Compute the coefficient of friction at block:
The frame shown in Figure rotates about a vertical axis. The coefficient of friction under block A is 0.4. Compute the coefficient of friction at block B if B starts to rise when the frame rotates at 40 rpm.
Solution
As the table rotates, block A shall try to move outwards.
We have, ω = (40 × 2 π )/60
= 4.19 rad / sec
The acceleration acting on Block A towards axis of rotation shall be
r ω^{2} = 21.06 m / sec^{2} (r = 1.2 m)
let FBD of Block A (Figure (b)), writing equilibrium equation, we have
T = (100/g ) × a_{n} - F
We get,
T = (100 /g) × a_{n} - 0.4 F_{1}
= (100 /9.81) × 21.06 - 0.4 × 100
= 174.67 N
Now considering FBD of Block B, (Figure (c)).
Figure 6.15(c)
We get,
T = 80 + (80 /9.81) × 21.06 × μ
∴ μ = (174.67 - 80)/171.74
= 0.55