Question

If the maximum tension in rope 1 is 18000 N calculate maximum acceleration of the helicopter before the rope breaks. The mass being held by rope 1 = 900kg

Answer 1

`\begin{gathered} Given: \\ mass\text{ of the object=900Kg} \\ maxmum\text{ tension =18000N} \end{gathered}`
`to\text{ find: the maximum acceleration of the helicopter}`
`\begin{gathered} from\text{ Newton's second law of motion} \\ F=ma \\ F=\text{ net force on the object } \\ a=acceleration\text{ of the object} \end{gathered}`
`\begin{gathered} force\text{ working on the mass 900Kg object} \\ mg\text{ in downward direction } \\ tension\text{ T in upward direction } \\ m=mass\text{ of the object.} \\ a\text{ = acceleration of the object} \end{gathered}`
`\begin{gathered} applying\text{ Newton's law} \\ T-mg=ma \\ (since\text{ the acceleration is in the upward direction\rparen} \end{gathered}`
`\begin{gathered} since\text{ due to the tension force the object is going in the upward } \\ direction\text{ and the maximum tension force can be 18000N if the tension } \\ increases\text{ beyond this value the rope will break. } \end{gathered}`
`\begin{gathered} put\text{ T=18000N in the above equation} \\ 18000N-900Kg*9.8m\text{/s}^2=900Kg*a \\ 9180N=900Kg*a \\ a=(9180)/(900)m\text{/s}^2 \\ a=10.2\text{ }m\text{/s}^2 \end{gathered}`

so when the acceleration of the helicopter will be 10.2 m/s² then the rope

will break down.