Forces

What is a Force? A force is a push or pull acting on an object that changes the motion of the object.

Types of Forces Contact Force – Forces that act through direct contact between two objects Applied Forces, Friction Long Range Forces – Forces that can act over distances Gravity, Electromagnetic Force (EMF)

Newton’s Second Law of Motion Newton discovered the idea of a Force He found the Force is proportional to the Acceleration of an object (more Force = more Acceleration) He found the Force is proportional to the mass of the object (more mass = more force needed).

Newton’s Second Law of Motion Moving objects accelerate when an unbalanced force (F) acts on them. The stronger the force, the greater the acceleration (a). Also, the greater the mass (m) the greater the force required to change the motion. Force = mass x acceleration F = ma

Newton’s Second Law of Motion Force is a Vector Quantity and therefore has magnitude and direction. The direction of the force is the same as the direction of the acceleration.

S.I. Unit For Force The Unit for Force is a Newton (N) 1N = 1kg m/s 2 A Newton (N) is defined as the amount of force required to accelerate 1 kg of mass at a rate of 1 m/s 2.

Net Force When Multiple forces are acting on an object. The Net Force is the amount of force that is left after adding all the forces on the object. Net force (F NET ) = Resultant Force (F R )

Balanced Forces Balanced Forces are forces that are equal and opposite so that they cancel out. 10 N East 10 N West  Net Force = +10 N N = 0

Unbalanced Forces Unbalanced Forces are forces that when added do not cancel out and cause a change in the motion of the object. 30 N East 10 N West  F net = +30 N N = +20 N East

Inertia Inertia measures the tendency of an object to resist changes in motion. Galileo came up with the idea of inertia Objects do not want their motion to change Mass measures how much inertia an object has (More mass = More inertia)

Newton’s First Law of Motion (Law of Inertia) If no unbalanced forces act on a moving object, then the object will continue to move with a constant velocity (constant speed in a straight line). If an object is at rest it will stay at rest. Newton took his concept of forces and combined it with Galileo’s idea of inertia

Equilibrium First Condition for Equilibrium If the Net Force acting on the object is zero F NET = 0 a = 0 The object is either stationary (v = 0) or traveling with a constant velocity (v = constant)

Free Body Diagram (FBD) A diagram that looks at all the forces acting on a single object. A FBD has all the forces labeled with their magnitude and direction as well as the motion of the object.

Mass and Weight Mass is amount of matter that an object possess. Mass does not change with location. Weight is the gravitational force that a large body (such as a planet) exerts on another object.

Weight Weight is a Force! It is measured in Newtons. Weight = Mass x Acceleration due to Gravity (Newton’s 2 nd law) W = mg Weight does change with location! (“g” will change with location)

Solving Net Force Problems 1. Make a Free Body Diagram (Label all forces and the acceleration of the object) 2. Use the following Equations to solve for the unknown F NET (x-direction) = ma x F NET (y-direction) = ma y f =  F n

Microgravity Microgravity is the illusion of weightlessness experienced in freefall. (All objects are falling at the same rate) Apparent Weight is the weight a scale gives you but may change if are not in equilibrium.

Friction Friction resists motion. Friction causes moving objects to slow down. Friction produces heat.

Friction 1. Static Friction – occurs between stationary surfaces in contact. 2. Sliding Friction – occurs when one surface slides over another. 3. Rolling Friction – occurs when a rounded surface rolls over another.

Ways to Reduce Friction Use wheels or rollers Lubricants - produce a smooth layer between the surfaces Sanding the Surfaces – smooth the surfaces

Friction and Newton’s Laws Friction is a force (Newton’s laws apply) Friction causes an acceleration (slowing down the motion of an object) Friction always acts parallel to the surface in the opposite direction of motion

Calculating the Frictional Force Friction depends on: 1. Forces acting between the surfaces (Normal Force) 2. Nature of the surfaces (Coefficient of Friction)

Calculating the Frictional Force Normal Force (F N ) – Force that acts perpendicular to the surface and away from the surface The Normal Force (F N ) is usually found by summing the forces in the y-direction

Calculating the Frictional Force Coefficient of Friction (  ) – describes how rough/smooth the surfaces are Rough Surfaces – High value of    > 0.5 Smooth Surface – Low value of   < 0.5

