A biophysicist grabs the ends of a DNA strand with optical tweezers and stretches it 28um . How much energy is stored in the stretched molecule if its spring constant is 0.046pN ?
E=kx²/2
Why did the biophysicist stretch the DNA strand with optical tweezers? Because it wanted to see how much energy it could store, of course! Now, let's get down to some stretching calculations, shall we?
The equation to calculate the energy stored in a stretched molecule is:
Energy = (1/2) * k * x^2
where k is the spring constant and x is the displacement. In this case, the displacement is given as 28 um (micro-meters), and the spring constant is given as 0.046 pN (pico-Newtons).
Let's do some unit conversions first to make it easier on ourselves. 28 um is equal to 0.000028 m, and 0.046 pN is equal to 0.000000000046 N.
Now we can plug these values into the equation and calculate the energy:
Energy = (1/2) * 0.000000000046 N * (0.000028 m)^2
And now, it's time for the magic of multiplication and exponentiation:
Energy ≈ 1.696 x 10^-14 Joules
So, the energy stored in the stretched DNA molecule is approximately 1.696 x 10^-14 Joules. Keep in mind that's a pretty small amount of energy, so don't go trying to power your clown car with it!
To calculate the energy stored in the stretched DNA molecule, we can use the formula:
Energy = (1/2) * k * x^2
Where:
- Energy is the energy stored in the molecule
- k is the spring constant
- x is the displacement or stretch length
Given:
- k = 0.046 pN (piconewton)
- x = 28 um (micrometer) = 28 * 10^-6 m (conversion to meters)
Let's plug in the values and calculate the energy:
Energy = (1/2) * 0.046 * (28 * 10^-6)^2
First, let's convert the spring constant to newton (N) from piconewton (pN):
1 pN = 10^(-12) N
Energy = (1/2) * 0.046 * (28 * 10^-6)^2
= (1/2) * 0.046 * (28 * 10^-6)^2
Now, let's calculate the result using a calculator:
Energy = 7.5 * 10^(-18) joules
Therefore, the energy stored in the stretched DNA molecule is approximately 7.5 * 10^(-18) joules.
To calculate the energy stored in a stretched DNA molecule, we can use the formula for the potential energy of a spring:
Potential Energy (U) = (1/2) * k * x^2
Where:
- U is the potential energy
- k is the spring constant
- x is the displacement or stretch length
In this case, the spring constant is given as 0.046 pN (piconewton), and the DNA molecule is stretched by 28 μm (micrometers).
First, let's convert the stretch length from micrometers to meters:
28 μm = 28 * 10^-6 m
Now we can calculate the energy stored in the stretched DNA molecule:
Potential Energy (U) = (1/2) * 0.046 pN * (28 * 10^-6 m)^2
Let's simplify the equation step by step:
Potential Energy (U) = (1/2) * 0.046 pN * (28 * 10^-6 m)^2
= 0.023 pN * (28 * 10^-6 m)^2
= 0.023 pN * (28 * 10^-6)^2 m^2
= 0.023 pN * 784 * 10^-12 m^2
= 0.023 pN * 7.84 * 10^-10 m^2
≈ 1.8032 * 10^-11 pN * m^2
Therefore, the energy stored in the stretched DNA molecule is approximately 1.8032 * 10^-11 pN * m^2.