1.) Inertia/Newton's 1st Law
2 Net force and Equilibrium
3.) Velocity
4.) Acceleration
3+4.) Constant Velocity vs. Constant Acceleration
5.) Using a graph (the equation of a straight line) to solve problems
In each of these concepts, I learned a significant amount of info, formulas, and how they can be applied to everyday situations. In order to avoid confusion, I will break it all down into an easier format for myself and for whoever may read this post. Let's begin with Inertia/Newton's 1st Law!
Part one: Inertia/ Newton's 1st Law
1.) What is Newton's 1st Law?
Newton's 1st Law states (the Law of Inertia) ," an object at rest or an object in motion will remain at rest or in motion at the same speed in the same direction, until acted upon by an outside force."
2.) What is mass?
Mass is the measure of Inertia.
3.) What are the units for measuring mass?
The units are Kg (Kilograms)
4.) How are Inertia and mass related?
Mass is the measure of Inertia. Let's say there was a box. The mass would tell the student the amount of stuff in the box, at rest or in motion.
5.) What is force?
Force is how hard an object is pushed or pulled.
6. ) What are the units for measuring force?
N (Newtons)
Examples & Practice Problems
1.) Go watch the video under the title," Newton's First Law of Motion:Inertia." Then read the explanation below the video or the explanation posted here. If one is unable to watch the video, I have summarized what occurs in the video and why, down below.
In that video, the playing card was resting on the cup with a penny placed in the center of the card.
The person then flicked the card and the penny fell straight down. The main question here is, why did the penny fall straight down, even though an external force moved the card off of the cup? To answer that one must understand a few things. In the video, the card and the penny were at rest.
According to Newton's First law, " an object at rest or an object in motion will remain at rest or in motion unless acted upon by an external force."The objects were at rest because gravity was pushing down on the card/penny and the normal force counteracts the force of gravity. This means the forces were balanced. When the hand (the external force) acts upon the card, the card is then in motion and will remain in motion until acted upon by an outside force. The coin fell straight down because due to the absence of the card, there wasn't a large enough force to balance out the force of gravity. Therefore, the penny fell straight down because of an imbalance in forces.
2.) You accidentally leave a Starbucks cup of coffee on the trunk of your car. When you take off it falls to the ground. Why do you find it on the ground below where you were parked?
The car and the coffee cup are both at rest. This means the forces are balanced. Then an outside force acts upon the car to set it in motion. However, there was no outside force acting on the coffee cup, so it stayed at rest. This is an example of Newton's First Law. The law states that " an object at rest or an object in motion will remain at rest or in motion unless acted on by an external force." So the coffee cup fell to the ground because below where you parked because the force of the car pushing up was no longer there to counteract the force of gravity. Therefore, it fell straight down where it was originally at rest.
3.) A crate is sitting at rest. You push on the crate with 100N and the crate doesn't move. What is the force of friction on the crate that opposes your push? How do you know this?
The force of friction opposing the crate must be 100N. I know this because if forces are pushing in opposite directions and the object doesn't move then it is at equilibrium.
Part Two: Net force & Equilibrium
1.) What is Net force?
Net force is the sum of all of the forces on an object.
2.) What is Equilibrium?
Equilibrium occurs anytime the net force adds up to 0 Newtons.
3.) What is a force?
A force is a push or a pull.
4.) What is the amount of force and the units of measurement?
The amount of force is how hard something is being pulled or pushed and is measure in Newtons or (N). In addition, 1/4 lbs. = 1N.
5.) Are force and Kg related?
No, they are not related because kg is, as stated in part one, the mass. The mass, again, tells us how much stuff is in the box. It doesn't not tell us the force being applied on the box. So remember that mass has nothing to do with force!
6.) What is difference between weight and mass?
The weight of an object tell us the force the earth is pulling down will, while mass is the measure of inertia.
7.) Can something be moving and not have any forces acting on it?
Yes, a rock traveling through space. This is because in space, there is no gravity to act upon the rock nor any forces that could stop it.
8.) Can something be moving and have a net force of zero acting on it?
Yes, Something in which either friction or an opposite force counteracts the force already acting on the object.
Examples & Practice Problems
1.) Imagine there are two boxes!
- Box one: It has 5N of force pushing on the upper left side and 5N of force pushing on the lower left side of the box. When the force are going in the same direction, add them up. 5N+5N=10N. This means the goal net force on the box is 10N. Therefore, it is not at equilibrium and the force is causing it accelerate (speed up or slow down).
- Box two: This has 5N of force pushing on the left side of the box and 5N of for pushing in the opposite direction on the right side of the box. When forces are going in opposite directions, you must subtract one force from the other. 5N-5N= 0N. When the force is 0, the object is at equilibrium. This means the object could be at rest or at a constant velocity.
