The omitted part of the question shown in bold format
The lead of the threaded shaft of the C-clamp is 0.05 in., and the mean radius of the thread is r = 0.15 in. Assume μs = 0.18 and μk = 0.16. What couple must be applied to the shaft to exert a 30-lb force on the clamped object?
Answer:
C = 0.967 in. lb
Explanation:
Given that:
The lead of the threaded shaft of the C-clamp is 0.05 in.
∴ the pitch of the screw = 0.05 in
the mean radius of the thread is r = 0.15 in.
Assuming:
(μs)= 0.18 which implies the coefficient of the static friction
(μk) = 0.16 (coefficient of kinetic friction)
Force = 30-lb
What couple must be applied to the shaft to exert a 30-lb force on the clamped object?
To determine the Couple (C) that must be applied; we use the expression:
C = Fr tan ([tex]\theta_k[/tex] + [tex]\alpha[/tex])
where; F = force
r = mean radius
[tex]\theta_k[/tex]= angle of kinetic friction
[tex]\alpha[/tex] = pitch angle
NOW, let's take then one after the other.
From the coefficient of the static friction and the kinetic friction; we can solve for their respective angles, so we have:
Angle of static friction ([tex]\theta_s[/tex]) [tex]= tan^{-1}(U_s)[/tex]
([tex]\theta_s[/tex]) = [tex]tan^{-1}(0.18)[/tex]
([tex]\theta_s[/tex]) = 10.204°
Angle of kinetic friction ([tex]\theta_k[/tex]) [tex]= tan^{-1}(U_k)[/tex]
[tex]\theta_k[/tex] [tex]= tan^{-1}(0.16)[/tex]
[tex]\theta_k[/tex] = 9.0903°
To determine the pitch angle([tex]\alpha[/tex]); we apply the expression:
([tex]\alpha[/tex]) = [tex]tan^{-1}(\frac{p}{2 \pi r} )[/tex]
([tex]\alpha[/tex]) = [tex]tan^{-1}(\frac{0.05}{2 \pi 0.15} )[/tex]
([tex]\alpha[/tex]) = [tex]tan^{-1}(0.0530516 )[/tex]
([tex]\alpha[/tex]) = 3.0368°
Have gotten our parameters to solve for Couple (C); then we have:
C = Fr tan ([tex]\theta_k[/tex] + [tex]\alpha[/tex])
substituting our values; we have:
C = (30 × 0.15) tan ( 9.0903 + 3.0368)
C = 4.5 × tan ( 12.1271)
C = 4.5 × 0.2148761968
C = 0.96669428854 in.lb
C = 0.967 in. lb
Therefore, 0.967 in. lb couple must be applied to the shaft to exert a 30-lb force on the clamped object.
