Unit 3 Summary

NEWTONS THIRD LAW: Every action has an equal and opposite reaction

Just a few posts ago, I explained Newton’s Third Law in relation to Harry Potter and the platform nine and three quarters. Thinking back to that, we know that according to the law, every action has an equal and opposite reaction, and that Harry’s cart and the platform hit with the same force. An action reaction pair is a term used to describe the relationship between two interacting objects. In this case, the reaction pair is “cart hits wall, wall hits cart”

Don’t forget that the cart will experience a greater acceleration than the wall. This is because mass and acceleration are inversely proportional (Newton’s Second Law), so the object with a larger mass (wall) will have a smaller acceleration, and the other way around.

If you have ever played a game of tug of war, you may wonder what makes one team win over the other. According to the law, we know that each team is pulling the other with an equal force. However, the team that wins is the team that exerts a greater force on the GROUND. Refer to the diagram below for details…

 

Team red and team blue pull eachother with equal and opposite forces. However, the blue team pushes the ground with more force than the red team, which causes them to pull left with more force, and win.

VECTORS: A visual tool used to add up opposing forces

Say you have a weight hanging from a string, if the weight is on one side of the string, which side has more tension?

 

The longer the tension vectors (red) the more tension that piece of the string has. So there is more tension near the weight, and less on the other side. This means that the longer side of the string with more tension (left) is more suseptable to breakage.

GRAVITATIONAL FORCE: Everything with mass attracts all other objects with mass

Depends on…

àthe mass of the objects  

àdistance between the two objects. The more distance, the less force

Below is a the equation for finding the gravitational force between two objects, and the force of gravity itself.

 

Here is how you would use the equation

Force is directly proportional to mass

Force is inverse squared to distance

Double distanceà force is a ¼ of the original

Triple distanceà force is a ¹/₉ of the original

Cut d by ½à force is 4x’s greater

Cut d by ¹/₃à force is 9x’s greater

TIDES: As stated in my previous blog post, tides are created by the differences in force on opposite sides of the earth.  Once side of the earth has a greater force, since it is closest to the moon, and the other side which is farther from the moon experiences less force. These unbalanced forces created a “bulge” or “potato” around the earth (red)

Spring tides are high tides that are higher than usual, and occur when the sun, moon, and earth are all in one line. Similarly, neap tides are lower than typical low tides, which occur when the earth and moon create a right angle.

CONSERVATION OF MOMENTUM

p=mv

∆p=p_final-p_initial

the total momentum of a system remains constant before and after a collision

àmomentum can be neither created nor destroyed

P Total Before= P Total After

Before                 After

MaVa+MbVb=Ma+b(Vab)

MOMENTUM AND IMPULSE RELATIONSHIP

Impulse: the force exerted on something by a specific time interval

j=∆p

j=fx∆t

Have you ever wondered exactly how seatbelts keep us safe? This can be answered with knowledge of momentum and impulse…

Since change in momentum equals impulse, we know that the car will stop moving  regardless of how it stops.

àthe ∆p and j are constant

with airbag                J=F∆t

without airbag            J= F ∆t

As you can see above, force and change in time are inversely proportional. The seatbelt increases the time of the impulse, and therefore decreases the force. Less force, means it is less likely for you to be injured.

Tides

Having grown up on a peninsula, it is important to know how the tides work. The moon exerts gravitational force on the earth, which creates a difference in force on opposite sides of the earth. Since one side of the earth is closer to the moon (side A), it will have a greater force. And the side furthest away from the moon (side B) is influenced less by gravitational force. These opposing forces create an imaginary “bulge” or “potato” around the earth. Sides A and B with the bulge are at high tide, and C and D at low tide. (Insert diagram here) Spring tides are when high tides are higher than average. These tides occur during a full moon, when the moon sun and earth are all in one straight line. Similarly, neap tides are unusually low tides. These occur during the half moon phase, when the moon and earth are in a line, with the sun across from it. There are four tides every in one full day. Two low tides each lasting 6 hours, and two high tides each lasting 6 hours. Watch this video of the Bay of Fundy, in Nova Scotia Canada, home to the highest tides in the world. Below is this weekend’s tide table for Halls Harbor, Nova Scotia. At 5:18 this morning, the Harbor experienced a high tide of 32.5 feet. At 11:20, the water will leave the harbor, and the low tide will reach a height of 9.8 feet. The current phase of the moon at Halls Harbor is the “Last Quarter”, which means that at this time, the tides will be their average height for this area.

