Newtons Problems

These days in physics class, we're learning new stuff about Newton. First of all, he devised 3 laws:

1. The law of inertia : Things don't like to stop doing what they're already doing (lazy) e.g if the object is moving it doesn't like to stop and if the object is still, it doesn't like to get up and move.

2. Force = Mass x Acceleration

3. For every action, there's an equal and opposite reaction.

With these three laws, there are many different questions known as "Newton Problems" that can be devised. The four simplest ones being objects in equilibrium, objects static on an incline, objects kinetic on an incline, pulleys, and trains.

EQUILIBRIUM

When an object is considered to be in "equilibrium" it means that the object is in a state where all the forces acting upon it are balanced and it is stationary. No acceleration in the x OR y direction is present.

Therefore, for these types of questions, the resultant Force (net force) should equate to zero; or at least very close to 0.



An object in equilibrium



Assumptions for equilibrium questions:

-no air resistance/friction

-no acceleration in the x or y direction

-1 free body diagram in total

-Fg = mg = m(9.8) = Fn, in which Fn is the force keeping the object up

-there's a constant positive axis

-forces acting on the x-axis are equal on both directions





STATIC INCLINE

When an object is static while being on an incline, this means that the object is on a slant, at an angle just before the force of gravity overcomes the force of the friction pulling it back. The object is still in equilibrium, there is no acceleration in either the x or y direction.

Therefore, for these sorts of questions, the sum of all forces acting upon the object should still equate to 0.

Assumptions for static incline:

-no air resistance

-no acceleration in the x or y direction

-1 FBD

-positive axis on a slant dependent on the direction the incline is facing (if the incline is like /, the left will be positive)

-Friction static = miu static x Force normal, in which miu static is the coefficient of friction in this case (also the tan of theta [the angle measured for the incline])

-gravity is split into the x and y component (y is usually opposed by the normal force and x is usually opposed by friction)

KINETIC INCLINE

When the object is kinetic on an incline, this means there is acceleration and there IS motion of the object (due to gravity) as opposed to static when the object is held still by friction. In this case, there is also friction, but it is overpowered by gravity.

For these sorts of questions, the net force no longer sums to 0. There will be a direction of travel. 

Assumption for kinetic incline: 

-no air resistance

-acceleration is consistent (not 0)

-1 FBD

-positive axis on a slant dependent on the direction the incline is facing (the direction the object travels)

-Friction kinetic = miu kinetic x force normal, in which force normal is equivalent to the force of gravity (y), which is in turn the mass of the object multiplied by gravity (9.8)

-gravity > friction (that's why the object is moving)

PULLEYS

A pulley is a tool where there are two objects (yes that means 2 free body diagrams now) where they are connected by a rope of cable of some sort. This means that the side with the heavier object will dominate the side with the lighter object.

The net force should not be 0 unless the mass is equivalent on both sides of the pulley.

Assumptions for pulleys:

-frictionless pulley

-frictionless rope/cable

-no air resistance

-2 systems -> 2 FBDs

-T1=T2 (the tention on both sides of the pulley should be equivalent due to Newton's 3rd law)

-acceleration is the same in the y direction

-positive axis on the direction of travel (one side will be going down, and one side will going up)



TRAINS

Trains are pretty much pulleys, except rather than having movement on the y-axis, their movement is on the x-axis. BTW trains are exactly what they sound like (chugga chugga chugga choo choo) One mass pulling the rest.

Net force is in one direction, and greater than 0 because friction is overpowered by the applied force.

Assumptions for trains:

-2+ FBD (as many as there are parts added)

-no air resistance

-acceleration in the y-axis = 0

-cables weightless

-the direction of the + axis is the direction of acceleration

-acceleration is consistent

Projectile Motion

So for the past two days, physics class was composed of determining projectile motion

On the first day, we all attempted an experiment with a marble and a ramp on a table. The marble was rolled off the ramp, and the elapsed time was taken from the point the marble left the table to the point it hit the ground.

On the second day, we just learned the conceptual stuff behind projectile motion.

So basically, when an object it released at speed, the gravity is taken into account while the object slowly drops.
However, there are two points in which to take into consideration. The first one being the movement on the x-axis (horizontal movement), and the second one being the movement on the y-axis (vertical movement). The horizontal movement is always at a constant velocity (the velocity at which the object was released), and the vertical movement requires the addition of gravity (9.81 m/s²). Usually, the vertical component begins with a V1 of 0, because it is dropped onto the ground, therefore, there is no initial velocity. Also, the height of the object is usually the distance the y component travels before it hits the ground.

Furthermore, the elapsed time of the x component should be equivalent to the time for the y component. Knowing these facts, many different pieces of information can be obtained using the big 5 equations.

That is a brief summary of projectile motion :)