Newton’s Laws of Motion CHHS Physics Dept. Mr.Puckett

Unit Objectives After studying this unit the student will be able to explain and work problems on Newton’s 3 Laws of motion. Define inertia and compute problems with it. Differentiate between mass and weight. Explain why force and acceleration are proportional. Explain and diagram net force. Solve problems with Net force. Distinguish between force and pressure. Draw and label free body diagrams. Explain and ID why forces appear in pairs.

What is a Force? A Force is a push or a pull on an object. Forces are vectors because they have magnitude and direction. Force is equitable to energy in later chapters. Make a list of all the forces you can think of…. Think back to the elementary playground – your first physics lab.

Units of Force: The Newton A force is measured in terms of the acceleration it gives a standard mass. The SI unit of force in physics is named after the father of physics; Newton. The Newton (N) is defined as the force that will cause a 1.00 kg mass to accelerate at 1.00 meter per second squared. Proof: F = m a =(1.00 kg)(1.00 m/s2) = 1 kg x m/s2 = 1 N

The 4 Forces in Nature: There are four basic forces in nature: Gravity- the attractive force between all matter in the universe. Electromagnetic – the forces of attraction in atoms and magnets. The Strong nuclear force that keeps the nucleus together. The Weak nuclear force that causes radioactive decay.

Formulas: F = ma; Force = mass x accel. Weight = mg; Force of weight = mass X accel of gravity. NOTE: 1 g =1 gravity force and 2 g = 2 X gravity (2 x 9.8m/s2) etc. P= F/A; Pressure = Force/Area

Newton’s Laws Newton’s First Law Law of Inertia- Keeps doing what it’s doing, unless it is forced to change. Newton’s Second Law F = ma – the acceleration is proportional to the force applied to it. Newton’s Third Law Action/ Reaction – forces in pairs. For every action in nature there is an equal and opposite force.

Newton’s First Law Law of Inertia “A body remains at rest or moves in a straight line at a constant speed unless acted upon by a force.”

Newton's First Law of Motion – The Law of Inertia The name for this tendency is INERTIA - the tendency for an object to remain in the same state of motion (or rest). An object will continue in its state of rest or uniform motion in a straight line unless an outside unbalanced force acts upon it. When forces are balanced, there is no acceleration. All situations on Earth’s surface are called inertial reference frames. A non-inertial reference frame is one in which an object is in freefall or accelerating and may not obey the law precisely.

Newton’s Second Law F  a S F = (mass) a The Sum of the Forces acting on a body is proportional to the acceleration that the body experiences F  a S F = (mass) a

Newton’s Second Law of Motion: Force  Acceleration One of the most important formulas in all of physics is F = ma . This says that the summation of the forces on an object is directly proportional to the acceleration of the object. It says if you push hard on a basketball it goes fast and when you push easy, it goes slow….. You already knew that ! Force is a vector quantity and is the net force of the sum of all acting forces in all directions. The acceleration will vary directly with the net applied force and inversely with the mass.

Net Force Net Force The Net force is the sum of all the forces acting on an object from each direction.

Newton’s Third Law Action-Reaction For every action force there is an equal and opposite reaction force When you stand on the earth it pushes up equal to you pushing down.

Newton’s Third Law of Motion: Forces in Pairs. Forces in Pairs states that every balanced force in nature is accompanied by an equal and opposite force. Forces always are in pairs between pairs of objects. The action and reaction forces act on different bodies.  Examples are a rocket blasting off, a hang glider flying in air and you sitting in your desk. You push down on the chair and it pushes back up on you.

Weight vs Mass The weight of an object FW is the gravitational force acting downward on the object. Weight = FW = mass x gravity FW = ma = mg Mass is the amount of matter in an object. ( Number of atoms ), It can also be a measure of the inertia.

Weight and Mass: Mass is a measure of the inertia of a body. It depends upon the amount of matter contained within an object. The relationship between mass and inertia is direct. The unit of measurement for mass is the Kilogram (kg). Formula: m = F/a. Mass is CONSTANT. Weight is the gravitational force exerted object. Weight is a vector force and a negative symbol shows force in a downward direction. A medium apple weighs about one Newton. Formula: W (weight) or Fg = m x g. Weight changes according to where you are and the acceleration of gravity changes (outer space).

Which is variable? Mass or Weight? If you weigh 150 lbs on earth and you go to the moon; how much will you weigh? Since the moon is 1/6 as massive as the earth you will weigh 25 lbs. Your mass always stays the same… unless you lose atoms or body parts. How many kg body mass do you have to divide your pounds by 2.2 = kg

Weight in Newton’s In physics, we express weight in the unit of Newton’s. 1 Newton is defined as the force of 1 kg of mass accelerated by gravity. Formula: Weight = mass x acceleration. So a person with a 100 kg body mass has a weight of 981 Newton’s. How much do YOU weigh in Newton’s?

