1.) Newton's 3rd Law + Action/Reaction- Pairs
2.) Tug of War/ Horse and Buggy
3.) Forces in Perpendicular directions
4.) Gravity and Tides
5.) Momentum+ Impulse relationship
6.) Conservation of Momentum (including the lab)
In each of these concepts, I learned an exceptional amount of formulas, information, and applications to everyday situations. As usual, to avoid confusion, I'm going to break it down into sections. However, what'll be different about this section is that I will include more exercises from the textbook our class uses. The exercises help to test your knowledge and whether or not you retained any of the actual information I included in this unit summary. Don't panic, I will also have my usual crazy made up problems, to leave you with a little smile!
Part One: Newton's 3rd Law + Action/Reaction- Pairs
1.) What is Newton's 3rd Law?
For every action there is an equal and opposite reaction.
2.) What is the relationship between acceleration and force?
They are directly proportional.
3.) What is the relationship between acceleration and mass?
They are inversely proportional.
4.) What would an action reaction pair look like?
Apple pulls Earth up
Earth pulls apple down
5.) What do action reaction pairs have in common? (refer to the previous answer)
The verb/action is the same. If the action is "pull" for the top one, then the bottom action will also be "pull."
6.) Are action reaction pairs equal and opposite to other action/reaction- pairs?
No, each pair is only equal and opposite to itself and not another pair.
Examples and Practice Problems (Some are from our assigned textbook)
1.) Its 5:30am and I enter the library with my backpack, which weighs probably half as much as I do. I'm tired and decide to drop my bag on the desk. Can you name the action-reation pair or pairs in this situation?
First pair: Table pushes Bag up
Bag pushes table down
Second pair: Bag pulls Earth up
Earth pulls Bag down
2.) It's almost christmas and I want to hide a present on the top shelf of my closet. I'm pushing up on the present and the earth is pushing down on the present. Do these two forces form an action and reaction pair? Why or why not?
No, because according to Newton's 3rd Law, "for every action there is an equal and opposite reaction." This means they must have the same action in order to have equal and opposite reactions.
3.) The Polar Express runs into a sled. Which one exerts the larger force on the other? Explain why.
Which one will have the greater acceleration? Explain why.
They exert the same amount of force because according to Newton's third law, "for every action there is an equal and opposite reaction. This means the amount of force one vehicle applies the other one will apply the same amount. The vehicle with the greater acceleration is the sled because the mass is smaller. According to Newton's 2nd Law, " mass is inversely proportional to acceleration." So as one increases, the other decreases.
Instructions: Now is the section where I will pull a few question from my textbook. If you happen to have the book
Conceptual Physics eleventh edition, by Paul G.Hewitt, refer to the sections I state before I begin the questions.
Chapter 5 exercises 1,8, and 11
1. ) "A rocket becomes progressively easier to accelerate as it travels through space. Why is this so?"
. In the beginning the mass was larger compared to the force because it was still inside the Earth's atmosphere Gravity was weighing it down, but once it entered space there was no gravity. With gravity being absent, the mass of the rocket decreased and the acceleration increased. In other words, a greater acceleration due to a smaller mass.
8.) "What physics is involved for a passenger feeling pushed backward into the seat of an airplane when it accelerates along the runway during takeoff?"
Action reaction pair: Seat pushes person forward
Person pushed seat backward
In this situation, Newton's 1st Law states that, "An object at rest or in motion will remain at rest or in motion unless acted upon by an external force." Therefore, you stay at rest because you are already at rest. Now Newton's 3rd Law states that, " for every action there is an equal and opposite reaction." Therefore, the chair pushes you and you react with an equal and opposite reaction.
11.) " Is it true that when you drop from a branch to the ground below, you pull upward on the Earth? If so, then why is the acceleration of the Earth not noticed?
Yes, because the Earth's mass is so great that it's acceleration is so small.
Part two: Tug of War/Horse and Buggy
Answer the practice problems using knowledge I taught you in the lesson above and...
1.) What are two things that can affect the force of friction?
The nature of the the surfaces (this has nothing to do with speed or surface area) meaning rough or smooth. Secondly, how hard the surfaces are pushed together.
Examples and Practice Problems
The dogs and sled example uses the same concept as the horse and buggy.
1.) You are sledding down one of our many wonderful snowy hills in the midst of winter. The team of asheville faculty dogs have been assembled and are running you and your friend all over campus. Your friends thinks the sled is moving forward because the dogs are pulling really hard on the sled. However, she is incorrect. How would you correct her? Use the labeled vectors in your explanation (when attempting this on your own, try to draw the picture I've given you and label the vectors on your own, then compare.)
