a) A crate of mass 67.9 kg rests on a level surface, with a coefficient of kinet
ID: 1553185 • Letter: A
Question
a) A crate of mass 67.9 kg rests on a level surface, with a coefficient of kinetic friction 0.98 . You push on the crate with an applied force of 840 N. What is the magnitude of the crate's acceleration as it slides? ________m/s2
d)Different situation now. Youre out in space, on a rotating wheel-shaped space station of radius 326 m. You feel planted firmly on the "floor", due to artificial gravity. The gravity you experience is earth- normal, that is, g=9.8 m/s2. How fast is the space station rotating in order to produce this much artificial gravity? ___________revolutions per minute (rpm)
e)What would the radius of the space station have to be, rotating at the rate you calculated in part (d), to produce artifical gravity of 30 m/s2? ____________m
Please show all work!
Explanation / Answer
a)
Fnet = F - uk*m*g
from newtons second law
Fnet = m*a
acceleration a = (F- uk*m*g)/m
a = (840-(0.98*67.9*9.8))/67.9 = 2.77 m/s^2
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b)
Fnet = mg*sintheta - uk*m*g*costheta
Fnet = m*a
mg*sintheta - uk*m*g*costheta = m*a
g*(sintheta - uk*costheta) = a
a = 12.4 m/s^2
9.8*(sintheta - (0.98*costheta)) = 2.77
sintheta = x
costheta = sqrt(1-x^2)
9.8*(x - (0.98*sqrt(1-x^2))) = 2.77
sintheta = 0.83
theta = sin^-1(0.83)
theta = 56.1 degrees
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(c)
if uk = 0
9.8*(sintheta ) = 2.77
theta = 16.42 degrees
==============
(d)
acceleration of space station a = r*w^2
given a = 9.8 m/s^2
9.8 = 326*w^2
w = 0.174 rad/s
w = 0.174*(60/(2pi)) rpm
w = 1.66 rpm
====================
e)
acceleration of space station a = r*w^2
given a = 30 m/s^2
w = 0.174 rad/s
30 = r*0.174^2
radius = 991 m <<<<-------------answer
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