Free Body Diagrams Free Body Diagrams are pictures of how forces act upon an object or system. W is the weight and Fn is the normal force. T is tension.

Tension (Tensile Force) Tension is the force in a string, chain or tendon that is applied tending to stretch it. Like hanging from the monkey bars with your arms. Example: If you hang a box in the air by one rope the tension force (FT ) is the same as the weight: mass x acceleration ( due to gravity in vertical direction). If the box is held by 2 or more ropes, then the amount of tension is split between the ropes. FT

Normal Force The normal force on an object that is being supported by a surface is the component of the supporting force that is perpendicular to the surface. This is the force of the earth pushing back up against your feet. FN = FW

The Normal Force is the Earth’s response to Weight. Newton’s 3 law of action- reaction forces can be shown in the Normal force of the Earth pushing up against our weight.

The Law of Gravity Every mass exerts a force of attraction on every other mass. The math… G = 6.67  10-11 N·m2/kg2

Field Forces and the Inverse Distance Squared In a field force like gravity, magnetic and electrical fields; the force will vary by the inverse of the distance. Fg = 1/ d2 So if you double your distance: Fg = 1/ 2d2 = ¼ as much force.

Gravity Questions Did the Moon exert a gravitational force on the Apollo astronauts? What kind of objects can exert a gravitational force on other objects?

Typical Problems for Forces:

Vertical Forces in an Elevator Note how the motion increases and decreases the apparent weight on the scale.

Elevator Vertical Analysis The “UP” side. The “Down” side.

Tension in Ropes and Life Tension in physics is the forces we put through ropes – not the tests we give.

Frictional Force Friction is a force that opposes the motion of two objects that are touching each other. It does this by creating temporary electromagnetic forces between the contact points of the two surfaces. Friction acts in a direction parallel to the surfaces in contact and opposing the motion. The force exerted by a two surfaces touching is called a contact force. When a contact force acts perpendicular to the common surface of contact it is called a Normal Force (meaning perpendicular). Friction is independent of the areas of the surfaces in contact but is directly proportional to the mass.

What Causes Friction? Rough surfaces- a side view of smooth steel. Electrostatic attraction between atoms.

Friction Opposes Motion Note that the vectors of force / motion are opposite from friction.

Types of Frictional Force 1.        Static friction is the force of friction that resists the start of motion. This is always greater than the sliding frictional force. 2. Sliding friction (also called Kinetic Friction) is the force that resists the existing or continuing motion. 3. Air resistance is a special case of sliding friction. This is due to air molecules colliding with a moving object. Ff air v2. The air friction force is a square function of the velocity and in reality a function of the air density altitude. We ignore it in this course.

Friction in Life Kinetic Friction is opposing continued motion. Static friction is opposing the starting of motion.

Relationship between Static and Kinetic Friction.

Steps to Solve Force Problems a.       Read and label the problem. b.       Draw an accurate diagram (free body diagram). Show all forces exerting force on the object. c.       Choose a convenient x-y coordinate system for resolution of vectors. d.       Determine knowns and unknowns to assist in choosing equations. e.       Solve it roughly to get an idea of the range of reasonable answers. f.        Solve with equations. g.       Keep track of units throughout the equation and check the answer.

Teeter Totter Problem: Torque Force1 x distance1 = Force2 x distance2

Vector Analysis of Pulling a Sled with a 25o Angle

Force and Acceleration of an 80 kg Sled pulled at 25o with 150N

Tension analysis of a Sled

Forces on a Hanging Sign Note how the two ropes have unequal angles. This means they will support unequal amounts of the weight of the sign.

Analysis of a Hanging Sign

Special Case Problem: The Inclined Plane Please note the special case with the skier going downhill (Inclined plane) . When the axis is chosen for vector resolution it is slanted to a normal Cartesian system. This means that the vertical and horizontal components in the vector switch trig functions: Fx (parallel to surface) = mg sin  and Fy (perpendicular to surface) = mg cos . This switch allows us to identify the force causing the sliding down force as the vertical sine.

The Inclined Plane Note that when you have an incline that the normal force is no longer directly opposite to weight

Analysis of an Inclined Plane

Now Add Friction to an Inclined Plane.

Analysis of Friction on an Inclined Plane. Note the change in axis for vertical and horizontal in this special case.

Inclined Plane with Pulley

Inclined Planes with Pulley Analysis

Hooke’s Law: the Spring Constant. Hooke’s Law is the application of Newton’s second law F = ma to springs. Formula: F = - kx where k is the spring constant and x is the distance the displacement. The negative sign is the “restoring” convention

Hooke’s Law of Springs Examples

Hooke’s Law Problem

May the Force Be With You Mr. Puckett flying from Clinch Mountain Tennessee 1979