Sphere A is attached to the ceiling of an elevator by a string. A second sphere
ID: 1421013 • Letter: S
Question
Sphere A is attached to the ceiling of an elevator by a string. A second sphere is attached to the first one by a second string. Both strings are of negligible mass. Here m1 = m2 = m = 3.22 kg.
(a) The elevator starts from rest and accelerates downward with
a
= 1.35 m/s2. What are the tensions in the two strings?
T1 =
T2 =
(b) If the elevator moves upward instead with the same acceleration what will be the tension in the two strings?
T1 =
T2 =
(c) The maximum tension the two strings can withstand is 93.3 N. What maximum upward acceleration can the elevator have without having one of the strings break?
m/s2
T1 =
NT2 =
NExplanation / Answer
from the force diagram , force equation for m2 is given as
m2g - T2 = m2 a
3.22 x 9.8 - T2 = 3.22 (1.35)
T2 = 27.21 N
from the force diagram , force equation for m1 is given as
T2 + m1g - T1 = m1 a
27.21 + 3.22 (9.8) - T1 = 3.22 (1.35)
T1 = 54.42 N
b)
when the acceleration is upward , force equation for m2 is given as
T2 - m2g = m2 a
T2 = m2 (g + a) = 3.22 (9.8 + 1.35) = 35.9 N
when the acceleration is upward , force equation for m1 is given as
T1 - T2 - m1g = m1 a
T1 - 35.9 - 3.22 x 9.8 = 3.22 x 1.35
T1 = 71.8 N
c)
when the acceleration is upward , force equation for m2 is given as
T2 - m2g = m2 a
93.3 - 3.22 x 9.8 = 3.22 a
a = 19.2 m/s2
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