The pull of the sled doesn't matter. The forces are equal and opposite according to Newton's 3rd Law which states, "for every action there is an equal and opposite reaction." What matters is how hard one pushes on the ground. The dogs press harder on the ground, so the sled will accelerate in the direction of the dogs.
2.) How does a team win a tug of war match?
Part Three: Forces in Perpendicular Directions
1.) The box is placed halfway down a steep ramp, what three things must be acting on it if it is not moving?
The three things acting on the box are a downward force ( F weight)/ up force (F support), net force, and friction.
The vector in purple pointing upwards= the F support
The vector in purple pointing downwards= F weight (force of gravity pulling down on the object)
The vector in red= Net Force
The dotted lines in green= how to find the net force using a drawing
2.) What are tension vectors?
The tension vectors here are in pink. They show the amount of tension in each of the ropes. The dotted lines are the net force upward, which is equal and opposite to the weight. The are drawn from the top of the arrow and continue downward, but parallel to the line opposite of it. The circle is the weight and the line straight down is the f weight (force of gravity pulling down on the ball).
2.) If one vector is longer than the other, is there more tension in the longer vector than the shorter one?
Yes!
3.) If there are equal angles, is there equal tension?
Yes!
4.) If you have a hanging weight on a rope, why can it never be straight?
It can never be straight because there always has to be an upward force. If it was straight, then there would be no upward force.
5.) What can you correctly say about two vectors that add together to equal zero?
They are equal and opposite.
6.) Can a pair of vectors with unequal magnitudes add to zero? Can three unequal vectors add to zero?
No and yes.
7.) When can a nonzero vector have a zero horizontal component?
When the vector is pointing straight down.
Examples and Practice Problems (With a problem from our textbook)
Chapter 5 exercise 29.) " Two people of equal mass attempt a tug-of-war with a 12m rope while standing on frictionless ice. When they pull on the rope, each of them slides toward the other. How do their accelerations compare, and how far does each person slide before they meet?:"
Their accelerations will be the same because without friction their mass doesn't matter because they can't press on the ground. They will each slide 6 meters.
Your super cute orange, but majorly obese cat is laying in your lap playing with a ball of string. Suddenly, an angry bird comes flying through the window, trying to hit your green pig poster. Your cat goes crazy and is flying around the room. They land on your banner hanging above the mirror. Will their be more tension in the banner if it sags a little or a lot?
There will be a greater tension in the banner if it sags a little.
Part four: Gravity and Tides
1.) Everything with mass ________ all other things?
The answer is attracts.
2.) What does force depend on?
The mass of the objects and the distance between them.
3.) What is the relationship between force and mass?
They are directly proportional.
4.) What is the relationship between force and distance?
They are inversely proportional. It follows the inverse square law.
5.) The farther apart the objects get, the less _____ there is on the two objects.
The answer is force.
6.) What is gravity written in scientific notation?
6.67x10^-11
7.) What is the universal gravitational formula?
F= (G) (M1)(M2)/ (d^2). This is how strong a force is between any two objects anywhere in the universe.
8.) If the distance is doubled, what happens to the original force?
It is 1/4 of the original force.
9.) If the distance is tripled, what happens to the original force?
It is 1/9 of the original.
10.) If the distance is cut in half, what happens to the original force?
The force is four times the original.
11.) If the distance is cut in third, what happens to the original force?
The force is nine times the original.
12.) Between the ____ and the Earth, there is a large force?
Th answer is the sun.
13.) Between the _____ and the Earth, the force is ______ than that of the sun?
The answer for the first blank is moon. The answer for the second blank is smaller.
14.) How is the blob of water around the earth going to affect the force of the moon?
The moon is pulling the Earth towards itself and with the same amount of force the Earth is pulling the moon toward itself. The forces are equal and opposite.The difference is the diameter. The Earth's diameter side A and B, the water will not experience the same force. It's not the fact the moon is pulling the Earth. It's the fact side A and B are experiencing a difference in force. The water is rushing to the areas of high tides.
15.) The earth takes _______ to spin around completely?
The answer is 24 hours.
16.) The moon takes _______ to do one rotation around the earth?
The answer is 27 days.
17.) What is the important location relationship?
The important location relationship is where the moon is in relationship to the sun and the Earth.
18.) During what phases of the moon do the spring tides occur? Are the high tides higher than normal or lower? Are the low tides higher than normal or lower than normal?
The spring tides are occur during a full and new moon. The high tides are higher than normal and the low tides are lower than normal.
19.) During what phases of the moon do the neap tides occur? Are the high tides higher than normal or lower? Are the low tides higher than normal or lower than normal?
The neap tides occur during the half moon. The high tides are lower than normal and the low tides are higher than normal.
20.) How long is there between a high to high tide and low to low tide?
