Question

An elevator is accelerating upward at a rate of 3.8 m/s2. A block of mass 24 kg hangs by a low-mass rope from the ceiling, and another block of mass 63 kg hangs by a low-mass rope from the upper block.
(a) What are the tensions in the upper and lower ropes?

upper rope N
lower rope N
(b) What are the tensions in the upper and lower ropes when the elevator accelerates downward at a rate of 3.8 m/s2?

upper rope N
lower rope N

Answer 1

Answer:

Explanation:

m1 = 24 kg

m2 = 63 kg

(a) Let the tension is T1 in upper rope and T2 in lower rope.

Use Newtons' second law on m2.

$T_{2}-m_{2}g = m_{2}a$

$T_{2}= 63(9.8 + 3.8)$

T2 = 856.8 N

Apply Newton's second law on m1

$T_{1}-T_{2}-m_{1}g = m_{1}a$

$T_{1}-856.8 = 24(9.8+3.8)$

T1 = 1183.2 N

(b)

Use Newtons' second law on m2.

$T_{2}-m_{2}g =- m_{2}a$

$T_{2}= 63(9.8 - 3.8)$

T2 = 378 N

Apply Newton's second law on m1

$T_{1}-T_{2}-m_{1}g = -m_{1}a$

$T_{1}-378 = 24(9.8-3.8)$

T1 = 522 N