2.) Imagine you board a hovercraft ride at the carnival. First, a large bulky football player gets on. The staff appointed to stop the rider seem to struggle to stop him. Then a little six year old girl gets on. The staff have no trouble stopping her. Why was she easier to stop than the large football player?
The little girl likely weighs 60 lb. Therefore, gravity has to pull down with only 60 lb. in order to keep her on the ground. Now when she is sitting on the hovercraft, she is at rest. The external force acting upon her and the hovercraft, in order to put her in motion, has to be more than her weight to upset the balance in forces. Now to stop her, it'll take the same amount of force to stop her. If the football player weighs 300 lb. it would take a lot more force to stop him. Since 1/4 lb= 1N.
Part three: Velocity & Speed
1.) What is the formula to measure the speed of an object?
The formula used is d/t=s or distance/time = speed.
3.) What is the formula used to find the velocity of an object?
The formula used is the same, d/t=v or distance/time=velocity. Now using that formal we can also find the time and the distance of an object. To find distance, the formula is now d=(v)(t). To find the time, the formula is now d/v=t.
2.) How can speed be measured?
The speed is measured using, mph (miles per hour), Km/h (kilometers per hour), m/h (meters per hour), m/s (meters per second), cm/s (centimeters per second).
3.) In physics, what is the common measurement of speed?
The common measurement is m/s.
4.) Compare and contrast speed and velocity
They both measure m/s and talk about the distance covered in a given time. Now velocity requires a specific direction while speed does not.
5.) What are the arrows often seen in physics diagrams?
The arrows are called vectors. They are used to show how much of something or the magnitude (how great the velocity is). In addition, they show direction.
6.) What is a major difference between constant acceleration and constant velocity?
An object at constant velocity requires a specific direction, while constant acceleration does not.
7.) Does changing velocity require a force?
Yes, because an external force was required to set it in motion.
8.) How does an object change velocity?
There are three ways to change velocity. The object must change direction, speed up, or slow down.
Examples & Practice Problems
1.) A race car is going around and around the track at 100 mph. Does it have a constant speed or a constant velocity?
When the car turns the corner it is changing direction. Therefore, the car is constantly changing direction. When an object is changing direction it can no longer be at a constant velocity, since velocity requires a specific direction. That is why it is at a constant speed instead.
2.) A bicycle rides for 1 hour at 5 mph. Then for 3 hours at 4 mph and finally for 2 hours at 7 mph.
- How many miles did you ride?
In order to find the distance use the formula, (t)(v)= (d) or (time)(velocity)= (distance).
So (5)(1)= 5, (3)(4)= 12, (2)(7)= 14. Then add 14+13+5= 32!
3.) A car maintained a constant velocity of 100 m/s!
How fast was the car going after 10 seconds?
4.) If a car is maintaining a constant velocity, then it will still be going 100 m/s no matter what time it is.
5.) How far did the car go after 10 seconds?
Using the formula (v)(t)= d, we can then use substitution to get (10)(100)= 1,000 meters.
Part four: Acceleration
1.) What is acceleration and how do I find it?
The change in velocity (speeding up, slowing down, or changing direction) over a certain time interval.
2.) What are the units for acceleration?
The units are meters per second squared or m/s^2.
3.) What is the formula used to find out how fast an object is going? (used only when the the acceleration is constant)
The formula used is v=(a)(t) meaning velocity= (acceleration)(time).
4.) What is the formula used to find out how far (the distance) of an object? (used only when the acceleration is constant)
The formula used is d=1/2(a)(t^2) meaning distance= 1/2 (acceleration)(time squared).
5.) What are the three ways someone can identify acceleration?
The three ways are if an object is slowing down, speeding up, or changing direction.
6.) What is the acceleration of an object falling straight down?
The acceleration is 10 m/s^2 for all free falling objects!
Examples & Practice problems
1.) A ball is just rolling down the highway, and there isn't any friction to take into account, what is the acceleration of the ball. How do you know?
The acceleration of the ball is zero because if a ball is accelerating it must be speeding up, slowing down or changing directions. The ball is not speeding up, slowing down, nor is it changing directions. If the velocity is constant then their can be no change in acceleration.
2.) You are watching a soccer game and you see a player kick the ball. You notice the following...
at 0s it is moving at 0m/s
at 1s it is moving at 4 m/s
at 2s it is moving at 8 m/s
at 3s it is moving at 12 m/s
-Question: what is the acceleration and how do you know?
Tip: To figure out the acceleration, divide the change in velocity by a certain interval of time. To find the change in velocity, we subtract the velocity of the first observation from the velocity of the second observation. Using that strategy we can also find the interval of time!
