4 Newton Problems!



Sir Isaac Newton





So it all started

out with Newton

sitting under an

apple tree .......  

Newton's three laws of motion:

1. INERTIA: "An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force."

(Inertia is the tendency of an object to resist changes in its state of motion.)

2. F = MA: "The acceleration of an object depends directly upon the force acting upon the object, and indirectly upon the mass of the object."

As the force acting upon an object is increased, the acceleration of the object is increased. As the mass of an object is increased, the acceleration of the object is decreased.

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


 

There are four types of Newton's problems:
Equilibrium, inclines, pulleys, and trains.

EQUILIBRIUM When forces are balanced.

Assumptions:
- no friction

- positive axes
- a = 0 (ax = 0 and ay =0, there is no movement in the x axis or y axis)

INCLINES

STATIC:When the object is not moving while on an incline. Static friction is preventing motion on a stationary object.

Assumptions:
- a = 0
- Fn is perpindicular to surface
- positive axes in the direction of acceleration
- no air resistance
- static friction = coefficient of static friction x normal force
- μ = tanΘ

KINEMATIC:
When the object is moving down an incline. The kinematic friction is working against the moving motion.

Assumptions:

- ax ≠ 0, ay = 0 (because it is moving in the x axis)
- positive axes in direction of acceleration
- Fn is perpindicular to surface
- no air resistance
- kinetic friction = coefficient of kinetic friction times normal force

PULLEYS
When objects are held by pulleys.

Assumptions:
- frictionless pulleys + rope
- no air resistance
- multiple FBDs
- positive axes in direction of acceleration
- T1 = T2
- acceleration of system is the same

TRAINS
When the problem deals with a train.

Assumptions:
- 1 FBD for acceleration
- 3 FBDs for T1 & T2

- no air resistance
- weightless cables
- positive axes in direction of acceleration
- ay = 0
- a is consistent

And remember that for each problem,
BREAK DOWN THE X and Y COMPONENTS and SET YOUR POSITIVE AXES.  

PROJECTILE MOTION

 CLICK HERE!!! CHECK THIS VIDEO. IT'S REALLY GOOD. It's a really simple explanation of projectile motion.

PROJECTIVE MOTION:
events where object moves under the influence of gravity and is not self powered.

A horizontal constant motion plus an accelerating vertical motion = parabolic motion (curved motion).



This diagram shows a ball that is thrown in a parabolic motion.

  As you can see from the above illustration, the velocity components are at different positions.

Vx, the velocity for the x component is constant because it's displacement is the same everytime and there is no acceleration, since it goes on in a continueous speed. Due to no air resistance, the velocity in the horizontal direction is constant.

The Vy factor that represents the y component is not constant. Vy1 is 0 because it is clearly shown when the ball is at it's peak height the Vy1 is 0 because there is a x vector which means there will not be a y vector. As the ball goes higher in the first half of the projectile, the Vy magnitude decreases and soon after it starts coming down on the second half of the projectile motion, it increases in magnitude in a negative direction. The change in Vy is due to gravity.


Solving projectile problems:

Look at the given values and split into x and y components.

X: ax = 0
     Vx = constant
     Dx = range/ horizontal displacement

Y: ay = -9.8 m/s2
    Vy = changing
    Dy = height/ vertical displacement

Remember that x and y component share only ONE same component which is TIME.
Tx = Ty

For X:
Dx = VxTx

For Y:
Use BIG 5 EQUATIONS ... Dy = Vyt + 1/2 at²

Let's take a ride on a ROLLERCOASTER



Canadian Mind Buster

 Okay, I'm going to admit that I'm not too crazy about rollercoasters. I dread waiting in line for them but right after I just  can't wait to get back on them. But still, I hate that stomachy feeling you get when you're falling down and it feels like you're going to die. I really don't have a favourite rollercoaster but the one that I've rode on a lot would have to be the wooden Canadian Mindbuster at Canada's Wonderland. Yeah, it's old, wooden and doesn't look like a lot of fun, but I like it. It's tame and controllable and I love the riggity sounds it makes.


Let's first take a look at energy:

Potential Energy

Potential energy is the same as stored energy. When you lift a heavy object you exert energy which later will become kinetic energy when the object is dropped. A lift motor from a roller coaster exerts potential energy when lifting the train to the top of the hill. The higher the train is lifted by the motor the more potential energy is produced; thus, forming a greater amount if kinetic energy when the train is dropped. At the top of the hills the train has a huge amount of potential energy, but it has very little kinetic energy.

Kinetic Energy

"Kinetic energy" is the energy of motion - it's ability to do work. The faster the body moves the more kinetic energy is produced. As the train accelerates down the hill the potential energy is converted into kinetic energy. There is very little potential energy at the bottom of the hill, but there is a great amount of kinetic energy.


How roller coasters work:

A motorized chain pulls the roller coaster to the top of the first hill (that's why you hear that click, click, click sound). The first hill is always the tallest one unless the coaster has more motorized chains later on (more clicking), which means that the first hill has the largest large amount of gravitational potential energy. We know from our previous unit, that this is the amount of work an object will be able to do with the energy it builds up from falling. The energy the roller coaster builds up from falling down that first hill will be enough to take you all the way to the end of the ride.


This diagram demonstrates the force of gravity
on the rider's weight while on a roller coaster

  

The physics of roller coasters:

Now that the roller coaster has made it to the top of the first hill, gravity takes over. When the roller coaster goes down the hill, it speeds up. As it accelerates down the hill, the potential energy gets converted to kinetic energy.The weight of the roller coaster is pulled down by gravity (which means it's falling).

Newton's Law of Roller Coasters:

Sir Isaac Newton (the dude who explained gravity) figured out the concept of inertia.
It's the law of physics that says that any object in motion will stay in motion until acted on by an equal but opposite force. When the roller coaster is at the bottom of the first hill, the kinetic energy is at it's biggest. Now that the coaster is whipping around loops and other hills, its energy is being lost to other forces like friction (energy created by two things being rubbed together) and air resistance. By the time the roller coaster gets to the end of the ride it has lost enough energy to come to a stop (usually with a little help from the brakes).

Adding Vectors

VECTORS: magnitude AND direction.

These are the simple steps for adding vectors by components:

1. First, set your positive axes.

2. Break the vectors down into two components: X and Y.

For example the question is A - 3D. (Vector A minus three times vector D)

A chart would help to organize and visualize the X and Y components easier.

3. Solve for the sum of X and the sum of Y.

4. Using the Pythagorean theorem, the two sums can be added to get the resultant.

R = √ A2 + B2
R = √ (65.5)2 + (-14.4)2
R =  67

5. Use trigonometry to solve for the angle.

tanθ = opposite/adjacent

tanθ= 65.5/-14.4

       = -77

Therfore the completed answer is: 67 [ S 77° E]