Unit 3 Summary

In this unit I learned about Newton’s 3^rd Law and all the things it can be applied to. Newton’s 3^rd Law states that: every action has an equal and opposite reaction. For example:

If an apple is at rest on a table, the apple pushes down on the table, and the table pushes up on the apple.

This concept goes a long way in explaining why various things work. If you have ever gone on a horse-drawn carriage ride, I am sure you remember it being a fun, and almost magically unique experience. Well, it is nearly magical how perfectly Newton’s 3^rd Law fits into a horse and buggy system. Without this law of physics, there would be no carriage rides. You may be wondering how this works…

The horse and buggy pull on each other with equal and opposite force- the horse pulling on the buggy alone does not cause the buggy to move. They both, however, exert force on the ground. The horse pushes on the ground with more force than the buggy so the ground pushes back on the horse with more force than it pushes on the buggy; thus the horse and buggy move in the horse’s direction.

This explanation applies to tug of war, and a plethora of other real life situations.

I also learned about adding vectors. Using the horizontal and vertical velocities of an object, you can find the actual velocity.

To predict accurately the direction of the actual velocity vector, you use dotted lines that are parallel to the other vectors and the arrow of the actual velocity should be drawn through the point where these intersect. This can be used to find the direction of a boat when the velocity of a current and the velocity of a paddle are taken into account. It can also be used to explain why a box slides down a ramp.

The force of the box’s weight must be drawn straight down as that is how gravity pulls it, and the support force of the ramp is drawn perpendicular to the ramp itself. When the dotted lines are drawn parallel from these vectors, a parallel line should be sketched out to show the net force on the box, showing that the net force pulls the box down the ramp.

A similar concept is applied to tension. If a ball was hung by two ropes, the force of the ball’s weight would be drawn as a vector pointing down, then an equal and opposite vector would be drawn upwards from the ball to show its net force. After drawing lines parallel to the ropes but which intersect at the tip of the net force vector, you can draw (from the ball to the point which these dotted lines intersect the ropes) arrows depicting the force of tension on each rope. The longer arrow shows which rope has a greater tension.

Thus far, I have talked a lot about force on the Earth. However, force exists outside of our planet as well. Before considering this, it is important to know that…

 Force is directly proportional to mass: F ~ m

 Force is inversely proportional to distance squared: F ~ 1/d^2

With this in mind, we learned that there is a universal gravitational force. The formula for this is:

F = G(m1xm2)/d^2

G is equal to (6.67 x 10)^-11. This equation helps us to find the force of gravity between two object by using their masses (m1 and m2) and dividing them by the distance between the objects squared. It is very important to square the distance.

Believe it or not, the tides of the ocean are actually connected to this universal gravitational force. The Earth is so large that the distance from one end of the ocean to the opposite is great enough for each of these points to have a significant difference in their distance from the moon. This difference in distance causes the tides. The moon’s gravity pulls the water ever so slightly towards it, giving the Earth’s water an oblong shape in reality. Due to this oblong shape, when it is high tide on the end of the Earth closest to the moon, it is high tide on the opposite end farthest from the moon. Likewise, it will be low tide at the top and bottom of the Earth at this time.

If the moon pulls on point A with 25 N of force, pulls on B with 5N of force, and pulls on the center of the Earth with 15N of force, how does all this tide business work? Using simple math, we can see that 25-15= 10 N with which side A is pulled to the Earth. 5-15= -10N with which side B is pulled to the moon. Like the forces addressed in Newton’s 3^rd Law, these forces are equal and opposite. Therefore the sides are pulled with the same amount of force in opposite directions, causing the oblong shape and corresponding tides.

It takes 24 hours for the Earth to rotate once; the length of one day. There are 2 high tides and 2 low tides in every day- each tide occurs about 6 hours apart. They change as the world spins and different part of the world are closer to the moon. However, the moon moves as well. It takes the moon about a month to complete its orbit around the Earth. Each month, it is not in the exact same spot on the same days, which causes the tides to be a little different every time, just as they are a little bit different every day due to the imprecise and varying location of the moon from day to day. Since the tides change and the moon’s location changes, there are Spring and Neap tides at different times of the month. During Spring tide, the moon is either new or full, being in a line with the Earth and the sun. At this time, the high tides are higher than normal and the low tides are lower than normal. Low tide during a Spring tide is a great time to go clamming. At Neap tide, the moon is neither between the Earth and the sun nor on the other side of the planet in a line from the sun. It is on either side of the Earth; “on top” or “beneath” the planet. During Neap tides, the high tide is lower than normal and the low tide is higher than normal.