Step one: 8 m/s- 4 m/s = 4 m/s (the change in velocity)
Step two: 2s-1s= 1s (the interval of time)
Step three: 4 m/s (the change in velocity)/ 1s (the interval of time) = 4 m/s^2
Answer: 4m/s^2
3.) If a ball was rolling at the end of the ramp with an acceleration of 4 m/s^2 and rolled for 5s.
- How fast was it rolling at the end of the ramp?
Tip: To figure this out, we need to use the formula (v)= (a)(t), and then substitute what we already know.
Step one: v= (4m/s^2)(5s)
Answer: v= 20 m/s
- How far did it roll during this time?
Tip: To figure this out, we need to use the formula d=1/2(a)(t^2), and then substitute what we already know.
Step one: d= 1/2 (4m/s^2)(5s^2)
Step two: d= 1/2 (4m/s^2)(25s)
Step three: d=1/2 (100m)
Answer: d= 50m
Part 3+4: Constant Velocity vs. Constant Acceleration
1.) What are the formulas used when an object is maintaining constant velocity?
How far: d=(v)(t)
How fast: v=d/t
2.) What are the formulas used when an object is maintaining a constant acceleration?
How far: d=1/2(a)(t^2)
How fast: v= (a)(t)
3.) If something has constant velocity, can it have constant acceleration? Why or why not?
It cannot because an object maintaining a constant velocity is covering the same distance at the same rate in the same amount of time. While an object maintaining constant acceleration, would be increasing or decreasing its speed by the same rate. Therefore, it would be covering a greater distance each time, but within the same amount of time.
4.) If something has constant acceleration, can it have constant velocity.
The answer is the same as number three.
5.) If something has increasing acceleration, is its velocity increasing, decreasing, or constant?
The velocity would be increasing.
6.) If something has decreasing acceleration, its velocity increasing, decreasing, or constant?
The velocity is increasing because the object is still accelerating. The object is just not accelerating as quickly as it was.
Example & Practice Problem
1.) After analyzing the two situations below, decide which one is an example of constant acceleration and which one is an example of constant velocity. Explain your answer!
Situation one:
A glass sphere is just rolling on a crystal floor in the white house.
Situation two:
- You are enjoying a nice sunny day, on top of one of our many luscious hills, with your pet hamster. He is sleeping in his little plastic ball, but after a while you forget he is there! You get ready to leave and sling your backpack on, but it hits his ball. The ball begins to roll down the steep hill.
You observe the following....
at 0s it is moving at 0 m/s
at 1s he is moving at 6 m/s
at 2s it is moving at 12 m/s
at 3s it is moving at 18 m/s
Answer Situation one: This is an example of constant velocity because the surface is flat and there is no friction.
Newton's first law best supports why know the object is maintaining a constant velocity! According to Newton's first law states, " an object at rest or in motion will remain at reset or in motion at the same speed in the same direction until acted upon by an outside force." As we know from the "Speed and Velocity" section, if an object is going in the same direction at thee same speed then it is maintaining a constant velocity because for an object to maintain a constant velocity, the object must remain maintain speed in one direction. If the objects changes direction it is now maintaining a constant speed. Think of it like a race car going around a track. The car maintains the same speed, but changes direction every time he goes around a turn on the race track.
Answer Situation two: This is an example of constant acceleration because the ball is increasing in speed, but by the same amount and it may change direction. To prove this, we can use the formula
v=(a)(t).
6m/s=(?)(1s)
(6m/s)/(1s)= 6m/s^2
12m/s^2=(?)(2s)
(12m/s)/ (2s)= 6m/s^2
18m/s=(?)(3s)
(18m/s)/ (3s)= 6m/s^2
Answer: We can see here that the ball is increasing in speed each time, but it is also increasing by 6m/s^2 within each interval of time.
Part 5: Using a graph (the equation of a straight line) to solve problems
1.) What is the equation for a straight line?
y=mx+b
2.) How does velocity equal slope?
Velocity equals (distance)/(time). The slope is rise/run or in other words
(the change in y)/ (the change in x). In this equation.....
- y= distance
- m= the slope
- x= the time
-b= the y-intercept.
3.) In the equation, d=1/2(a)(t^2) what part of this equation represents slope?
The acceleration represents the slope. In other words, 1/2 of the acceleration equals the slope.
Example
Example one: Compare the two graphs below and label each one either constant acceleration or constant velocity.
Graph one
Graph two
Comparison: Graph number one is constant velocity, while graph number two is constant acceleration. Graph number one has a straight line because the object maintained the same speed in the same direction constantly. Therefore, it covered the same distance in the same amount of time. While in graph number two, the object covered a greater distance in the same amount of time, increasing in speed with each interval of time. That is why the line is gradually getting higher, while the line in constant velocity remains straight.
No comments:
Post a Comment