Answer:
0.48
Step-by-step explanation:
m = mass of disc shaped grindstone = 50 kg
d = diameter of the grindstone = 0.52 m
r = radius of the grindstone = (0.5) d = (0.5) (0.52) = 0.26 m
w₀ = initial angular speed = 850 rev/min = 850 (0.10472) rad/s = 88.97 rad/s
t = time taken to stop = 7.5 sec
w = final angular speed 0 rad/s
Using the equation
w = w₀ + α t
0 = 88.97 + α (7.5)
α = - 11.86 rad/s²
F = normal force on the disc by the ax = 160 N
μ = Coefficient of friction
f = frictional force
frictional force is given as
f = μ F
f = 160 μ
Moment of inertia of grindstone is given as
I = (0.5) m r² = (0.5) (50) (0.26)² = 1.69 kgm²
Torque equation is given as
r f = I |α|
(0.26) (160 μ) = (1.69) (11.86)
μ = 0.48