Newton's Third Law meets Platform Nine and Three Quarters

(end 0:08) We are all familiar with the “Platform Nine and Three Quarters” scene from Harry Potter and the Sorcerer’s Stone. Now, lets analyze the physics behind it… When Harry first tries to enter the platform, he hits the brick wall with his cart head on. Which do you think experienced the greater force during the collision; Harry’s cart, or the brick wall? Many people would assume that the brick wall would have more force since it has more mass. However, this is not the case… Newton’s Third Law states that every action has an equal and opposite reaction. That being said, the cart and the platform actually exert equal forces on each other. Which object experiences a greater acceleration? Think back to Newton’s second law… The force is the same, and mass and acceleration are inversely proportional. This means that since the mass of the platform is greater than that of the cart, the acceleration will be smaller. And similarly, since the mass of the cart is smaller, it’s acceleration will be greater. It’s magical, isn’t it?

Unit 2 Summary

In this unit, we focused solely on how things fall. Appropriate for the season...

FREE FALL-THINGS FALLING STRAIGHT DOWN

Free fall is when objects fall due to the acceleration of gravity. There is no air resistance, and hence, weight has no affect.

Say you throw a penny off a cliff, and you want to know how far it will have fallen after 3 seconds.

You would use the formula d=1/2at²

Plug in 10 (acceleration of gravity) for a, and 3 for t

d=1/2 (10X3²)

d=45 meters

If you want to know how fast the penny fell…

Use the formula v=at

V=10X3

V=30m/s

FREE FALL-THROWING THINGS STRAIGHT UP

We already know that objects accelerate at a rate of 9.8 m/s squared. So if you throw a ball upwards, every second it's speed will decrease by 10m/s, which as stated above, is the force of gravity. Similarly, when objects fall, their speed will increase by 10m/s

Use this diagram to help you visualize...

 

To find the balls height at 2 seconds, you would find the total height that it traveled, and subtract that by it’s height at 2 seconds

d=1/2at²

d=1/2 (10X3²⁾

d=45 meters

d=1/2 (10X2²)

d=20 m

45m-20m= 15 meters high at 2 seconds

FREE FALL-FALLING AT ANGLES

Lets say an airplane is delivering supplies to an army base. The pilot needs to know how far ahead he should drop the package so that it lands in the right spot.

(Please excused my poor attempt at drawing an airplane. Prime example of why we can't have nice things) 

 

To determine when he should drop the package, use the formula v=d/t as shown below

You can also find how long the package has been falling using d=1/2at²

So the package of supplies needs to be dropped 480 meters before the designated spot.

Also, you might want to find the velocity of the falling object at any given place in it’s path. To do this, you use the formula v=at

THROWING THINGS UP AT AN ANGLE

Say you are throwing a baseball across the field (120 meters), and you know that the ball is in the air for 4 seconds.

In order to find the horizontal velocity, you would use the formula v=d/t

v=d/t

v=120/4

v=30 m/s

The vertical velocity is 20m/s, because the ball is in the air 4 seconds

Now that we know the horizontal (30 m/s) and vertical velocities (20m/s), we can use this information to find the true velocity…

The path of the two velocities create a triangle, and use can use the Pythagorean Theorem to find the balls true velocity

 

NEWTON’S SECOND LAW

a=f/m

Mass is Inversely proportional to Acceleration

Force is Directly proportional to Acceleration

Use this helpful pneumonic device to remember…

MIA FDA

Another helpful formula to know is w=mg

Say you have an object with a mass of 30 newtons…what is it’s weight?

w=30X10

w=300 kg

During the lab we did in class we used a cart, a hanger, some weights, and a track, and experimented with Newton's Second Law. 

Trial A

Mass increased, force stayed constant

àacceleration decreased

y=   m    x

a=  1/m   f

Trial B

Force increased, mass stayed constant (weight transferred)

àacceleration increased

THINGS FALLING WITH AIR RESISTANCE- SKYDIVING

Since net force decreases as you fall, your F weight and F Air will eventually equal each other, and your F Net will become zero. This is called terminal velocity, where you will begin to move at a constant velocity.

Parachutes

Once you are through skydiving, you will want to slow down to ensure that you don't hit the ground with extreme speed, for obvious reasons. You can use a parachute to do this. 