You can use the universal gravitational force formula to talk about tides, but you can also use it to find the force between planets. You can find the pull between the Earth and the sun, and the Earth and the moon, alike. The farther two objects are, the weaker the force is between them because of the relationship force and distance share. However, the sun does not have a weaker pull on the Earth than the moon does just because of their distances from the planet. The sun’s mass is so much greater than the moon’s that its force is greater nonetheless.

Next, I learned about momentum.

Momentum, or inertia in motion, is mass times velocity. (p=mv)

Change in momentum is simply the final momentum of an object minus its original momentum. (change in p = p final – p initial). It can also be written as change in p = mv final – mv initial.

Momentum is also equal to impulse. Impulse is force times a time interval (J= F x change in time)

All of this information may seem random when presented like this, but answering one big question can bring it all together: why do airbags keep us safe?

When a car crashes, it and you go from moving to not moving. The change in momentum here is the same no matter how you are stopped because your momentum is changed to zero since change in momentum = p final – p initial. Change in momentum is equal to impulse (change in p = J), so the impulse is also the same no matter how you are stopped. Since impulse equals force times change in time (J = F x change in t), when the time of the impulse is very long, the force is small, and vice versa. Thus, the airbag is soft and takes a long time o stop your movement, so the force is less. The smaller the force, the less you are injured. This is why airbags keep you safe.

This unit, my group made a podcast about momentum, impulse, and the relationship between the two. Here it is, hopefully it adds clarification to the concept:

According to Newton’s 3^rd Law, in any collision, all forces have an equal and opposite force. So what about momentum? If ball A and ball B are headed towards each other and collide with equal and opposite forces, the collision could be noted as F(A) = -F(B). J = F x change in t, so F(A) x t = -F(B) x t, since they both experienced the force for the same amount of time. This equation can be rewritten as J(A) = -J(B), which can then be rewritten as change in p of A = - change in p of B (because J= change in p). Change in p (A) – change in p (B) = 0, since they were equal. Therefore, this system has no leftover or extra momentum. Momentum is conserved in systems, meaning there is no net change in momentum. Collisions like this can be examined using the equation  p total before = p total after. This is rewritten as M(a)V(a) + M(b)V(b) = M(a+b) x V(ab), which presents the equation in a form to which you can plug in numbers (the mass and velocities of two different objects). It is important to remember to make one of the velocities negative since the objects are moving in opposite directions before they collide. This equation is for objects that collide and then stick together. It can be reversed to apply to objects that detach in the interaction. If the objects do not stick together, the equation M(a)V(a) + M(b)V(b) = M(a)V(a) + M(b)V(b) can be used. This is the most basic form of p total before = p total after.

If an object bounces before it stops it undergoes two changes in momentum: when it stops and when it starts moving again. Thus the object has two impulses and therefore twice the force. Bouncing objects can be more dangerous.

What I have found difficult about what I have studied is separating the equations involving force from unit 2 and the equations involving force from unit 3. F = ma seems like it should be used but it is not relevant to this unit, so it has been a struggle to keep all the equations straight in my head in correspondence with the proper concepts.

I overcame this difficulty by reviewing the material and thinking more closely about what each concept was saying. This clarified the connection between the information and the equation for me.

I put in a little less effort to the class after Thanksgiving break; this is partially due to being sick and also because it is hard to transition back into school after a longer break in the midst of the end of the semester. I still continued to try and learn everything as thoroughly as possible, though. I feel very confident about this material as it makes sense to me and I understand the connections between the concepts introduced in this unit. My confidence in my knowledge of physics this unit helped me in all aspects of group collaboration these last few weeks. Whether discussing with a partner, working together on a lab, or completing a group project, I felt that I understood what was going on and was able to help others understand a bit better as well.

My goal for next unit is to find more creative ways to apply, present, and restate the information. This would help me to deeply learn the information in a versatile way. It would also make studying more fun.

I thought that the most interesting part of this unit was tides. I encounter them frequently enough, whenever I visit the beach they affect my entire time there. The connection between natural disasters and tides is especially interesting for me. Last fall, a very serious storm hit the northeast. Hurricane Sandy caused tons of destruction, injury, and chaos. One of the reasons it was such a bad storm was that it hut during Spring tide. Using the high high tides of Spring tide, Sandy caused more damage than it would have if it had hit during Neap or normal tides. This is just how nature works, though. The seemingly placid day-to-day workings of the world can just as easily turn events into drastic occurrences. I find this fascinating and I love that I now know the scientific reasoning behind this. It is also interesting to me how so much of our lives on Earth are affected by things outside of the planet itself.