Dynamics – Notes

1. Introduction
    
1. Dynamics is the branch of mechanics that deals with the causes of motion.
2. Essentially this is a study of forces.
         
1. A force is a push or pull capable of causing a mass to accelerate.
2. The Four Fundamental Forces
1. Science has classified forces into 4 fundamental categories.
        
1. Gravitational Forces
            
1. Gravity is an attractive force that exists between any two masses in the universe.
2. The greater the mass of the two objects the greater the gravitational force that exists between them.
3. Therefore the total number of subatomic particles an object contains is the basis for the gravitational force.
4. Gravity is the weakest of the four fundamental forces but acts over the greatest distance.
2. Electromagnetic Forces
            
1. E-M forces can be attractive or repulsive forces that exists between charged objects.
2. E-M forces are determined by the number of charged particles (protons (+) or electrons (-)) an object posses.
3. This consist of the common forces we see in our daily lives such as friction, tension, shear, compression, normal forces, etc.
3. The Strong Nuclear Force
            
1. The strongest of the four fundamental forces.
2. The strong nuclear force exists inside the nucleus of the atom. It is the force that binds the protons and neutrons of the nucleus together despite the natural repulsion of the protons from each other.
4. The Weak Nuclear Force
            
1. Is a second force found inside the nucleus of the atom.
2. Physicists believe it is responsible for the radioactive decay of atoms.
3. Some physicists believe that this is simply another example of the electromagnetic force and have combined these two fundamental force into what is know known as the electroweak force.
2. Scientists searching for a Grand Unified Theory (GUTs) believe that the similarities among the four forces (all having their origin inside the atom) is a promising step to developing a theory.
        
1. One of these current theories is known as the Super String Theory.
3. Newton’s Laws of Motion - The first person to study the relationship between forces and the acceleration they cause was Isaac Newton who published his findings in 1687.
1. The First Law of Motion – The Law of Inertia
        
1. A mass will maintain its current state of motion unless it is acted upon by a net external force.
            
1. Therefore an object at rest will remain at rest until a net external force causes it to change its motion.
2. An object traveling at 10 m/s W will not deviate from this path or speed until it is acted upon by a net external force.
2. This resistance to changes in motion has been termed – INERTIA.
           
1. All masses posses the property of inertia
2. The amount of inertia can be determined by measuring the mass of the object. (i.e. mass = inertia)
3. An objects mass, and therefore its inertia, is a fundamental property of the object and will remain constant regardless of location.
3. Mass vs. Weight
            
1. While mass is a measure of inertia, weight is a force.
2. Weight is a measure of the pull of gravity on an object. As such an object’s weight will change with location.
3. Although mass and weight are two different quantities they are related to each other. Weight is directly proportional to an object’s mass. The more massive the object the greater its weight.
4. For example a 1 kg mass on earth has a weight of 9.8 N (2.2 lbs), while on the moon the mass is still 1 kg but its weight is now 1.63 N (0.455 lbs).
4. Remember an object’s weight may change in different locations but its inertia (resistance to changes in its motion) will remain unchanged regardless of location.
            
1. Therefore it will be just as difficult to push an object on the moon as it is here on earth.
2. The Second Law of Motion – The Law of Acceleration
        
1. The second law is summed up by the formula F = ma. The force imparted to an object is equal to the mass of the object times the acceleration of the object.
2. It is important to note the relationships inherent in this formula.
            
1. If mass is held constant force is directly proportional to the acceleration (F a a). If the force is doubled, the acceleration doubles.
2. If force is held constant mass is inversely proportional to the acceleration (m a 1/a). If the mass doubles, the acceleration is cut in half.
3. If acceleration is held constant force is directly proportional to the mass (F a m). If the mass doubles the force doubles.
3. These relationships are important to understanding the results of physical events.
            
1. If an identical force is applied to 2 objects the object with the least mass will undergo the greatest acceleration.
4. The unit for force in the metric system is the Newton (N) named for Isaac Newton.
            
1. A newton is defined as a kilogram times a meter per second squared. N = kg m/s²
2. Since weight is a force it is also measured in newtons in the metric system.
3. The second law may be used to convert between mass and weight in the following form: W = mg. Where "W" is weight, "m" is mass, and "g’ is the acceleration due to gravity.
Example: How much does a 1 kg mass weigh?
W = mg
W = 1 kg X 9.8m/s²
W = 9.8 N

4. Remember the conversion factor 1 kg = 9.8 N = 2.2 lbs.
3. The Third Law of Motion – The Law of Interaction
1. It states for every action there is an equal but opposite reaction.
2. This law may also be phrased as, "If object A exerts a force on object B, then object B will exert a force on object A.
3. This indicates that forces must always occur in pairs. These action-reaction pairs are created by the interaction of two different masses. As soon as there is no more interaction, there is no more force.
4. For example:
            
1. A boy punches a wall. The reaction is the wall produces a force on the boy’s hand. The force on the wall and the force on the hand are of equal magnitude. If it is a solid wall, the boy’s hand will undergo a greater acceleration (in the form of muscle deformation or broken bones) as a result of its smaller mass (2^nd Law)
2. A boy punches a paper bag. The reaction is the paper bag produces a force on the boy’s hand. As a result of this interaction a much smaller magnitude force pair is produced. If the bag tears when 50 N of force is applied to it then the maximum force the boy can hit the bag with is 50 N because there is no more interaction after the bag tears. In this case the bag undergoes the greater acceleration as a result of its smaller mass.
5. This leads to the conclusion that you can only hit an object as hard as it can hit you back.