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The History of Dynamics

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Natural motion was caused by some internal quality of an object that made it seek a certain “preferred” position without any application of force. The Greeks

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Unnatural motion was anything else. Unnatural motion was thought to require applied force to be sustained. The Greeks

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Natural motions were divided into two categories: Terrestrial (near the earth) Celestial (in the heavens) The Greeks

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Aristotle taught that an object’s “heaviness” determined how “vigorously” it sought its natural place. The Greeks

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began by collecting facts and establishing a description of motion This is called kinematics. Galileo then inductively developed workable theories of dynamics. Galileo

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Experiments showed that the rate at which an object falls is not proportional to its size or mass. Astronauts later verified his theory on the moon. Galileo

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a hypothesis based on conjecture rather than observation, usually in an attempt to explain a natural phenomenon Ad hoc

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Galileo’s experiments of “unnatural” motion indicated that the “natural” state of motion of an object could include moving as well as resting. Inertia

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Galileo’s Principle of Inertia: An object will continue in its original state of motion unless some outside agent acts on it.

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Inertia A moving object does not require a continuous push to maintain a constant velocity! A push causes a change in an object’s motion.

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built on the work of others studied gravitation Principia only in recent decades have scientists discovered any exceptions to his work Newton

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Forces

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Summing Forces Forces are often described as “pushes” and “pulls.” Forces are vectors. Forces can be added just as vectors are added.

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Summing Forces Notation: ΣF ≡ F 1 + F F n The Greek capital letter sigma (Σ) is used to indicate a sum.

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Summing Forces If forces are balanced... ΣF = 0...and no change in motion will occur. ΣF = 0 ↔ ΣF x = 0 and ΣF y = 0

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will change an object’s state of motion there may be two, or more than two, forces which are unbalanced Unbalanced Forces

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To find the sum of unbalanced forces, you add the force vectors acting upon the object. This usually involves finding and adding the vector components. Unbalanced Forces

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Equilibrant Force a force that balances one or more other concurrent forces

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Equilibrant Force a vector having the same magnitude as the vector sum of the other unbalanced forces but pointing in the opposite direction F equil. = -Σ F other

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Equilibrant Force If the sum of all forces on an object is zero, then any unknown force must be the equilibrant of all the known forces.

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Weight the force of gravity acting on an object a vector pointing straight downward often notated F w

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Types of Forces All forces are classified as either fundamental forces or mechanical forces. There are four fundamental forces.

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Fundamental Forces Gravitational force proportional to the masses of interacting objects can exert its influence over theoretically infinite distances

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Fundamental Forces Gravitational force all objects exert gravitational force on all other objects

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Fundamental Forces Electromagnetic force used to explain both magnetism and electricity a long-range force a short-range force

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Fundamental Forces Strong nuclear interaction force Weak nuclear interaction force

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Classification of Forces Noncontact Forces gravity electromagnetic forces sometimes called “action-at-a-distance” forces

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Classification of Forces Noncontact Forces field theory attempts to explain these virtual particles have been offered as an explanation

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Classification of Forces Contact Forces transmitted only by physical contact between objects include the following:

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Classification of Forces tensile (pull things apart) compressive (push things together or crush) torsion (twist)

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Classification of Forces friction (oppose motion between two objects in contact) shear (cause layers within matter to slide past one another)

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Measuring Forces instruments used include: spring scale load cell pressure gauge

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Measuring Forces instruments used include: ballistic pendulum accelerometer force table

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Newton’s Laws of Motion

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These are the central principles of dynamics. Their proper use requires an understanding of what a system is. Newton’s Laws

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In physics, a system is whatever is inside an imaginary boundary chosen by the physicist. It is isolated from its surroundings. Systems

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A system at rest will remain at rest, and a moving system will move continuously with a constant velocity unless acted on by outside unbalanced forces. Newton’s 1 st Law

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If all external forces on a system are balanced, then its velocity remains constant; the acceleration is zero. Newton’s 1 st Law

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If all forces acting on a system are not balanced, then a nonzero resultant force exists and the velocity changes, resulting in an acceleration. Newton’s 1 st Law

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Stated mathematically: Newton’s 1 st Law Σ F = 0 ↔ a = 0 Σ F ≠ 0 ↔ a ≠ 0 or equivalently:

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Friction is a force that causes motion to change. Inertia is the tendency for a system to resist a change in motion. Newton’s 1 st Law

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Mechanical equilibrium occurs when the sum of all forces on a system is zero. Without unbalanced forces, objects tend to move in straight lines. Newton’s 1 st Law

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the most general of the three laws gives a working definition of force and a way to measure such force Newton’s 2 nd Law

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The acceleration of a system if directly proportional to the sum of the forces (resultant force) acting on the system and is in the same direction as the resultant.

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Newton’s 2 nd Law Stated mathematically: Σ F = m a a = ΣFΣF m or equivalently:

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Newton’s 2 nd Law A resultant force of 1 N, when applied to a mass of 1 kg, produces an acceleration of 1 m/s². This is how the Newton, a derived unit, is defined.

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Newton’s 2 nd Law component equations: Σ F x = m a x Σ F y = m a y Σ F z = m a z

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Newton’s 3 rd Law If system X exerts a force on system Y, then Y exerts a force of the same magnitude on X but in the opposite direction. F X→Y = - F Y→X

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Newton’s 3 rd Law forces have four properties that relate to this law: All forces occur in pairs. Each force in an action- reaction pair has the same magnitude.

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Newton’s 3 rd Law Each force acts in the opposite direction in line with the other force of the pair. Each force acts on a different system.

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Weight and Mass The force of planetary gravitational attraction on an object is called its weight, F w. Weight is directly proportional to mass. F w = am

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Weight and Mass Since this gravitational acceleration is downward: F w = mg g = m/s² The magnitude of an object’s weight vector is |mg|.

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Weight and Mass The weight vector, like the gravity vector, points straight down (toward the center of the earth). In scalar component form: F wy = mg y

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Weight and Mass Mass is measured on scales and reported in units of kg or g.

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