-Using a digital camera, you are taking a picture of your 1.80meter-tall friend standing at a distance of one meter from you. From the camera manual, you learned that the size of the sensor (electronic film) is 6mmx8mm. In other words, the sensor is rectangular with 6mm on one side and 8mm on the other. Calculate the focal length of the camera zoom lens that is required to fit the whole image of your friend onto the sensor.
Okay, here is what i got:
using the lens makers eq
(1/p)+(1/q)=(1/f)
so, f=6x8=48mm
(1/1000mm)+(1/q)=(1/48mm)
then,
q=50.42 so,
m=(q/p)= (50.42/1000)=0.0504
1.8meters=1800mm so,
1800mm x 0.0504=90.72mm
*Can someone check my calculation for this problem?*
-An average person needs 2,000 Kcal of energy a day. One Kcal = 1,000 calories and one calorie = 4.184 Joules.
-----Estimate the cost of foods that you take each day and calculate the cost for you to produce one Joule of energy, excluding health maintenance and clothing costs. This is referred to as direct human energy cost, excluding overhead charges.
*Okay so i figured that it takes 8368000 joules a day from the given info but how do i figure cost of one joule? i figure i use about $12 a day on food.
Last prob that i need help on:
Find out the baseline cost of electricity per KWxHour at home, where KW = Kilowatts. Since one joule = one wattxsecond, one KWxhour = 1,000watts x 3,600 seconds = 3,600,000 joules. Now calculate the electric energy cost per Joule.
So, the average is 1.5Kwatt=1500watts.How do i get the cost for one joule.
Srry, for the long post but i really need help, i tried all the problems to the extent that i know how too.
On the first. I absolutely do not understand how you got f=48mm
M=hi/ho=1.8/.008 figure ti.
M=do/di and you know do, so figure di
then use the lens equation to solve for f.
On the second.
cost/joule=12/joules=12/calories*4.2
Please post problems that are as long as yours one at a time. That way more people will see them who might have time to answer one or more.
I don't understand how you got the focal length to be 48 by multiplying 6 and 8. Those (6 and 8 mm) are the rectangular dimensions of the image. Your answer certainly does not follow from the lens maker's equation. The demagnification ratio of the 1.8 meter tall person onto the 8 mm dimension of the focal plane is 1800/8 = 225. That means di = (1/225)*do
di = 1000/225 = 4.444 mm
1/1000 + 1/4.444 = 1/f
f = 4.42 mm
That would be a very wide angle focal length setting.. not one commonly found with a zoom lens.
There are two things wrong with this question. It asks for the cost to PRODUCE (not consume) one joule of energy. The body is NOT 100% efficient in producing energy (doing work). Most of the rest produces body heat; some becomes added weight. Also, as you noted, the cost of food per Calorie depends upon what you eat and where you eat it. Right now, I am on a 1000 Calorie a day diet that only costs about a dollar a day. Some people spend 100 times that much a day eating in restaurants.
Sure, I can help you with these problems.
Problem 1: Calculating the focal length of the camera zoom lens
Your calculations seem to be correct. By using the lens makers equation, you found that the focal length of the camera zoom lens required to fit the whole image of your friend onto the sensor is approximately 90.72mm.
Problem 2: Estimating the cost per Joule of energy from food
To estimate the cost of one Joule of energy, you would divide the total cost of your daily food intake by the total energy consumed. Given that you spend around $12 on food and consume 8368000 joules, the cost per Joule would be:
Cost per Joule = Total cost of food / Total energy consumed
Cost per Joule = $12 / 8368000 J
To find the exact cost per Joule, you would need to perform the calculation using a calculator or computer. Remember to convert the answer to the desired unit, such as dollars per Joule.
Problem 3: Calculating the electric energy cost per Joule
To calculate the electric energy cost per Joule, you need to know the baseline cost of electricity per Kilowatt-hour (KWh) at home. You mentioned that the average power consumption is 1.5 Kilowatts (1500 Watts).
First, convert the average power consumption from Kilowatts to Joules per second:
Average power consumption = 1.5 Kilowatts = 1500 Watts
Next, convert from Watts to Joules by multiplying the average power consumption by the number of seconds in an hour (3600 seconds):
Conversion from Watts to Joules:
Average power consumption = 1500 Watts = 1500 Joules/second
Energy for one hour = 1500 Joules/second × 3600 seconds = 5,400,000 Joules
Finally, divide the cost of one Kilowatt-hour (KWh) by the energy consumption in Joules:
Electric energy cost per Joule = Cost of one KWh / Energy consumption in Joules
To find the exact cost per Joule, you would need to know the actual cost of one KWh from your electricity provider, and then perform the calculation using a calculator or computer.
I hope this helps! Let me know if you have any further questions.