- #1
hdp12
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Homework Statement
PROBLEM:
You have a horizontal grindstone (a disk) that is mass m, has a radius r, and is turning at f in the positive direction. You then press a steel axe against the edge with a force of F in the radial direction.
RANDOMIZED VARIABLES:
m= 95 kg
r= 0.33 m
f= 92 rpm
F= 25 N
a) Assuming the kinetic coefficient of friction between steel and stone is 0.20, calculate the angular acceleration of the grindstone in rad/s2
√ANSWER: α = -0.319
See section 3 for explanation
b) What is the number of turns, N, that the stone will make before coming to rest?
SUBMISSION HISTORY:
XN = 0.003
XN = 0.017
Homework Equations
τ=rFsin(θ)
τ=Iα
α=τNET/I
↓ Moment of Inertia of a uniform disk about its center of mass
I=[itex]\frac{1}{2}[/itex]mR2
Fk= μkF
ωf=ωi+αΔt
θf=θi+ωiΔt+[itex]\frac{1}{2}[/itex]αΔt2
The Attempt at a Solution
I solved part a) by doing the following
Kinetic Friction Force
Fk= μkFTorque by Fk
τ=rFsin(θ) = rFk = rμkFMagnitude of Angular Acceleration (will be negative)
α=τNET/I = rμkF/[itex]\frac{1}{2}[/itex]mr2= (0.33 m)(0.2)(25 N) / [itex]\frac{1}{2}[/itex](95 kg)(0.33 m)2
= -0.319 rad / s2
OKAY. Now onto the next part. Part b).
First I took the initial velocity, which is in rotations per minute, and converted it into radians per second
[STRIKE]rot[/STRIKE]/[STRIKE]min[/STRIKE] ·2∏r/[STRIKE]rot[/STRIKE] · 1 [STRIKE]min[/STRIKE]/60 s
=∏/30 rad/s
so if ωi = ∏/30 rad/s
& ωf = 0 rad/s
I can solve for time by using the formula ωf=ωi+αΔt
0 rad/s = ∏/30 rad/s + -0.319 rad/s2Δt
-∏/30 rad/s = -0.319 rad/s2Δt
Δt = 0.3283 s
now using this time, I plug it and the rest of my variables into the formula θf=θi+ωiΔt+[itex]\frac{1}{2}[/itex]αΔt2
=(∏/30 rad/s)(0.3283 s) + [itex]\frac{1}{2}[/itex](-0.319 rad/s2)(0.3283 s)2
=0.03438 rad + -0.0172 rad
=0.01719 rad
1rot/2∏rad · 0.01719 rad = 0.002736 rot
I tried entering that, and it was incorrect. Then I tried entering the answer I got in radians and that was incorrect too.. So I guess I'm just confused.