The work required to deflect a typical AFM cantilever by 0.10 nm is 1.2e-20 J. (
ID: 1404371 • Letter: T
Question
The work required to deflect a typical AFM cantilever by 0.10 nm is 1.2e-20 J. (a) What is the spring constant of the cantilever? (b) How much work is required to increase the deflection of the cantilever from 0.10 nm to 0.20 nm? The work required to deflect a typical AFM cantilever by 0.10 nm is 1.2e-20 J. (a) What is the spring constant of the cantilever? (b) How much work is required to increase the deflection of the cantilever from 0.10 nm to 0.20 nm? The work required to deflect a typical AFM cantilever by 0.10 nm is 1.2e-20 J. (a) What is the spring constant of the cantilever? (b) How much work is required to increase the deflection of the cantilever from 0.10 nm to 0.20 nm?Explanation / Answer
Energy stored in cantilever , E = work done to deflect = 1.2 x 10-20 J
deflection = X = 0.10 nm = 0.1 x 10-9 m
spring constant = K
a)
Energy stored is given as
E = (0.5) K X2
1.2 x 10-20 = (0.5) K (0.1 x 10-9 )2
K = 2.4 N/m
b)
Xi = initial deflection = 0.1 x 10-10 m
Xf = final deflection = 0.2 x 10-10 m
k = spring constant = 2.4
Work done is given as
Work done = Final energy stored - initial energy stored
W = (0.5) K Xf2 - (0.5) K Xi2
W = (0.5) (2.4) ((0.2 x 10-10 )2 - (0.1 x 10-10 )2 )
W = 3.6 x 10-22 J
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