The protein dynein powers the flagella of some one-cell organism. Biophysicists
ID: 1769474 • Letter: T
Question
The protein dynein powers the flagella of some one-cell organism. Biophysicists have found that dynein is intrinsically ocillatory and that it exerts a peak force of about 1.0 pN when it attaches to structures called microtubules. The resulting oscillations have amplitude 15 nm. A) if this system is modeled as a mass-spring system, what's the associated spring constant? B) if the oscillation frequency is 70Hz, what's the effective mass? C) what's the maximum speed and d) what is he total energy of the oscillations? The protein dynein powers the flagella of some one-cell organism. Biophysicists have found that dynein is intrinsically ocillatory and that it exerts a peak force of about 1.0 pN when it attaches to structures called microtubules. The resulting oscillations have amplitude 15 nm. A) if this system is modeled as a mass-spring system, what's the associated spring constant? B) if the oscillation frequency is 70Hz, what's the effective mass? C) what's the maximum speed and d) what is he total energy of the oscillations?Explanation / Answer
a) The question tells us that the force peaks at 1.0 pN. So from that we can say that we are at the maximum potential energy. Therefore we can use
E_total=U_elastic:
1/2*k*A^2=1/2*k*x^2.
From there we can conclude that A=x. A being the amplitude and x being the change in position. Therefore we can substitute A into the spring force equation: F_s=-k*x. With the substitution the new force equation would be F_s=-k*A.
For this question, your A is 15nm and your F_s=1.0pN. SO substitute those values in and get:
1.0pN=-k*15nm
to solve for k:
1.0pN/15nm=k <--- don't worry about the negative, this is not a vector
so:
6.7*10^-3 pN/nm=k
Conversion to N/m:
6.7*10^-5 N/m=k
b)Now that we have k, we can solve for the mass of the protein.
For this question we will use the formula for the frequency: f=Hz=(1/2pi)*sqrt(k/m)
Solve the formula for m:
m=k/(4pi^2*Hz^2)
So with these numbers:
m=(6.7*10^-5 N/m)/(4*(pi^2)*(66Hz^2))
m=3.9*10^-10 kg
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