Imagine you’re stuck on a desert island with no internet, no books, and an evil genius who will only let you go if you can tell him how much a million dollars weighs. Luckily, you’re a physicist, so you can figure it out using your mind! Here’s how you can do it by making smart approximations.
First, let’s think about the size of a dollar bill. We might not know its exact weight, but we do know its dimensions. A dollar bill is about 15 cm long and 5 cm wide. But what about its thickness? We don’t know that either, but we can make a good guess.
Money is made of paper, and we know that a thick book, like a ‘Harry Potter’ book, is about 5 cm thick with 400 sheets of paper. This means there are about 80 sheets of paper per centimeter. Using this information, we can estimate the volume of a dollar bill.
To find the volume of a dollar bill, we multiply its length, width, and thickness. So, 15 cm long times 5 cm wide times one 80th of a cm thick gives us a volume of 0.9 cubic centimeters for one dollar bill.
Now, we need to figure out how much this volume weighs. We know that a cubic centimeter of water weighs one gram. Since money is a “liquid asset,” let’s assume a cubic centimeter of dollars also weighs about a gram. This means one dollar weighs approximately 0.9 grams.
To find out how much a million dollars weighs, we multiply 0.9 grams by one million. This gives us 900,000 grams, which is the same as 900 kilograms or about 2,000 pounds.
So, why are approximations important in physics? They help us make quick and reasonable estimates without needing to do long and complicated calculations. In our example, we found that a million dollars weighs about a ton, which is actually quite close to the real weight according to the US Treasury.
Approximations are a valuable tool in physics and everyday life, helping us solve problems even when we don’t have all the exact details.
Gather a few dollar bills and a ruler. Measure the length and width of the bills to verify the dimensions mentioned in the article. Discuss with your classmates how these measurements help in estimating the volume of a dollar bill.
Find a thick book and count the number of pages. Measure the thickness of the book using a ruler. Calculate the average thickness of a single page and compare it to the estimation used in the article. Discuss why approximations are useful in this context.
Using the dimensions of a dollar bill, calculate its volume in cubic centimeters. Then, compare your results with the article’s estimation. Discuss any differences and the importance of making reasonable assumptions in physics.
Assume a dollar bill weighs approximately 0.9 grams. Calculate the total weight of different amounts of money (e.g., $100,000, $500,000) and compare these weights to everyday objects. Share your findings with the class.
Discuss with your classmates other scenarios where approximations are useful in everyday life. Create a list of situations and share how making quick estimates can be beneficial. Reflect on how this skill can be applied in various fields.
Dollar – A unit of currency used to measure value, often used in physics to discuss the cost of materials or equipment. – The physics lab needed to budget several hundred dollars for new experiment equipment.
Weight – The force exerted on an object due to gravity, measured in newtons. – The weight of the object was measured to be 50 newtons using a spring scale.
Volume – The amount of space that an object or substance occupies, measured in cubic units. – To find the volume of the cube, we multiplied its length, width, and height.
Grams – A metric unit of mass equal to one thousandth of a kilogram. – The mass of the small metal ball was measured to be 200 grams.
Kilograms – The base unit of mass in the International System of Units (SI), equivalent to 1,000 grams. – The physics textbook weighed about 1.5 kilograms.
Approximations – Estimates or near values used when exact values are not necessary or possible. – In physics, we often use approximations to simplify complex calculations.
Physics – The branch of science concerned with the nature and properties of matter and energy. – In physics class, we learned about the laws of motion and how they apply to everyday life.
Calculations – Mathematical processes used to determine a numerical result. – The calculations showed that the speed of the car was 20 meters per second.
Dimensions – Measurements that define the size and shape of an object, such as length, width, and height. – The dimensions of the rectangular prism were needed to calculate its volume.
Estimates – Rough calculations or judgments of value, number, quantity, or extent. – The students made estimates of the time it would take for the pendulum to complete one swing.
