Sphere A is attached to the ceiling of an elevator by a string. A second sphere

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 = 3.13 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 = N T2 = N (b) If the elevator moves upward instead with the same acceleration what will be the tension in the two strings? T1 = N T2 = N (c) The maximum tension the two strings can withstand is 87.8 N. What maximum upward acceleration can the elevator have without having one of the strings break? m/s2

Explanation / Answer

a) mg - T2 = m2 a

T2 = 3.13*(9.81-1.35)=26.48 N

for other sphere

T2 + mg - T1 = ma

T1 = T2 + mg - ma = 26.48 + 3.13*9.81 - 3.13*1.35= 52.96 N

b) T2 - mg = ma

T2 = ma + mg = 3.13*(9.81+1.35)=34.93 N

T1 - T2 - mg = ma

T1 = 34.93 + 3.13*(9.81+1.35)= 69.86 N

c) so T1 = 87.8 N

87.8 - T2 - mg = ma

and for T2 -mg = ma

87.8 - (ma + mg) - mg = ma

87.8 - 2*3.13*9.81 = 2*3.13*a

a=4.22 m/s^2

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