Problem 2 - College Physics

Question

(a) The recommended daily allowance (RDA) of the trace metal magnesium is \(410 \mathrm{mg} /\) day for males. Express this quantity in \(\mu \mathrm{g} /\) day. (b) For adults, the RDA of the amino acid lysine is \(12 \mathrm{mg}\) per \(\mathrm{kg}\) of body weight. How many grams per day should a \(75 \mathrm{~kg}\) adult receive? (c) A typical multivitamin tablet can contain \(2.0 \mathrm{mg}\) of vitamin \(\mathrm{B}_{2}\) (riboflavin), and the \(\mathrm{RDA}\) is \(0.0030 \mathrm{~g} /\) day. How many such tablets should a person take each day to get the proper amount of this vitamin, assuming that he gets none from any other sources? (d) The RDA for the trace element selenium is \(0.000070 \mathrm{~g} /\) day. Express this dose in \(\mathrm{mg} /\) day.

Step-by-Step Solution

Answer

(a) 410,000 µg/day, (b) 0.9 g/day, (c) 2 tablets/day, (d) 0.070 mg/day.

Step 1: Convert milligrams to micrograms

The recommended daily allowance (RDA) for magnesium is given as 410 milligrams per day. To convert milligrams to micrograms, use the conversion factor: \[1 ext{ mg} = 1000 ext{ µg}\]So, the calculation is \[410 ext{ mg} \times 1000 = 410,000 ext{ µg}\]Therefore, 410 mg/day is equivalent to 410,000 µg/day.

Step 2: Calculate lysine requirement for given body weight

The RDA of lysine is 12 mg per kg of body weight. For a 75 kg adult, the lysine requirement can be calculated as:\[75 ext{ kg} \times 12 \text{ mg/kg} = 900 \text{ mg}\]Since we need the amount in grams, convert it by using:\[1 ext{ g} = 1000 ext{ mg}\]Therefore, \[900 \text{ mg} = 0.9 \text{ g}\]Thus, a 75 kg adult should receive 0.9 g of lysine per day.

Step 3: Determine the number of tablets for RDA of Vitamin B2

The RDA for vitamin B2 is given as 0.0030 grams per day. Each tablet contains 2.0 mg, so first convert the RDA from grams to milligrams:\[0.0030 ext{ g} = 3.0 ext{ mg}\]To meet the RDA, the number of tablets required is:\[\text{Number of tablets} = \frac{3.0 \text{ mg}}{2.0 \text{ mg/tablet}} = 1.5\]Since you can't take half a tablet easily, a person should take at least 2 tablets per day to meet the RDA.

Step 4: Convert grams to milligrams for selenium RDA

The RDA for selenium is given as 0.000070 grams per day. Convert it to milligrams using the conversion:\[1 ext{ g} = 1000 ext{ mg}\]Thus, \[0.000070 ext{ g} \times 1000 = 0.070 \text{ mg}\]Therefore, the RDA for selenium is 0.070 mg per day.

Key Concepts

Conversion of Units

Understanding how to convert between different units is crucial, especially when dealing with dietary recommendations in nutrition. It allows us to interpret and apply data correctly. For example, if you have a recommended daily allowance (RDA) for magnesium of 410 mg per day, converting this into micrograms helps in contexts where smaller amounts are relevant. To convert milligrams to micrograms, use the conversion rule:

• 1 mg = 1000 µg

This means that 410 mg is equivalent to 410,000 µg. By breaking down these conversions into simple steps, you can handle more complex nutritional data with ease.
Such skills are not only applicable to dietary guidelines but also in various scientific and technical fields.

Trace Metals

Trace metals like magnesium, selenium, and others play essential roles in the human body. These elements are required in only small amounts, yet they are vital for maintaining proper physiological functions. Magnesium, for instance, is crucial for nerve function and muscle contraction. The RDA for magnesium ensures you receive enough of this mineral to support these vital functions.
Similarly, selenium, another trace metal, is important for immune function and thyroid hormone metabolism. The RDA for selenium is very low, which reflects its role as a trace element required in minute quantities. Understanding the RDA for each trace metal helps maintain a balanced nutritional intake, critical for health and well-being.

Amino Acids

Amino acids are the building blocks of proteins and are essential for numerous bodily functions, from repairing tissue to synthesizing hormones. The RDA of amino acids like lysine is crucial for maintaining these functions. Lysine, for example, helps in the production of collagen and supports immune system functioning.
For adults, it's typically recommended to consume lysine at a rate of 12 mg per kilogram of body weight daily. For a 75 kg adult, this translates to 900 mg of lysine, or 0.9 g per day, emphasizing the importance of amino acids in everyday nutrition significantly.

Vitamins

Vitamins are organic compounds that people need in small quantities for normal functioning. Vitamin B2, or riboflavin, is crucial for energy production and the metabolism of fats, drugs, and steroids. The RDA for vitamin B2 is 3.0 mg per day.
People often obtain their vitamin intake through food or supplements. If a vitamin B2 supplement tablet contains 2 mg, a person requires 1.5 such tablets to meet their daily needs. Since it's impractical to consume half a tablet, two tablets suffice. Understanding how to achieve vitamin RDAs helps prevent deficiencies and supports overall health.

Selenium Requirement

The element selenium is vital, albeit in trace amounts, for the proper functioning of the body. It plays a crucial role in metabolism and protects the body from oxidative damage. The RDA for selenium is 0.000070 grams per day, which might seem negligible but underscores its importance as a trace nutrient.
When expressed in milligrams, the RDA converts to 0.070 mg per day. This conversion helps in understanding and managing this element's intake better, ensuring the body receives just enough to maintain optimal health. Paying attention to these small amounts is key in dietary planning and maintaining overall health.