Physics Notes on Newton's Laws of Motion

I noticed that I have not described the rule of F=ma in either the last email or this one. Where would you suggest it be described? Somehow the details of adding forces and balanced forces were missed in the last email and also it did not make perfect sense for me to note. As far as I am concerned the khan academy does not lecture it so I am not too sure in what to do about this. I am assuming finding velocity is the sole purpose of applying the law of conservation of momentum. Is this true? I also would like to note that a graph could not be drawn in some situations again due to me lacking the technology to send photos of handwritten notes. Hence there is sadly no examples of a problem for translational equilibrium and for the force-time graph in which impulse can be identified. I also have referred to explosions as divisions. Is this appropriate?

Newton's First Law of Motion:

A body will remain at rest or moving with constant velocity unless acted on by an unbalanced force. Example: • Q: while traveling in train if one throws a ball up it lands on his palm though the train is moving. my doubt is that though the ball is detached from motion how does it manage to land on his palm though he is moving along with the train? • A: he ball lands on your hand because the ball is, in reality, traveling at the same velocity as the train, you, and everything else on, or part of the train. The ball is not at rest, because assume while the train was accelerating, you were holding the ball. Since you were moving with the train, then the ball is moving at the same velocity you are, and therefore, the same speed the train is moving. Translational Equilibrium: The condition for translational equilibrium is for all the forces acting on a body to be balanced

Newtons Second Law of Motion:

Momentum is the product of mass and velocity (p = mv). It is measured in kg m /s and is a vector quantity. Impulse is the change in momentum when an object reacts to clashing with an external force (momentum after – momentum before) The rate of change of momentum of a body is directly proportional to the unbalanced force acting on that body and takes place in the same direction. Example: • Q: There is a car with 500 KG mass and constant velocity 50 mph. As the car hits a wall what force will be applied on the wall? as the velocity is constant the acceleration would be zero and substituting in the second law F = 500 x 0 =0 • A: In the first question, the acceleration is not zero. It is zero before the car hits the wall, but when it hits the wall, the car will go from a speed of 50 mph to 0 mph in a very short space of time, which is a big deceleration (acceleration in the other direction), until it's speed is zero. The wall will experience an acceleration away from the car. Hence there is a substantial force.

Newtons Third Law of Motion:

If body A exerts a force on body B, Body B will exert an equal and opposite force on Body A. Example: • Q: I have a pen and I push it with an arbitrary amount of force. The pen will exert the same amount of force on me. So wouldn't the forces cancel? And wouldn't the pen not move at all? • A: The forces are equal, but that does not mean this is no reaction. F=ma says that the reaction on each object (you and the pen) due to equal forces will be based on yours and the pens masses. If you and the pen are of equal mass, you and the pen will receive equal acceleration, just in the opposite directions. In space (no friction), the pen will start to move in one direction and you will start to move in the opposite direction, the speed of each based on the individuals or objects mass.

The Law of Conservation of Momentum: Basically, this is just a combination of Newton's 3 laws but is useful when solving problems. For a system of isolated bodies, the total momentum is always the same. When solving problems for impulse and momentum; in a hypothetical situation (in order for this law to apply), where everything in space is isolated from the rest of the universe; momentum before and after are equal and therefore impulse is 0. Hence, pronumerals such as velocity is found by interpreting questions where different bodies may collide or where a body may divide. The area under a force (y-axis) – time (x-axis) graph is equal to the impulse.

Work, Energy and Power:

These are quantities which help explain what enables one body to push another. • Work: ° Work = force x distance moved in direction of the force. It is measured in newtonmetres (Nm), which is a joule (J). Work is a scalar quantity. ° In the cases of the force being non-constant, the formula for work would only apply if the average force is used. Hence, by use of a graphical method, the area under force-distance graph is equal to the work done • Energy: ° Kinetic energy (KE) is the energy a body has due to its movement. For a body to gain this it has to have work done on it. The amount of work that is done is equal to the increase in kinetic energy. A gain in this is expressed by the formula: mv^2/2 ° Gravitational potential energy (PE) is the energy a body has due to to its position above the Earth. A gain in this is expressed by the formula: mgh ° loss of KE = gain in PE, gain in KE = loss in PE ° The law of conservation of energy states that energy cannot be created or destroyed and it is only changed from one form to another. ° KE and PE are the two most basic forms of energy. When more complicated systems are learnt, there is a whole variety of different forms of energy in which to do work. Exaples include petrol, gas, electricity, solar and nuclear. ° Energy, collisions and division: * Elastic collisions are collisions in which both momentum and kinetic energy are conserved. * Inelastic collisions are collisions in which not all momentum and kinetic energy are conserved. Therefore, this has many outcomes. * Divisions are always inelastic because without any work and therefore increasing the KE, the segments that seperate after the division would not have any KE and would therefore not be moving. The energy to initiate a division often comes from the chemical energy contained within a body. • Power: ° Power is the work done per unit time. It is measured in J/s, which is a watt (W). Power is also a scalar quantity. • Efficiency: ° Efficiency = useful work out / work put in. It is not measured in any units and is a scalar quantity. ° Due to the law of conservation of energy, efficiency can never be greater than 1. ° The useful work out is found by the unbalanced force on the box. ° The work put in is found by the work done by the pulling force.

Uniform Circular Motion:

When describing motion in a circle we often use quatities reffering to the angular rather than the linear quantities. Centripetal acceleration is where the change in velocity of a body is directed towards the centre of a circle in the frame of its motion being circular. This is expressed by the formula: a = v^2 /2 Centripetal Force is the force acting on the body towards the centre of the circle. This is expressed by F = mv^2 /r

N = kg/m/s^2

F = ma.

Force is mass times acceleration.

Acceleration is change in velocity over time.

Velocity is distance over time.

So acceleration is change in distance over time over time, or distance over time squared.