 2. = ma Change in motion Fnet v v 3. F = F 1 on 2 2 on 1
Solving Force Problems 1. State the knowns and desired unknowns. 2. Draw a force vector diagram, label everything and define direction. 3. Solve for the components of each force. 4. Use F net = ma on each direction to generate equations. 5. Derive a solution in terms of the given knowns. 6. Enter the numbers and solve for the desired unknown.
Force Vector Diagrams Show all the External forces acting ON the body only.
Force Vector Diagrams Align axes to simplify the problem!
Force Vector Diagrams Different Strings: Different Tensions!
Force Vector Diagrams Draw free-body diagrams for every object! Note: T and a are the same! Ropes connected by ideal pulleys have the same tension everywhere!
Force Vector Diagrams Tackle & Pulley Continuous Rope has same T everywhere! What is T?
Problem The magnitude of F 1 is 75.0N and F 2 is 50.0N. Ignore friction. What is the acceleration of the block? What if the coefficient of friction between the block and the floor is 0.04. How do you know which direction to put the friction?
Statics Problem Find the tensions in the wires. +y +x T 1 43 55 T 2 W
The Inclined Plane Orient your axes relative to the plane!!! Fig. 5.19, p.134
Inclined Plane Problems What is the acceleration of a box going down a frictionless incline? Convince yourself that the angle of the incline goes here
You Try: Incline Plane Problem Draw a free-body diagram of a block which slides down a frictionless plane having an inclination of = 15.0. If the block starts from rest at the top and the length of the incline is 2.00 m, find (a) the acceleration of the block and (b) its speed when it reaches the bottom of the incline.
What does the Scale Read?
Pulleys, Masses, Strings What is the acceleration of the system? (If they are connected, it is the same for both masses!) What is the tension in the string? 1. If it falls from rest 2. If it is dragged to the left 3. If the string is cut FIRST: Draw free-body diagrams for each mass!!!
Pulleys, Masses, Strings What is the acceleration of the system? (If they are connected, it is the same for both masses!) What is the tension in the string? 1. If it falls from rest 2. If it is dragged to the left 3. If the string is cut FIRST: Draw free-body diagrams for each mass!!!
Problem A force F = 40 N pulls the two masses. If the table is frictionless, find the tension in the string. m = 3 kg, m = 1.5kg a) 13 N b) 36 N c) 23 N d) 15 N e) 28 N 1 2
Problem A constant force F pulls the system as shown. The pulleys are frictionless. The coefficient of kinetic friction between the block and the table is μ. a) Draw free body diagrams for both masses. b) Find an expression for the acceleration in terms of the given variables.
Problem m = 2 kg, m = 3 kg, m = 5kg 1 2 3 The three blocks are pushed across a rough surface by a 40-N force. If the coefficient of kinetic friction between each of the blocks and the surface is 0.20, determine the magnitude of the force exerted by m2 on m3. a) 20 N b) 30 N c) 10 N d) 15 N e) 25 N
Problem In the figure shown, the coefficient of kinetic friction between the block and the incline is 0.29. What is the magnitude of the acceleration of the suspended block as it falls? Disregard any pulley mass or friction in the pulley. Draw the free body diagrams for each mass. Derive a general solution for the acceleration in terms of M, and g, box it, then put the numbers in and get a numerical value then box that too. Then find a numerical value for the tension in the string. Box that. Show all your work and make it pretty! Use 3 significant figures. 2M 2M 30 30 M
Tension Two 10 N weights are pulling on the spring scale as shown (the right side is attached to a hook, the left side is attached to the body of the scale) What does the scale read? a) 0 N b) 10 N c) 20 N
Newton s 3rd Law F hand on wall = F wall on hand To every force there is an equal but opposite reaction force.
Newton s 3rd Law F hand on wall = F wall on hand You can t TOUCH without being TOUCHED back!!
Newton s 3rd Law F hand on wall = F wall on hand This is an INTERACTIVE Universe.
Gravity is an Interaction F Earth on Rock = F Rock on Earth
Gravity is an Interaction The Earth pulls on you, you pull on the Earth. You fall to the Earth, the Earth Falls to you. You accelerate towards the Earth with g =9.8m/s 2. With what acceleration is the Earth falling towards you? F This is your weight: Earth on You mg a = F = M a = mg You on Earth E M E (65 kg)(9.8 m / s 2 ) a = = 1.1x10 22 m/ s 2 E 5.98x10 24 kg E E
Force is not Acceleration Force is the Same! Acceleration is NOT! F Earth on You = F You on Earth a Earth to You = a You to Earth
An interaction requires a pair of forces acting on two objects. kick Gun Pushes Bullet out. Bullet Pushes back on Gun (& Man)
Action Reaction Pairs kick Gun Pushes Bullet out. Bullet Pushes back on Gun (& Man)
Rocket Thrust Rocket Pushes Gas Out. Gas Pushes Back on Rocket.
Question You push a heavy car by hand. The car, in turn, pushes back with an opposite but equal force on you. Doesn t this mean the forces cancel one another, making acceleration impossible? How is it that the car moves? The System Action-Reaction forces act on different objects. For F = ma, the forces must act on ONE object: the system.