Respuesta :
The force with which the man presses the knife against the stone is 2.96 N.
Given that,
Diameter of the stone d = 45 cm = 0.45 m
Radius r = 45/2 cm = 22.5 cm = 0.225 m
Initial angular velocity ω₀ = 200 rpm = 200* 2π/6 rad/s = 20.94 rad/s
Final angular velocity ωf = (1 - 0.1)* 200 rpm = 180 rpm = 180* 2π/6 rad/s = 18.85 rad/s
Mass of the stone m = 25 kg
Coefficient of kinetic friction μ*k = 0.2
Time t = 10 s
Part a:
By using the equation of motion with uniform angular acceleration we will find out the angular acceleration of grindstone:
ω* f = ω₀ + α*t
⇒ α = ( ω* f - ω₀) / t = (18.85 rad/s - 20.94 rad/s)/ (10s) = -0.21 rad/s²
Negative sign shows that the wheel is decelerating.
Part b:
Consider the rim of grindstone as a solid disk, therefore the moment of inertia
I = 0.5*m*r² = 0.5*25* (0.225)²
We know that, Torque = Force* perpendicular distance
τ = (μ*k*F)*r ----(1)
Also:
τ = I* α = 0.5*25* 0.225²* 0.21 = 0.133 N-m
F = 0.133/(0.2*0.225) = 2.96 N
Thus, the force with which the man presses the knife against the stone is 2.96N.
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