1. The price of gold is 200 dollars/oz. How much did 1 g of gold cost that day? (1 oz = 28.4 g)Use dimensional analysis.
2. How many minutes does it take light from the sun to reach Earth? (Distance from sun to Earth is 93 million mi, speed of light= 3 x 10^8 m/s) Use dimensional analysis.
Please, and thank you!
These are easy to do if you follow through and check the units. All of them are as follows:
something x factor = another unit.
For #1.
We have gold at 200 dollars per oz. We want to convert that to dollars per gram. The problem tells us that the factor is 1 oz = 28.4 and we can write that as 1 oz/28.4 g OR 28.4 g/1 oz.
cost per gram = cost per oz x factor
cost per g = $200/oz x (1 oz/28.4 g) =??.
Note that oz in the denominator of the first term will cancel with the oz in the numerator of the second term and we are left with $/g for the cost which is what we want. We COULD have written $200/oz x (28.4 g/1 oz) but then the final answer would be in units of $*g/oz2 and that is NOT the unit we want. You will ALWAYS know which way to place the factor if you follow the units and make sure the final unit is the one you want. I hope this helps. I will leave #2 for you for practice.
8 minutes
1. To find out how much 1 g of gold cost on the given day, we can use dimensional analysis.
First, we know that 1 ounce (oz) is equal to 28.4 grams (g). We can set up our dimensional analysis equation like this:
1 oz = 28.4 g
We are given that the price of gold is 200 dollars per ounce. To find the price of 1 gram, we need to convert the price per ounce to price per gram using dimensional analysis:
200 dollars/oz * (1 oz/28.4 g) = (200/28.4) dollars/g
Simplifying this calculation, we get:
200/28.4 ≈ 7.04 dollars/g
Therefore, on that day, 1 gram of gold cost approximately 7.04 dollars.
2. To determine how many minutes it takes for light to travel from the sun to Earth, we can use dimensional analysis.
We are given the distance from the sun to Earth as 93 million miles and the speed of light as 3 x 10^8 meters per second. To find the time it takes for light to travel this distance, we need to convert miles to meters using dimensional analysis.
First, we convert miles to meters:
93 million miles * (1609.34 meters/1 mile) = (93 million * 1609.34) meters
Next, we divide the distance by the speed of light:
(93 million * 1609.34) meters / (3 x 10^8 meters per second)
Simplifying this calculation, we get:
(93 million * 1609.34) / (3 x 10^8) seconds
To convert seconds to minutes, we can divide this result by 60:
((93 million * 1609.34) / (3 x 10^8)) / 60 minutes
Evaluating this equation, we find that it takes approximately 8.31 minutes for light to travel from the sun to Earth.