An atomic force microscope cantilever, of rectangular cross section,
has a length, L of 200ππ
a width, b of 20ππ
and a depth, h of 1ππ
It is made of silicon nitride, which has a Young's modulus, πΈ of 300πΊππ.
What is the maximum force that can be applied with the cantilever, if the maximum strain in the beam is to be limited to 0.1%?
To find the maximum force that can be applied to the cantilever while keeping the maximum strain within the desired limit, we need to use the formula for strain:
Strain (Ξ΅) = (F * L) / (E * b * h^2)
where
Ξ΅ = strain
F = force applied
L = length of the cantilever
E = Young's modulus
b = width of the cantilever
h = depth of the cantilever
We can rearrange the formula to solve for the force (F):
F = (Ξ΅ * E * b * h^2) / L
Now, let's plug in the given values:
Ξ΅ = 0.001 (0.1% expressed as a decimal)
E = 300 GPa (convert to Pa by multiplying by 10^9)
b = 20 ΞΌm (convert to meters by multiplying by 10^-6)
h = 1 ΞΌm (convert to meters by multiplying by 10^-6)
L = 200 ΞΌm (convert to meters by multiplying by 10^-6)
F = (0.001 * 300 * 10^9 * 20 * 10^-12) / (200 * 10^-6)
Simplifying the expression:
F = 0.006 N
Therefore, the maximum force that can be applied with the cantilever is 0.006 Newtons.