a) A crate of mass 50.1 kg rests on a level surface, with a coefficient of kinet
ID: 1554420 • Letter: A
Question
a) A crate of mass 50.1 kg rests on a level surface, with a coefficient of kinetic friction 0.73 . You push on the crate with an applied force of 753 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 1097 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
Explanation / Answer
a)
acceleration a = Fnet /m
Fnet = F - fk = F - uk*m*g
a = (753 - (0.73*50.1*9.81))/50.1
a = 7.87 m/s^2 <<<--------answer
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(b)
acceleration a = Fnet /m
Fnet = m*g*sintheta - fk = m*g*sintheta - uk*m*g*costheta
a = g*(sintheta - uk*costheta)
7.87 = 9.8*(sintheta - (0.73*costheta))
sintheta = x
costheta = sqrt(1-x^2)
7.87 = 9.8*(x - (0.73*sqrt(1-x^2)))
sintheta = 0.97
theta = 76 degrees <<<--------answer
==============
(c)
if uk = 0
a = g*sintheta
7.87 = 9.8*sintheta
theta = 53.4 degrees <<<--------answer
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(d)
acceleration a = r*w^2
9.8 = 1097*w^2
w = 0.0945 rad/s
w = 0.0945*60/(2pi)
w = 0.902 rpm <<<--------answer
===============
(e)
for a = 30 m/s^2
30 = r*0.0945^2
r = 3360 m <<<--------answer
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