Question

A helicopter is lifting two crates simultaneously. One crate with a mass of 2.800 × 102 kg is attached to the helicopter by a cable. The second crate with a mass of 1.700 × 102 kg is hanging below the first crate and attached to the first crate by a cable. As the helicopter accelerates upward at a rate of 1.39 m/s2, what is the tension in each of the two cables?

Answer 1

Explanation:

It is given that,

Mass of crate 1, $m_1=2.8\times 10^2\ kg$

Mass of the crate 2, $m_2=1.7\times 10^2\ kg$

It is also mentioned that the second crate is hanging below the first crate and attached to the first crate by a cable.

The acceleration of the helicopter, $a=1.39\ m/s^2$ (upwards)

The tension in the cable 1 is given by :

$T_1=m_1(a+g)$

$T_1=2.8\times 10^2(1.39+9.8)$

$T_1=3133.2\ N$

The tension in the cable 2 is given by :

$T_2=(m_1+m_2)(a+g)$

$T_2=(2.8\times 10^2+1.7\times 10^2)\times (1.39+9.8)$

$T_2=5035.5\ N$

Hence, this is the required solution.