There are six hours.
21.) How many hours is there between a high to low tide?
There are twelve hours.
22.) When the sun, moon, and Earth are in _____ we have spring tides? When the sun, moon, and Earth are on ___ and _____ we have neap tides.
The answer for the first blank is line. The answer for the second blank is top. The answer for the third blank is bottom.
23.) The moon has a greater ____ due to the difference in side A and B than the sun has a ____ on side A-B on the Earth.
The answer for both of the blanks is pull.
Example Problem
Use the Gravitational formula for this problem. We already know the gravity, but if the first mass was 8x10^30, the second mass was 3x10^24, and the distance (which is squared) was 2x10^6, what is the force? For the sake of simplicity, we are going to round the 6.67 for gravity and raise it up to 7.
Part five: Momentum+ Impulse relationship
1.) The total momentum before a collision or explosion is____ to the total momentum after a collision.
The answer is equal.
2.) P total before equals ________ after
The answer is P total.
3.) If the objects are stuck not stuck together then are after, what is the formula?
(Ma)(Va)+(Mb)(Vb)= (Ma+b)(Vab)
4.) The change in Pa equals what?
The negative change in Pb.
5.) Pa+Pb equals what?
Pa+ Pb because P total before equals P total after.
6.) If the objects are separate before and after, what is the formula?
It is (Ma)(Va)+(Mb)(Vb)= (Ma)(Va)+(Mb)(Vb)
7.) What is the formula for impulse?
J= Ft.
8.) what is the formula to find the change in momentum?
The change in p (represented by a delta symbol followed by the capital letter P) = P final - P initial.
9.) What is needed to cause bounce?
There has to be two changes in P, two impulses, and two forces. The bouncing doubles the force.
10.) What is impulse measured in?
It is measured in Newtons seconds.
11.) Are impulse and force the same thing?
No, they are not because impulse depends on time while force itself does not.
Part six: Conservation of Momentum
1.) How does the total momentum of a system compare before and after a collision or explosion? How do we know?
They are equal because it'd only be zero after, if it was zero before.
2.) What causes a change in momentum? what is the formula to calculate this?
The impulse causes a change in momentum. The formula to calculate this is JA= - JB.
3.) What is the relationship between the change in momentum and impulse?
They are equal and opposite.
4. ) If a bug crashes into a window, how does the change in the momentum of the bug compare to the change in momentum of the window the movers are transporting?
They are equal and opposite.
Example and Practice Problems
1.) Two little kids are reenacting the tragic marshmallow battle of 2001. One takes out his marshmallow gun and the other takes out his gummy bear gun. The criminal with the marshmallow gun fires a fluffy bullet....
a.) Which experiences the greater force?
b.) Which experiences the greater change in momentum?
c.) Which experiences the greater impulse?
d.) Which experiences the greater impulse?
e.)Justify that both the gun and the bullet were at rest at the start, so the net momentum is 0kgm/s, but at the end they both moved so there is momentum for each. How is this possible?
a= equal and opposite
b= equal and opposite
c= equal and opposite
d= one will be greater, the bullet
e= The change in the momentum of the bullet is equal to the change in momentum of the gun.
2.) Comparing total momentum before and after a collision
Cart A with a mass of 5kg was pushed toward another cart B of 1kg, which was at rest. After a couple of trials, the velocities of cart A before the collision and cart A and B after the collision. To find out the momentum the class had to graph the momentum of cart A (Pa) on the y-axis and the velocity (Vab) of the carts when stuck together on the x-axis. See the graph below for more information and questions.
a.) Translate the equation of the line for what is on the x and y-axis.
Y= PA
Slope= Ma+b
X= Vab
b.) Based on this graph and the knowledge I've presented in this unit summary, what does the slope represent?
The slope represents the total mass of the carts put together.
c.) Using the picture above, calculate what the slope should be?
The slope should be 6.0676.
d.) Compare the value above to the slope. Does this data confirm the law of conservation of momentum?
Pa= (Ma+b)(Vab)
Pa= ( (5) + (1) ) (Vab)
Pa= (6)(Vab)
Using our translated equation of a line, we see that the slope is 6kg. If we compare this to our calculated 6.0676 in question c, then we can see that it is within 10% if the value. Therefore, our data does confirm the law of conservation.
3.) You decide to go shopping at Publix (a grocery store further down south). As you wander the isles at 10m/s, you start to fill up your cart. The cart with groceries in it now weighs 15kg. You bump into an another shoppers cart, which weighs 5kg and was parked in front of the ice cream isle! As if it wasn't enough they were blocking the creamy goodness, a broken section of their cart catches yours. The two carts are now stuck together. How fast are they moving?
They are moving at about 4 m/s.
