Unit 3 Summary
A) In this unit I learned about...
- Newton's 3rd Law / Action and Reaction Pairs
- Tug of war / horse and buggy reactions
- Forces in perpendicular directions
- Gravity and Tides
- Momentum and impulse-momentum relationships
- Conservation of Momentum
Newton's 3rd Law / Action and Reaction Pairs
Newton's 3rd Law states that, "For every action, there is an equal and opposite reaction." This means that every time a force is applied to an object, and equal and opposite force is applied to the opposite side of it. When talking about Newton's 3rd Law, you have to mention action and reaction pairs to fully understand the concept. But BE CAREFUL, a lot of people get tripped up on the difference between action/reaction pairs and simply just two forces being equal and opposite. An example easily demonstrates the difference.
Example of an equal and opposite action/reaction pair:
A girl, weighing 5N, is standing on the earth. The earth is also pushing up on this girl with 5N of force. This, therefore, creates a net force of 0N because the girl's force cancels out the earth's force (and vice versa). This is an example of an action and reaction pair.
Example of an equal and opposite NON-action/reaction pair:
This same girl, still weighing 5N is now standing on top of a table. The force of the girl pushing down on the earth is still the same as before, but now the force of the table must also be taken into account. The earth will now be pushing up on the girl and the table. The force will remain equal and opposite, but this reaction does not create an action/reaction pair. (The action/reaction pairs would be between the girl and the table and the table and the earth.)
Horse and Buggy & Tug of War (another example of action/reaction pairs)
The horse and buggy reaction and a game of tug of war are both easy examples to further prove Newton's 3rd Law.
Horse and buggy- First of all, there is the force of the horse pulling on the buggy and the buggy pulling back on the horse. This creates an action and reaction pair and the forces and both equal and opposite. Then there is the horse pushing the ground back and the ground pushing the horse forward. This is also an action & reaction pair of equal and opposite forces. The last set of action and reaction pairs is between the buggy pushing the earth forward and the earth pushing the buggy backwards. There is one thing you have to remember about the horse/ground reaction and the buggy/ground reaction. In order for the buggy to be moving (which in this case, let's say that it is), the arrows that you draw between the horse and the ground when making a diagram must be bigger than the set of arrows between the buggy and the ground.
Tug Of War- You may be surprised to know that when you are in a tug-of-war, the winner is really not determined by who is stronger, it is more so who exerts the greater force on the ground. This means that whichever side of the rope has the bigger action/reaction pair, will win the war.
Forces in Perpendicular Directions
Forces in perpendicular directions is basically all to do with lines and vectors. We show the amount of force exerted on a object with these vectors and that is how we can tell where the most force is being applied.
Example:
Box A is sliding down a ramp that is not so steep, while box B is sliding down a very steep ramp. You must show the force of gravity on each box (with lines that are equal in length) pulling down on the box, and then the supporting force pulling up on the box. To find out how fast the box is actually moving down the ramp, you can draw dotted lines parallel to the opposite line and then you will be able to see that the acceleration vector will be much longer in Box B sliding down the steeper ramp.
Gravity & Tides
Gravity and tides was a very interesting topic, and probably my favorite, throughout Unit 3. I think that I liked it so much because it really made sense and was relevant to my everyday life. To understand tides, you first need to understand gravity. Gravity equals 6.67 x 10 to the negative 11th power (a very very small number) is a force that pulls an object towards it, like the earth's pull on us. Everything with mass attracts all other things to it making f ~ m. Although, as you move farther away from that object, the force becomes less and less strong making f ~ 1/m as well. The Universal Gravitational Law is F=Gm1m2/d2.
Example:
Planet A has a mass of 8x10 to the 30th kg, and planet B with a mass of 6x10 to the 15th kg. The two planets are a distance of 4x10 to the 22nd m. What is the force between them?
To solve this problem you have to sub in the two masses multiplied by gravity, divided by and the distance (squared) and you will be able to calculate the force.
Gravity is the main reason why we have tides. To understand tides you must know why a tidal bulge occurs on opposite sides of the earth and what a Spring and a Neap tide is.
FUN FACT: Between every high-tide and low-tide, 6 hours pass. Therefore, it takes a full 12 hours to reach another high-tide!
