### Part 2 : Equation Analysis

Equation 1: E = mc^{2}

**Question 1: **Find out what the things in this equation (using your book or a net search will do it) are and identify them as either variables or constants.

E = **energy** (**variable** measured in Joules)

m = **mass** (**variable** measured in kilograms)

c² = **speed of light squared** (a **constant** 34,596,000,000 miles per second)

**Question 2:** What is the size of c^{2}?

The size of **c²** in miles per second is **34,596,000,000**

**Question 3:** Are mass and energy related? Answer yes or no and then provide a brief explanation of your answer based on the analysis of the equation.

**Yes** mass and energy are related. **Energy increases** as **mass** of an object **increases**.

**Question 4: ** Analyze the statement: “if it is possible to change mass into energy a little bit of mass could produce a lot of energy”. Is it true or not? Provide a brief explanation based on your analysis of the equation

Yes, it is true. Given the equation if you take say 10kg of mass, the difference in joules of electricity is **enormous**, while the difference in kg of m is rather **insignificant** in comparison

Equation 2: d = gt^{2}/2

**Question 5. **Which of the following statements do you agree with and why? Use the equation to support your answer (you can also refer to the learning from equations module files).

a) heavy objects fall faster than lighter objects

b) objects fall at the same speed (if no air resistance) and weight doesn’t matter.

I agree with statement b (objects fall at the same speed (if no air resistance) and weight doesn’t matter)

There is no w, or weight in the equation. Meaning simply it doesn’t matter to the equation.

Equation 3: v = gt

**Question 6: **Which of the following statements do you agree with and why? Use the equation to support your answer (you can also refer to the learning from equations module files).

c) heavy objects fall faster than lighter objects

d) objects fall at the same speed (if no air resistance) and weight doesn’t matter

Again, I agree with statement d (objects fall at the same speed (if no air resistance) and weight doesn’t matter). There still is no variable weight, in the equation v = gt which means it simply doesn’t matter to the outcome of the equation.

**Hammer VS. Feather (YouTube video that illustrates a feather and a hammer dropped simultaneously on the moon)**

**Question 7: **For most of recorded history, people thought that heavy objects naturally and under all conditions fall faster than lighter objects. Why did it take us so long to realize the true state of affairs?

We couldn’t conduct experiments under little or now air resistance here on earth. Scientific Method states that once an experiment debunks the previous known results, then we have to trash validity. Once we conducted this on the moon, only the conspiracy theorists still believe that object don’t fall at the same speed.

**Question 8: **The Earth’s gravity DOES exert a greater force on heavier objects than lighter ones (these forces are called weight). However, with no air resistance objects fall at the same speed in a given gravity field. The weight difference can be thousands of pounds to one and the objects still fall at the same speed. What physical property of mass compensates for the difference in applied forces?

Inertia.

Equation 4: e = 1 – T_{cold}/T_{hot}

*This is the equation for the efficiency of a heat engine (your car is a heat engine unless you have an electric model). An e = 1 is 100% efficiency, meaning 100% of the energy gets used to do what you want to do with no “wasted”, unrecoverable energy. An e = 0 is an efficiency of zero with none of the energy going to what you want to do and all of the energy being “wasted” or in unrecoverable forms.*

*The temperatures in this equation are in the Kelvin scale where the lowest temperature is 0 degrees. There are no negative temperatures in the Kelvin scale. A temperature we might encounter on Earth would be about 300 degrees Kelvin.*

**Question 9: **Is it possible to achieve 100% efficiency, *in theory,* by lowering the temperature of the environment surrounding the heat engine (T_{cold})? Why or why not?

Yes, in theory if you could lower the temperature to absolute zero 100% efficiency can be achieved.

**Question 10: **Is it possible, *in practice*, to achieve 100% efficiency by lowering the temperature of the environment surrounding the heat engine (T_{cold})? Why or why not?

No, you cant operate an engine in absolute zero temperatures.

**Question 11: **Is it possible to achieve 100% efficiency, *in theory,* by raising the internal operating temperature of the heat engine (T_{hot})? Why or why not?

In theory yes, it is possible but it’s just not practical.

**Question 12: **Is it possible to achieve 100% efficiency, *in theory,* by raising the internal operating temperature of the heat engine (T_{hot})? Why or why not?

Again, in theory yes. If you could either operate your car in an absolute zero temperature environment, OR operate your engine at an infinitely high temperature the result would be 100% efficiency. Although it’s incredibly impractical because of the temperatures needed are very extreme.

**Question 13****:**** **If your car is not electric, it is a heat engine and is subject to the efficiency equation. Is it possible to build a car, using any kind of burning fuel, that is 100% efficient? Explain.

No, it’s not possible. No burning fuel burns that hot. Carnot’s equation also explains that this is not possible. Friction is always present in ALL engines and so 100% efficiency is simply not possible. Even in the absence of friction it’s not possible.