A crane lowers a 600kg generator by attaching 4 cables to it at an angle of 67° compared to the horizontal. The generator moves at a rate of -2.12m/s². How much tension is on each cable?

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A crane lowers a 600kg generator by attaching 4 cables to it at an angle of 67° compared to the horizontal. The generator moves at a rate of -2.12m/s². How much tension is on each cable?

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Answer 1 · 2016-02-29T18:26:17

$= 1253.12 N$ $=1253.12N$ rounded to 2 places of decimal

Explanation:

mycomputer

See figure above.

Let $T$ $T$ be the tension in each cable. Assuming all cables to be similar. Each cable is making an angle of $67^{\circ}$ $67^@$ with the horizontal.

The vertical upward component of tension in each cable $= T {sin 67}^{\circ}$ $=Tsin 67^@$
$= 0.92050 T$ $=0.92050T$
Total vertical upward component of tension in all 4 cables $= 4 \times 0.92050 T$ $=4xx0.92050T$
$= 3.6820 T$ $=3.6820T$

The generator is being acted upon by two forces.
1. Weight given by $g = 9.81 m s^{- 2}$ $g=9.81ms^-2$
2. Downward acceleration $= - 2.12 m s^{- 2}$ $=-2.12ms^-2$

As the downward acceleration is in the direction of gravity hence net downward force is given by $= 9.81 - 2.12 = 7.69 m s^{- 2}$ $=9.81-2.12=7.69ms^-2$

Net downward force $= m \times a = 600 \times 7.69 = 4614 N$ $=mxxa=600xx7.69=4614N$

Equating the total vertical tension with net downward force we obtain
$3.6820 T = 4614$ $3.6820T=4614$
or $T = 1253.12 N$ $T=1253.12N$ rounded to 2 places of decimal

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A crane lowers a 600kg generator by attaching 4 cables to it at an angle of 67° compared to the horizontal. The generator moves at a rate of -2.12m/s². How much tension is on each cable?

1 Answer

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