# Find Distance of Car, given Rest-Energy

• blue_lilly
In summary: But unfortunately, the calculation was based on the assumption that all the aspirin's mass could be converted into energy, which is not possible in reality.
blue_lilly

## Homework Statement

Suppose one gallon of gasoline produces 1.01×108 J of energy, and this energy is sufficient to operate a car for 18.2 miles. An aspirin tablet has a mass of 332 mg. If the aspirin could be converted completely into thermal energy, how many miles could the car go on a single tablet?

## The Attempt at a Solution

1 gallon of gas= (1.01E8) J
Distance of car(on gas)= 18.2 miles
Mass(aspirin)= 332 mg
Looking for
Distance of car(on asprin)=?

I converted the mass from grams to kilograms.
332mg = (332E-3)g = (332E-6)kg

*After this I'm not sure if I'm doing the right thing.*
The problem says "converted completely into thermal energy" so I'm assuming that this means I need to find the rest energy.
Erest=mc^2 [m=mass in kg; c=speed of light=(3E8)m/s]
=(332E-6)(3E8)^2
=(332E-6)(9E16)
=(2.988E13) J​

I then set up the energy of gas, distance on gas and the energy I found abvoe of the asprin, to solve for distance on asprin?
(distance of gas)/(energy of gas)=(distance of aspirin)/(energy of aspirin)
=(18.2 miles)/((1.01E8)J)=(?distace of asprin?)/((2.988E13)J)
=[(18.2)(2.988E13)]/(1.01E8)
=(5.43816E14)/(1.01E8)
=5384316.832 miles = (5.38E6) miles​

However that answer is incorrect and I'm not sure if I am even using the right formulas for this problem.

Any help would be greatly appreciated!

im not a guru btw

The correct answer is (5.38E6)mi. My calculations were correct, I just had my units of measurement wrong.

1 person
errr so a gallon of gas get you 18 miles and an aspirin 5.38*10^6 miles ?

i guess we been using the wrong fuel all this time...

Patolord said:
errr so a gallon of gas get you 18 miles and an aspirin 5.38*10^6 miles ?

i guess we been using the wrong fuel all this time...

If only it really worked like that, we would saving a lot of money. C:

## 1. What is the rest-energy of a car?

The rest-energy of a car refers to the energy of the car when it is at rest, meaning it is not moving. It is a measure of the car's mass and is typically represented by the famous equation E=mc², where E is energy, m is mass, and c is the speed of light.

## 2. How is the rest-energy of a car calculated?

The rest-energy of a car can be calculated using the equation E=mc², where m is the mass of the car in kilograms and c is the speed of light in meters per second. Simply multiply the mass of the car by the square of the speed of light to get the rest-energy in joules.

## 3. Why is it important to know the rest-energy of a car?

Knowing the rest-energy of a car is important because it helps us understand the relationship between mass and energy. It also plays a crucial role in understanding the behavior of objects at high speeds, such as in the case of a moving car.

## 4. How does the rest-energy of a car affect its movement?

The rest-energy of a car does not directly affect its movement. However, as the car's speed approaches the speed of light, its mass increases and therefore its rest-energy also increases. This can have an impact on the car's acceleration and overall behavior.

## 5. What other factors besides rest-energy affect the distance traveled by a car?

There are several other factors that can affect the distance traveled by a car, such as the car's initial velocity, the force applied to the car, and the presence of external forces like friction. The car's rest-energy may also play a role in its movement, as explained by Einstein's famous equation E=mc².

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