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Force and the resulting motion. Dynamics. Unification Theory). Force (Modern). Basic Idea of Forces. Push or Pull. Influence. Types of Influence. Contact. No contact. The push or pull is delivered through contact. Examples are kick, tug, punch, heave, friction, buoyant force, etc.

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Dynamics

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Force and the resulting motion

Dynamics

Unification Theory)

Force (Modern)

Push or Pull

Influence

Types of Influence

Contact

No contact

The push or pull is delivered through contact.

Examples are kick, tug, punch, heave, friction, buoyant force, etc.

The influence is delivered through space without contact.

Examples are magnetic, electric, gravity, etc.

Note

• Electromagnetic force results from the interactions defined by law of poles and law of charges, in the basic level.

• Involves the concept that a proton attracts an electron; an electron repels another electron.

• Gravitational force is present between matter as a result of their mass.

• Greater mass, greater gravity; reduce the distance by half, the force becomes four times as great.

Note

• Strong nuclear force keeps the nucleus together.

• Weak nuclear force rips apart nucleons into other particles: beta decay

• Involves the release of neutrinos and positrons

Fundamental Forces

http://ngm.nationalgeographic.com/2008/03/god-particle/achenbach-text

Newton’s Laws of Motion

Force (Classical)

Aristotelian

Why do objects differ in the way they fall?

A rock would fall faster than a leaf,

smoke tends to rise

and flame always point upward.

Generally motion in the vertical

Movement of celestial objects: stars, sun, moon, planets.

Movement that results from an application of an effort

Natural

Motion

Celestial Motion

Violent Motion

Aristotelian

For Aristotle, the natural tendency of an object is to be in its stable state (stay in its proper hierarchy).

For violent motion to persist, a constant effort must be exerted on the object.

Galilean

Wait, there’s a lot of problems in the natural setting. I will proceed with reason and experiments in my mind.

Thought Experiments

First Observation: The roughness of the surface (takes something) reduces the speed of the object

Thought Experiments

First Observation: The roughness of the surface (takes something) reduces the speed of the object

Thought Experiments

First Observation: The roughness of the surface (takes something) reduces the speed of the object

Rough surface

Smooth surface

Thought Experiments

First Observation: The roughness of the surface (takes something) reduces the speed of the object

Perfectly smooth surface

Thought Experiments

Second Observation: The motion of an object is affected by a slope

Thought Experiments

Third Observation: An object that is not moving will stay in that way unless an effort is exerted on it.

Galilean

Therefore I can say that no effort is required to keep an object moving. No effort is required to keep it at rest.

Galilean

That means, the natural tendency of every object is to maintain its state of motion.

I will call that property as inertia.

Inertia comes from the Latin word iners, which means idle or lazy.

Galilean

To change state of motion, apply an effort on the object.

If it resists, still that is inertia.

Galilean

To change state of motion, apply an effort on the object.

If it resists, still that is inertia.

I will make that into a law!!

Law of Inertia

• Born premature, three months after his father’s death, Isaac Newton Sr.

• At 3, his mother remarried. He was left at the care of grandparents. “Threatening my father and mother Smith to burn them and the house over them.”

• Early part of his education… a school drop out… Asperger syndrome.

• At 16, his mother (now widowed again) tried to make a farmer out of him. The legend of the falling apple.

• Returned back to school, “motivated partly by revenge to a schoolyard bully, he became the top-ranked student.”

• Undistinguished as a Cambridge student. Advancement in mathematics and science and all that came from it, including calculus and mechanics fundamentally grow from seclusion to self-study.

Newton’s Three Laws of Motion

Law of Inertia – every object maintains its state of motion unless a net force acts on it.

Law of Acceleration – the change in the state of motion of an object is directly proportional to the net force acting on it, but inversely proportional to its mass.

Law of Interaction – for every action, there is an equal but opposite reaction.

Law of inertia – every object tends to maintain its state of motion unless a net force acts on it.

So an object maintains its motion if there is no net force or zero total force acting on the object.

Review on the concept of resultant vector.

What is the resultant of the following vectors:

30 newtons East

50 newtons West

20 newtons East

Changes in the state of motion

• Change in the direction

• Change in the speed

• In short, changes in velocity are changes in the state of motion.

Summary

• Inertia is the resistance of an object to changes in its state of motion.

• Inertia is the property of matter to maintain its state of motion.

