6) If a flea has a mass of 2.0x10^2 micrograms jumps vertically to a height of 65mm and 75% of the energy comes from elastic potential energy stored in the protein, determine the initial quantity of elastic potential energy.
drwls said to use:
(1/2)M g H = (0.75)E where E is the potential energy stored in protein and H is the height that the flea can jump.
I don't understand how that would work. Also would you convert 2.0x10^2ug to kg?
He is right. The gravitational PE the flea gains is equal to .75 * the initial stored energy. BTW: energy stored in protein is chemical energy, not elastic.
Yes, convert grams to kg, and H to meters, and of course, g is 9.8m/s^2.
I got 8.4x10^-8. Is that right?
Energy=.5*200E-6*.065/.75
paste .5*200E-6*.065/.75 into the google search engine.
To solve the problem, you can start by understanding the equation provided by drwls:
(1/2)Mgh = (0.75)E
where M is the mass of the flea, g is the acceleration due to gravity, h is the height the flea can jump (given as 65 mm), and E is the initial quantity of elastic potential energy.
Now, let's break down the equation and understand it step by step:
1. Convert the mass of the flea from micrograms (μg) to kilograms (kg):
To convert 2.0x10^2 μg to kg, you divide it by 1,000,000 (since there are 1,000,000 micrograms in a kilogram). Therefore:
Mass (M) = 2.0x10^2 μg / 1,000,000 = 2.0x10^(-4) kg
2. Calculate the gravitational energy (Mgh term):
The gravitational potential energy in this case is given by the product of the mass (M), acceleration due to gravity (g), and the height (h):
Gravitational Potential Energy = Mgh
3. Substitute the given values into the equation:
- Mass (M) = 2.0x10^(-4) kg
- Acceleration due to gravity (g) = 9.8 m/s^2
- Height (h) = 65 mm = 65/1000 m (as we need to convert it to meters)
4. Calculate the initial quantity of elastic potential energy (E):
Using the given equation: (1/2)Mgh = (0.75)E
- Solve for E:
E = (1/2)Mgh / (0.75)
5. Substitute the values of M, g, h into the equation and calculate E.
Once you substitute the values and perform the calculations, you will be able to determine the initial quantity of elastic potential energy.