Physics Digital Portfolio: April 2012

Reflection:

Part A -

I learned that Kinematics has been divided into two types, One Dimension and Two Dimensions. Kinematics. I have also learned to solve Kinematics problems using the five kinematics equations. Kinematics is the study of motion, without the components of mass and forces (dynamics).

One Dimension Kinematics is pretty simple and uses the basic concepts of motion which are velocity, distance, acceleration, and time, but Two Dimension Kinematics is much more complicated. It goes into Projectile Motion, Relative Motion, Circular Motion, and even requires trigonometry (sin, cos, tan). These go deeper into kinematics and bring up even more equations to use to solve the problems.

Two Dimension Kinematics requires analyzing the problem a lot and figuring out what to do with next. Sometime it is quite easy and only need one step such a putting your given information into an equation, but other times there are multiple steps to get there. I find it helpful to know all the equations or have a equation sheet so that I can find the equations that will give me the answer. Another strategy to solve problems dealing with Kinematics is writing out your given information and draw a picture to understand what is happening in the problem if necessary.

For example:

An airplane accelerates down a runway at 3.20 m/s² for 32.8 s until is finally lifts off the ground. Determine the distance traveled before takeoff.

Given:

a = +3.2 m/s²

t = 32.8 s

v_i = 0 m/s

Find:

d = ??

d = v_it + 0.5at² <= Kinematics equation!

d = (0 m/s)(32.8 s)+ 0.5(3.20 m/s²)(32.8 s)²

d = 1720 m

Part B -

Kinematics is present everywhere in our lives. Running requires velocity, jumping has acceleration due to gravity, driving in a circle uses circular motion, and throwing a rock around uses projectile motion. Everything that we do that requires motion relates to kinematics.

In my Pre-calculus class I noticed several problems that relate to Physics, especially kinematics. When we were learning trigonometry, I found that many two dimensions kinematics problems had trigonometry in it, such as sine, cosine, and tangent.

Another example of Kinematics in real life is driving. For example, everyday people have to maintain a constant speed, or close to it, to remain at the required speed limit and when the speed limit changes we accommodate by accelerating or decelerating.

Also, NASA has to use kinematics a lot and have to be extremely careful with their calculations or everything could go wrong. They have to accelerate a lot at lift-off to get through the atmosphere, and they have to do much more.

Project:

1. Content -

One Dimension Kinematics

Kinematics Equations

These equations help solve kinematics problems:

Vf = Vo + at
Vav = 1/2 ( Vf + Vo )
Xf = Xo + 1/2 ( Vo + Vf )t
V^2 = Vo^2 + 2ax

Kinematics Vocabulary and Relationships

Kinematics involves relationships between the quantities displacement (d), velocity (v), acceleration (a), and time (t). The first three of these quantities are vectors while time is a scalar.

Vector- It is a quantity with both magnitude and direction, such as velocity and acceleration.

Scalar- It is a quantity with ony magnitude, such as time.

Displacement- Is the change in position of an object. It can also be called distance.

Velocity- Is the distance that can be traveled during a certain amount of time. Velocity can be negative since it can suddenly change direction. Fro example, you could be driving forward at a constant speed and then suddenly drive in reverse at the same speed. Your speed remains constant, but your velocity changed from positive to negative.

Velocity = Distance / Time

Acceleration- Is the change in velocity. When velocity is speeding up, you are accelerating, and when you are slowing down you are deccelerating. When an object is accelerating at a constant pace, its velocity is still going up.

Acceleration = Velocity / Time

Graphs- There are many types of graph for Kinematics such a Position-Time Graph, Velocity-Time Graph, and Acceleration-Time Graph.

Velocity-Time Graph-

A and E show constant velocity, but E is negative.
B shows a positive velocity and acceleration.
C shows a positive velocity, but it is deccelerating until it is at a stop.
D shows a positive acceleration that slows to a stop when velocity is negative, but speeds up when it is positive.

Two Dimension Kinematics

Relative Motion: X and Y Component of Vectors

Relative motion is the basic form or two dimension kinematics. In realtive motion, we are not just measuring a vector going straight, but going diagnol. When an object moves at an angle, it has a X-component and Y-component. The X-component is the measure of a vector going horizontal to the ground. The Y-component is the measure of a vector moving vertically. The X and Y components with the angle creates a right triangle. By using the concepts of right triangles and sine, cosine, and tangent, we can figure out the vector of the angle.

*SOHCAHTOA*-use this to help figure out the vector.

Example! - Imagine you are trying to sailing a boat across a flowing stream. Your boat is trying to move straight, but ends up moving diagonally and at a new speed due to the stream's current that is perpendicular to your boat in the beginning. The boat's velocity in the beginning is your X-component while the speed of the stream is your Y-component. Using 'tangent' (trigonometry), you can figure out your new speed.

Projectile Motion

Projectile motion shows the movement of an object due to only the force of gravity. Gravity has an acceleration of 9.8 m/s^2 on an object that is falling, but when thrown up, it causes the acceleration on the object to be -9.8 m/s^2.

When throwing a ball into the air it starts slowing to a stop and then as it falls back down to the persons had ( at the same height it was thrown). As it falls, it starts accelerating and right before it hits his hand, the velocity is equal to the velocity at the beginning.

In Dynamics we learned about Newton's Laws and how an object in motion stay in motion unless a force is acted upon it. We don't really see objects moving for a infanite amount of time due to all the forces such as friction, air resistence, applied force, and most of all Gravity. Gravity causes the ball shot from the cannon (below) to move in a parabolic path instead of straight. Also, the path is curved and not diagonal because gravity causes acceleration and decceleration so the velocity is effected gradually instead of a sudden and constant change.

When solving Projectile motion equations, you basicly use the same kinematics formulas except the acceleration is always gravity and it only effects the Y-component. We are ignoring air resistance in Projectile Motion.

Equations : *Note: Sometimes the gravity is negative depending on the problem. Analyze!*

Original Equation X-component Y-component

X = Xo + Vot + 1/2 at^2 X = Voxt Y = Yo + Voyt + 1/2 (9.8)t^2

V = Vo + at Vx = Vox Vy = Voy + 9.8t

V^2 = Vo^2 + 2aX Vx^2 = Vox^2 Vy^2 = Voy^2 + 2(9.8)Y

Circular Motion

Uniform Circular Motion- the movement of an object at constant speed around a circle. The radius must stay constant.

Centripetal Acceleration- The 'center-seeking' acceleration of an object that is moving in a circle at a constant speed. This is caused by centripetal force which exerts the net force to the center of the circle.

Although the acceleration is towards the center of the circle, when the object is released or stops moving in a circle, it continues moving straight in the direction it was in before it was released.

Equations:

*Note: second equation finds the Fnet (net force) which relates to Dynamics.*

ac=(v^2)/r

F=mac=(mv^2)/r

2. Application -

Relative Motion

Relative motion can be found in sailing boats, ships, planes, and swimming. As long as there are two components acting on an object, relative motion will be present.

Projectile Motion

Projectile Motion is everywhere around us because gravity is always present. We see it when we play catch, watch fireworks, and drink from a water fountain.

Circular Motion

In Circular Motion, spinning an object around a fixed point allows there to be a centripetal acceleration and force. That is why things like the sport and ride below have circular motion.