• Without external forces, an object at rest will remain at rest.

• Without external forces, a moved object will proceed in a straight line at constant velocity.

• Inertia is measured by mass.

Law of acceleration

Acceleration of an object is directly proportional to the net force applied on it but inversely proportional to its mass.

Problem: According to Law of Gravitation, greater mass results to greater gravitational attraction. Then why do objects fall at the same rate when one experiences greater force?

Summary

• Law of Inertia

• ΣF = 0 ; the object has zero acceleration (at rest, constant velocity

• Law of Acceleration

• ΣF = ma; the object is accelerated (the direction of acceleration is the same as the direction of the net force)

• Law of Interaction

• F action = F reaction

Variations on the Application of Newton’s Laws

• The simple force plus kinematics equation

• The Atwood machine

• The frictionless slope

• Friction plus the three above

Example

• A 1.0kg object is brought to Mercury where the acceleration due to gravity is 0.38 times its value on Earth.

• What is the weight of the object on Earth?

• What is the mass of the object on Mercury?

• What is its weight on planet Mercury?

Example

• A 10 kg object resting on a frictionless surface is subjected to two forces: F1=30N directed east and F2=50N directed west.

• Find its acceleration

• Find its displacement after 10s starting from rest.

Example

What is the acceleration of a 100kg object when subjected to a 10 N of force? If it starts from rest, what is its speed after 5 seconds? Ignore friction.

Quiz

If a force of 15.0 N directed East acts on a stationary 5.0 kg mass, what are its acceleration (include direction), displacement and velocity after 10.0 seconds?

Air resistance is air friction

• Dependent on the surface area that is perpendicular to the direction of motion

• Affected by streamlines

• Affected by the speed of the object

Review

• If forces are balanced, the net force is zero.

• If the net force is zero, the object is either at rest or at constant velocity.

Characteristics of Friction

• Independent of the surface area; generally not affected by the surface area

• Not affected by speed (though friction is less when the object started moving)

• Mostly dependent on the weight of the object; and,

• Nature of the surfaces in contact

• A reaction force; does not exist by itself

• Opposes the direction of motion or impending motion

Problem Solving in friction is fun

f – friction, whether static or kinetic

u- coefficient of friction of the surfaces

in contact

n – normal force

Guidelines

• If the object of analysis is not moving, the convention for positive and negative directions applies.

• If the object of analysis is accelerated, the positive direction follows the direction of acceleration (second law).

Solving an Atwood machine

What must be the acceleration of the system on the left if m1 = 5.00 kg and m2 = 8.00 kg? What magnitude of tension is present on the string? Assume that the pulley is frictionless.

m2

m1

Sample

Find the tension between m1=5.00kg and m2=8.00 kg below as they are pulled by a 500.N of force in the direction shown, if the coefficient of friction for both objects is 0.600.

Determine also the acceleration of the system as the force is applied.

500. N

m1

m2

Sample

• Block A weighs 2.70N and B weighs 5.40N. The coefficient of kinetic friction between all surfaces in contact is 0.25. Find the magnitude of force F necessary to drag block B to the left at constant speed.

A

F = ?

B

Sample

A 3.00 kg object slides down at a constant velocity of 2.00 m/s down a 3o.0o slope. What must be the coefficient of kinetic friction between the object and the surface?

Sample

A 1.00 kg book is pressed against a vertical wall. If the coefficient of static friction is 0.250, what minimum horizontal force is required to press it at rest on the wall?

F = ?

Exercises

• Solve Problem #3 and #9 on pages 102-103.

Seatwork (25 points)

• #4a and 4b15 minutes

• #5a5 minutes

• #5b5 minutes

• #5c5 minutes

#4

A 2.00 kg mass resting on a plane inclined at an angle of 40.0o with the horizontal is attached to a hanging mass by means of a frictionless pulley as shown. The hanging mass takes 1.62 seconds to fall through a distance of 1.52 meters starting from rest. What is the mass of the hanging mass if (a) the inclined surface is frictionless? (b) if coefficient of friction between the sliding mass and surface is 0.2?

#5

• Two blocks A and B are connected by a rope and attached to the ceiling by another rope. The mass of block A is 6.00 kg; the mass of block B is 4.50 kg. Find the tensions in the rope when the elevator (a) is at rest, (b) accelerates upward at 2.00 m/s2, and (c) accelerates downward at 2.00 m/s2