- Tides have to do with the earth, moon, and sun. The gravitational pull of all three of these create our tides, although the most important is the moon. The moon has a gravitational pull on the earth causing the water on the surface of the earth to actually rise and move towards the moon. The rising and falling of the water are what we call our tides. This creates a tidal bulge around the surface of the earth. The bulge will be the same size on the opposite sides of the earth. It may seem like the side closest to the moon should have a higher tide than the side farthest away from the moon, but this is not the case. The side closest to the moon rises because there is a strong force on it, but the side farther away from the moon also rises because it is so much farther away therefore with much less force acting upon it.
- Spring Tide occurs when the gravitational pull of the moon and the sun are combined. This creates very high high-tides and very low low-tides. There can be either a full moon or a new moon during Spring tides.
- A Neap Tide occurs when the force of the sun and the moon are perpendicular to one another, cancelling each other out. Neap tides have a much smaller difference between high and low tides. Neap tides occur during quarter moons.
Conservation of Momentum
Any moving object has a momentum (p=mv). In every single case, the total momentum before and after an explosion or collision will be equal to each other. An example of this would be with a canon and a cannon ball. The cannon can only push the cannon ball as far as strong as the cannon ball can push back (equal and opposite). This can be expressed in the formula ∆p=ptotal before-ptotal after. We know this because momentum is conserved in this kind of reaction, making the net external impulse = 0N. BUT WAIT, what's impulse? Well, impulse is the force upon something and how long that force is applied. It is what causes and is equal to a change in momentum (∆p=m∆v).
- Another good example to mention is the bug crashing into a windshield. You would guess at a glance that the difference in size proportions would make there be no change in momentum for the car (since it is so much bigger than the bug), however that is not the case. Something can only be pushed as hard as it can be pushed back.
- In some special cases, such as explosions where both objects are initially at rest, one object will move forward with a positive velocity while the other moves backwards with a negative velocity. It may seem as if the ptotal before and ptotal after could not possible equal each other. Although, when you add the + velocity and the - velocity, you will find that they will cancel each other out to equal zero like before the explosion.
I think that it is important that I explain a little bit more thoroughly how momentum compares to impulse in real life situations. We already know that momentum = mass x velocity, and we also know that the total change in momentum before a reaction = the final momentum - the initial momentum. Therefore, we can conclude that the ∆p will be the same regardless of how it is actually stopped. All that matters is that we know that the object goes from moving to not moving in a certain amount of time. The ∆p = J. The only difference is that the units chance from kgm/s to Ns. We learned one very important example of this in order to prepare for the test.
Example:
Explain why someone who jumps off of a cliff into the snow would not get as badly injured (if injured at all) as someone who jumped off a cliff and landed on an icy surface.
- First, I would reference the p=mv formula: The person will go from moving to not moving regardless of what surface they hit.
- ∆p=pfinal-pinitial: The change in momentum will always be the same, regardless of what surface stops it. All that matters is that it will go from moving to not moving over a specific period of time.
- ∆p=J: The change in p is the same as the impulse as long as you change the units. They are the same regardless of what surface brings the person to a stop.
- J= F•∆ t: Since J remains the same, the snow will increase the time to stop. When there is more time to stop, the force will become less and less. With less force, there is less of a chance that you will get injured.
With snow: J= F • ∆ t (less injury)
Without snow/on ice: J= F • ∆ t (more injury)
One last thing to know!
In some collisions, we have created things in order to catch or succumb to an object rather than have it bounce off. This happens with a bulletproof vest for a police officer and why cars don't have rubber bumpers anymore. In both of these cases, bouncing will occur. Bouncing is not good and has actually caused more injury than it has justice for us. When there is bouncing (bullet bouncing off of vest/cars bouncing off of each other in a crash) it creates double the force. There is 2 ∆p's, 2 J's and 2 forces. This is why our bulletproof vests work the way they do and cars do not have rubber bumpers.
B) This unit connects with our everyday lives better than any other unit we have had so far. Every example we dealt with, (whether it was pool balls hitting off of each other, hanging a picture, or getting in a car crash), the event is an everyday occurrence. I think that this factor helps especially when trying to understand Unit 3 as a whole. I hope this blog post has cleared up some confusing topics for you and good luck on your next assignment regarding this information!
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