FORCES AND NEWTONS LAWS Force A force is

FORCES AND NEWTON’S LAWS

Force A force is a push or a pull. It is the cause of an acceleration, or the change in an object’s velocity It is measured in Newtons (N) which is the amount of force need to accelerate 1 kg by 1 meter/s 2

Two Categories of Forces • Contact Force – Force that arises from the physical contact of two objects • Examples: friction, applied force • Field Force – A force that can exist between objects, even in the absence of physical contact between the objects • Examples: gravitational, electromagnetic

Newton’s First Law • Law of Inertia – an object at rest will remain at rest, and an object in motion will continue in motion with constant velocity unless acted on by some outside force. * Inertia is the tendency of an object to maintain its state of motion and resist changes in velocity and acceleration * Mass is the measure of an object’s inertia

Newton’s Second Law • F = ma; the acceleration of an object is directly proportional to the net force on it and inversely proportional to its mass. * Net external force – the total force resulting from a combination of external forces on an object. * Equilibrium – the state in which there is no change in a body’s motion, when the sum of the net external forces is zero.

Is there a difference between mass and weight? The answer of course is … yes!! Mass – the amount of matter or inertia an object has. No matter where you go in the universe your mass does not change. Weight – the magnitude of the force of gravity acting on an object. W = mg If you go to the moon you will lose weight and if you go to Jupiter you will gain weight.

Galileo proposed is was friction that caused a moving object to come to rest. Newton further noted that a force was not necessary to keep an object in motion. A force is required to bring it to rest.

Free Body Diagrams Tension Force (Ft) Gravitational Force (Fg) • Shows the forces acting on the object of interest • Assume all forces act on a point at the center of the object • Position object like it is, i. e. , on angle, etc. • Draw and label vector arrows representing all external forces acting on the object Ften= Tension Fair= Air Resistance Fnorm= Normal Force Fg= Gravity Ff= Fricitional Force FNet = Ft - Fg

Free Body Diagrams Tow Cable Force (Ftc) Road’s upward Force (FN) Frictional Force (Ff) Gravitational Force (Fg) FNet = ∑F • Force of towing cable • Gravitational Force • Road exerts upward force • Backward Friction force

Equilibrium The state in which there is no change in a body’s motion, when the sum of the net external forces ∑F is zero FNet = ∑F = ma FNet x = ∑Fx FNet y = ∑Fy We must resolve the forces into X and Y components to know if the object is in equilibrium. We can also then calculate the magnitude and direction of the net external force on the object if it is not in equilibrium.

4 N Equilibrant Force 3 N 5 N at 38° 5 N at 218° Equilibrant Force Net Force • The equilibrant force is the force that when added to a system will bring it to equilibrium • The equilibrant force is equal in magnitude and opposite in direction of the resultant (or net) force.

Practice Problem A crate is pulled to the right with a force of 52 N, to the left with a force of 36 N, upward with a force of 120 N, and downward with a force of 180 N. Draw a free body diagram of the crate. Find the net external force in the X direction. Find the net external force in the Y direction. Find the magnitude and direction of the net external force on the crate. Find the magnitude and direction of the equilibrant force.

Normal Force • Normal Force – a force that is exerted by one object on another in a direction perpendicular to the contact surface. • FN is just enough to maintain contact without “sinking” in • Normal force is equal in magnitude to gravitational force on a horizontal surface

Normal Force For an inclined plane - the normal force equals the gravitational force times the cosine of the angle of the incline FN = Fg cos ɵ FN = mg cos ɵ

Newton’s Third Law For every action there is an equal and opposite reaction. Action-Reaction Pairs Rocket boosters thrust down and the shuttle goes up!!!

Net Force vs Action-Reaction Pairs Action – reaction pairs work on different objects and they are always equal and opposite. The net force is the sum of all forces on the same object and it causes acceleration Equilibrant Force – A force that is equal and opposite to the net force; the force that will bring the system into equilibrium.

Four Types of Non-Contact Forces 1. Gravitational Force – attractive force that exists between all objects; weakest of the four forces, but acts over the greatest distance. 2. Electromagnetic Force – gives materials their strength, ability to bend, squeeze, stretch, etc. 3. Strong Nuclear Force – holds the particles in a nucleus together; strongest of the four forces, but acts over the shortest distance. 4. Weak Force – involved in the radioactive decay of some nuclei; form of the electromagnetic force.

Gravitational Force • Gravitational Force is two way – earth exerts a gravitational force on a falling object, the object exerts a gravitational force on earth. • Force of a 0. 2 kg apple falling equals mass times acceleration so 0. 2*9. 81 equals 2. 0 N • How much does that accelerate earth with a mass of 5. 97 X 1024? 3. 4 X 10 -25 m/s 2

Frictional Force – force that opposes motion between two surfaces that are in contact. ◦ Static Friction – force that opposes the start of motion (starting from a stationary position) ◦ Sliding (Kinetic) Friction – force that opposes motion once the object is moving. Static Friction is greater than sliding friction because of Newton’s First Law.

Friction Ff = µFN where µ is the coefficient of friction • Friction Force depends on the surfaces in contact µs µk Wood on wood 0. 5 0. 2 Waxed wood on wet snow 0. 14 Ice on ice 0. 1 0. 03 0. 1 • Friction Force is proportional to the normal force

Friction in One Dimension F = ∑FProblems = mass x acceleration Net Fapplied – Fopposing = ma When moving at constant velocity (zero acceleration), the applied force required is equal in magnitude to the frictional force When accelerating, the applied force required is equal in magnitude to the frictional force plus the force required for acceleration

Free Body Diagram FNet = Fa - Fo Force Applied (Fa) Force Opposing (Fo) The opposing force is the weight if lifting something ma = Fa - W

Free Body Diagram Force Normal (FN) Frictional Force (Ff) The opposing force can be friction FNet = FN - W Applied Force (Fa) Weight (W) ma = FN – W FN = W , a = 0 FNet = Fa - Ff ma = Fa - Ff

m 1 a = T – W 1 T W = m 1 g 0. 1 a = T – 0. 1 (9. 8) - m 2 a = T – W 2 T W = m 2 g - 0. 2 a = T – 0. 2 (9. 8)