àonce you open the parachute, your air resistance will increase for a brief moment, then immediately begin decreasing.

àvelocity decreases because you are accelerating in the opposite direction

àyou will enter a second terminal velocity, which has a slower velocity due to the higher surface area

Don't try this at home kids.

THINGS FALLING WITH AIR RESISTANCE

Have you ever crumpled up a piece of paper, and tossed it into your trashcan? I usually miss, but that’s not the point. Anyways, moving on…

If you drop a balled up piece of paper (A) and a flat sheet of paper (B), you will notice that the compressed paper hits the ground first.

Paper A has a faster velocity, because it has to accelerate longer to reach terminal velocity

Paper B has a slower velocity because with it’s extra surface area, it has initial F Air and does not have to accelerate for as long.

Similarly, if you drop a golf ball and a ping pong ball from a high enough point, the golf ball hits the ground first. This is because it has a greater F weight, and therefore a greater F Air in order to push it towards the ground. The ping pong ball has less F Weight and F Air, thus, will take longer to fall.

Unit 1 Summary

Unit Summary

Here is what I learned during the first Physics Unit...

→Inertia
Have you ever left something on the hood of your car, forgotten it was there, and driven off? If you have experienced this, you may wonder why the object, lets say a to go coffee cup, fell to the ground as you drove away.
This can be explained by Newton’s First Law, stating that objects in motion will stay in motion, and objects at rest will stay at rest, unless an unbalanced force is exerted upon it.
The hardest idea to grapple with while learning about inertia is why exactly objects keep doing whatever it is that they are doing. The answer is that they continue performing their actions purely because they are “lazy” in a sense, and they want to keep moving in the direction they have been moving, until something stops them. This concept cannot be further explained; it just has to be excepted.
….So why did the coffee cup fall? Both the car and cup were at rest, then when you drove away, the car was in motion, but the cup remained at rest. The cup essentially pulled out from under the car as it drove away, then gravity pulled it to the ground.

→Equilibrium and Net Force
If an object has a net force of zero Newtons, it is at equilibrium. This can occur when the object is moving at a constant velocity, or at rest. Net force is the total combined forces being exerted on an object at a given time. Watch our short video for more information on Equilibrium and Net Force! 


→Speed and Velocity
Speed and velocity are easily confused. The thing that differentiates the two is that velocity requires an object to change it's direction. Speed is the amount of time that it takes for an object to cover a certain distance. In other words, if an object’s velocity is changing, then its direction is also changing. Let me give you some examples to help you better understand...
If a runner is running laps around a track, they can maintain a constant speed, and also have a changing velocity. This is because they are changing their direction as they run around the track, therefore they are changing their velocity.
On the other hand, it is impossible to have a constant velocity and a changing speed at the same time, because maintaining a constant velocity means maintaining a constant speed.

Here are the equations for constant velocity…
When you want to know how far an object has moved at a constant velocity, use d=vt
When you want to know how fast an object is moving at it’s constant velocity, use v=d/t  

→Acceleration
Acceleration is a measure of the change in velocity over a given time period. In other words, it is the rate at which an object is gaining or reducing it's speed. An object can be accelerating when it is changing it’s direction, increasing speed, or decreasing speed. Acceleration is measured in m/s²  
a=change in velocity/time
For example, when a you were little and liked to roll down hills, you were accelerating, because your speed was changing as you descended. The steeper the hill, the greater the acceleration. And finally, gravity causes all objects to accelerate downwards at a rate of 9.8m/s²
When you want to know how far an object has moved at constant acceleration, use d=^1/₂ at²
When you want to know how fast an object has moved at a constant acceleration, use v=at


→Graphing
Learning how to use graphs and data was a huge challenge for me. I will break it down into a few steps to make it easier to understand
 1. After you create a graph, record the equation of the line in the form of y=mx+b
Ex. y=5x 

 2. Once you have your equation using excel, change it into words
d=y x t²

3. Now, look at the equation you have, and compare it to the other physics equations. Which one does it look the most like??

d=^1/₂ at²

4. Compare the equations from two steps above. What value is missing in the formula on question 2?
^½_a

5. In this case, ^1/₂ a  is the slope of the line
½ a=slope
½ a=5 

6. Use the above information, and solve
5= ^1/₂ a 
a=10m/s²