Calculating the Frictional Force The frictional force is the product of the coefficient of friction and the normal force Frictional force = (Coefficient of Friction) x (Normal Force) f =  F N

Air Resistance Free Fall – The situation where gravity is the only force acting on an object (Assume No Air Resistance) Air Resistance – The force the air applies on a moving object. It attempts to slow down falling objects (similar to friction)

Air Resistance and Terminal Velocity Terminal Velocity – The maximum speed a falling object reaches when dropped from rest An object reaches terminal velocity when the force of gravity is balanced with the force of air resistance

Air Resistance and Terminal Velocity 1. An object is dropped and at first the force of gravity (W) is much greater than the force of Air Resistance (F AR ) W >> F AR 2. The force of Air Resistance (F AR ) increases as the speed of the falling object increases

Air Resistance and Terminal Velocity 3. Eventually the force of Air Resistance is equal and opposite to the force of gravity and the Net Force acting on the falling object is zero. W = F AR Therefore F NET = 0

Air Resistance and Terminal Velocity 4. Since the Net Force acting on the object is zero, the object continues to fall but falls the rest of the way at a constant velocity (Newton’s First Law). This velocity is called the Terminal Velocity!

Air Resistance and Terminal Velocity F NET = 0 and F = ma therefore a y = 0 Object falls with a constant velocity (Terminal Velocity) Note: Terminal Velocity can be a Maximum or a Minimum!

Periodic Motion and Simple Harmonic Motion Periodic Motion - motion that repeats back and forth through a central position Simple Harmonic Motion (SHM) – periodic motion where the Force is proportional to the displacement from the equilibrium position (F  d)

Simple Harmonic Motion (SHM) In Simple Harmonic Motion the Net Force at the equilibrium position is zero. When the object moves away from the equilibrium position a Restoring Force pulls the object back. As “d”  then “F”  Examples; Spring, Pendulum

Simple Harmonic Motion (SHM) Objects in SHM can be described with two quantities. Period (T) – the time needed to complete one cycle of motion Amplitude (A) – is the maximum distance the object moves from the equilibrium position

Springs Hooke’s Law – the Force of a Spring is proportional to the distance from the equilibrium position F S = kd F S = Restoring Force of the Spring d = displacement from the equilibrium position k = spring constant for that particular spring

Period of a Spring To find the period of a spring (T S ) in simple harmonic motion: T S = 2  (m/k) 1/2 (Square Root) m = mass of the spring k = spring constant

Pendulums A Pendulum is a mass attached to a string or wire of length (L) that swings back and forth through the equilibrium position A pendulum swinging through small angles is an example of SHM

Pendulums Gravity is the restoring force and is proportional to the distance away from the equilibrium position The components of gravity change as the pendulum moves back and forth resulting in F g  d

Period of a Pendulum The Period of a Pendulum (T P ) can be found with; T P = 2  (L/g) 1/2 Square Root The Period of the Pendulum depends only on the length and the acceleration due to gravity (Not the mass)

Resonance Resonance is increasing the amplitude of vibration by adding a small force at regular time intervals Examples: Swing (Pendulum), and Sound

Newton’s Third Law of Motion States: Every Action has an equal and opposite Reaction. Forces always come in pairs! Action-Reaction Forces always occur between two objects.

Four Fundamental Forces of Nature 1. Gravity – Force of attraction between any two masses. Weakest of the fundamental forces but acts over the largest distances. 2. Electromagnetic Force (EMF) – force between charged particles. Stronger than gravity but does not reach as far. (Like charges repel, opposite charges attract)

Four Fundamental Forces of Nature 3.Strong Nuclear Force – Force of attraction between subatomic particles inside the nucleus. Strongest force in Nature but only acts inside the nucleus (shortest distance). Holds the atom together.

Four Fundamental Forces of Nature 4. Weak Nuclear Force – is the force observed in the radioactive decay of some elements Unification Theory – This theory looks to unify all the fundamental forces to a single unified force.

Forces on Ropes and Strings Tension (T) – is the force acting along a rope or wire. Tension always acts away from the object along the rope. Newton’s Third Law applies to Tension when looking at two objects. Only One Tension needs to be drawn on a Free Body Diagram