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Hooke's Law is a concept and equation that describes the relationship between the force produced by a spring when a mass is pulling on it. When a spring is at rest, and has no outside force weighing on it, it is at its original length and coil. As you attach a mass to it, considering the effect of gravity on that mass, the spring will stretch as it gets weighed down.

At rest, the original spring is referred to as "ideal". As it is stretched it becomes "deformed". I chose this concept because when we learned it in class I found it interesting to see the math behind something we rarely think about: What makes a spring stretch?

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I chose this problem because it is fairly simple, yet properly showcases all aspects of Hooke's Law.

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A vector is a way of describing precise direction while also incorporating strength or size. In day to day life we describe things usually based on direction, without thinking about how strong something is. A vector is a good way to describe direction and strength. For example, if a car is driving North we know which way it is headed, but if a car is driving North at 30 meters per second for 100 meters, we now know how fast and how long the car is traveling and it has now become a vector. Vectors provide extra case sensitive information that give an objects path more specific guidelines.

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On earth, we are able to calculate the force of gravity based on the pressure of the atmosphere on our individual masses, pressing into the earth. But the force of gravity differs on other planets. Everyone is familiar with the story of Sir Isaac Newton and the apple, but the concept of gravity expands way further than just our earth.

Newton's concepts and equations for Universal Gravitation explain how any objects with mass react to one another through gravity, and how gravitational forces and pulls vary in different settings.

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There are many types of energy in the world, constantly exchanging into other forms, but the most commonly thought of type of energy is Kinetic Energy. Kinetic Energy is the energy used to describe objects in motion and the energy they produce. Objects have higher Kinetic Energy when they move faster or have a greater mass than lighter or slower moving objects. An example of an object with a large amount of Kinetic Energy would be a rollercoaster going down a slope, whereas an empty water bottle being thrown in the air would have less Kinetic Energy.

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Mechanical Advantage is a concept that relates the input force to the output force of a simple machine. It is more literally a ratio between these input and output forces that measures the magnification force, or the difference in strength of the input versus the output force. Mechanical Advantage can be used on a wide range of simple machines, from levers, to pulleys, to gears. Mechanical Advantage, when solved, typically shows how much stronger the output force is than the input force.

I chose this concept because it was one of the last ones we learned so it was very fresh on my brain. I also found that it was a very interesting concept that I had not been familiar with prior to our unit, whereas I had at least heard of the majority of our previous physics concepts.

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I chose this problem because like a vector, it is straight to the point.

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I picked this question because it was a more challenging question, but still displayed Universal Gravitation in an easy to understand way.

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I chose this problem because it is a good way to relate Kinetic Energy back to its real life applications.

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I struggled to pick a question I really liked for Mechanical Advantage, so I decided it would be best choose something simplistic.

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Get access to files anywhere through secure cloud storage and file backup for your photos, videos, files and more with Google Drive.

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Get access to files anywhere through secure cloud storage and file backup for your photos, videos, files and more with Google Drive.

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Get access to files anywhere through secure cloud storage and file backup for your photos, videos, files and more with Google Drive.

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Get access to files anywhere through secure cloud storage and file backup for your photos, videos, files and more with Google Drive.

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The equation for Hooke's Law is:
F=-kx
The F stands for force, as in the force being exerted by the spring or the resultant force being produced by the deformed spring. The units for force are N, Newtons.
The lowercase K stands for the spring constant. The constant is the amount of force, divided by the distance the spring stretches or becomes deformed. The units for the constant are N/m, Newtons per meter. The k, in this case, is negative to show the spring responds to the deformation in the opposite direction. If a vertical spring has a mass pulling it downwards, the resultant force will be going upwards.
The lowercase X stands for the displacement from equilibrium, which is a fancy way of saying how far the spring stretches from its original length. The units for x are in m, meters.

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Adding Vectors
When adding vectors on a graph, we can use the equation:
d=d1+d2+d3 and so on for however many vectors there are.
The sole, lowercase D stands for the total distance covered by all the vectors being added and the individual d's with a number represent the unique vectors that you are adding. This equation solves problems where you are looking for the total distance covered by multiple vectors.

The same equation can be used when looking for an unknown force, but instead of distance you use:
F4=F1+F2+F3 or so on. The F stands for the force of the vectors.

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Newton's Law of Universal Gravitation is expressed through the equation:
F=G (m1m2/r^2)
The F stands for Force, measured in Newtons. The G stands for the Gravitational Constant, which is a value that stays the same for all situations involving gravity. The value for G is 6.67x10^-11 N m^2/kg^2. The unit for G is Newtons for meters squared per kilograms squared. The lowercase M1 represents the mass of the first object and the lowercase M2 represents the mass for the second object in the equation. Both masses are in units of kilograms. And the lowercase R represents the distance between the two objects. In this case, the distance is squared or to the power of 2 in the equation. The r is in units of m, meters.

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The equation for Kinetic Energy is:
KE=1/2(mv^2)
Believe it or not, the KE stands for Kinetic Energy which is what the equation solves for. The lowercase M stands for mass, which is measured in kg, kilograms. The lowercase V is for velocity, measured in m/s, meters per second and in this equation is squared or raised to the power of 2. The velocity squared is multiplied by the mass and they are divided by 2 to find Kinetic Energy. The equation for velocity is v=d/t, which is velocity equals the distance an object travels, divided by the amount of time it takes to travel.

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MAThe general Mechanical Advantage equation is:
MA=Fo/Fi
The MA stands for Mechanical Advantage. The Fo is the symbol for the output force which is divided by Fi, the input force, to solve for Mechanical Advantage.
F, Force, can be found by:
F=m*a (mass times acceleration).
Variations of the general Mechanical Advantage formula include:
MA=Li/Lo
In this case, the input and output values are switched, and the L stands for the force on a Lever.

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This concept is important in the real world for a variety of reasons. For example, a team of construction workers need to buy a large spring to lift a heavy box with a crane. They would need to use this equation to figure out the maximum length the spring could stretch, holding the box at the end, without breaking. Another example of how this concept could be used is the spring on the scale for fresh produce at the supermarket. Hooke's Law is all around us.

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Like I described in the beginning, vectors provide values for strength and size where normal direction does not. Adding vectors can be used in daily life when trying to find the original or final force of multiple cars in a collision. By taking a car's direction, distance traveled and speed or force, you can use these equations to calculate the final force of a collision.

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This equation is VERY important in engineering and astrology. An example of how this equation could be used is when NASA launches a space craft and they need to know the gravitational pull between the space craft and the planet it orbits. This equation would help them find the appropriate mass for the space craft so it doesn't crash into the planet. This equation could also be used to calculate the gravitational force of meteor flying by earth.

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Finding the value of an object's Kinetic Energy can be used for almost anything. Like I wrote at the beginning, it would be a safety hazard to build a rollercoaster without calculating its Kinetic Energy first because if its too strong, the riders may be injured. Furthermore, you can use the equation to calculate the Kinetic Energy of a baseball that a pitcher throws during a game, or a car moving down the freeway. You can use this equation to find the Kinetic Energy of any object in motion.

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Mechanical Advantage obviously comes in handy when using simple machines, but it can tell you so much more than that. When using a lever to lift a heavy box it is critical to know the correct Mechanical Advantage before hand so no one gets injured and so on. The same goes for other simple machines like pulleys and large gears. With powerful machinery it is important to use this equation to be safe first.