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Two blocks, each of mass m=3.50kg, are hung from the ceiling of an elevator as in above figure. (a) If the elevator moves with an upward acceleration aof magnitude 1.60m/s 2, find the tensions T 1​and T 2​in the upper and lower strings. (b) If the strings can withstand a maximum tension of 85.0N, what maximum acceleration can the elevator have before a string breaks.

Respuesta :

The tension in the upper and lower string is 79.8 N and 39.9 N  respectively and the maximum acceleration of the elevator at tension of 85 N is 2.34 m/s².

(a) Mass of blocks = m = 3.5 Kg

Acceleration of the elevator = a = 1.6 m/s²

Gravitational force experienced by both strings = G

= m X g

= 3.5 X 9.8

= 34.3 N

For the lower block, apply Newton's Second Law of Motion,

Net force on the lower block =

= F = T₂ - (m X g)

= (m X a) = T₂ - (m X g)

= T₂ = (m X a) + (m X g)

= T₂ = m X (a + g)

= T₂ = 3.5 X (1.6 + 9.8)

= T₂ = 39.9 N

For the upper block, apply Newton's Second Law of Motion,

Net force on the Upper block =

= F = T₁ - T₂ - (m X g)

= (m X a) = T₁ - T₂ - (m X g)

= T₁ = T₂ + (m X g) + (m X a)

= T₁ = 39.9 + 3.50 X (9.8 + 1.6)

= T₁ = 79.8 N

(b) Now we know that T₁ > T₂, thus the upper string will break before the lower string. So, acceleration will increase when the upper string breaks.

Tension given = T₁ = 85 N

Acceleration = a =

= T₁ = T₂ + (m X g) + (m X a)

But, T₂ = m X (a + g)

Thus,

= T₁ = m X (a + g) + (m X g) + (m X a)

= T₁ = 2 X (m X a) + 2 X (m X g)

= a = (T₁ - ( 2 X (m X g))) / (2 X m)

= a = (85 - [ 2 X ( 3.5 X 9.8)] ) / (2 X 3.5)

= a = 2.34 m/s²

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