## Construction Crane

Consider a construction crane in the below diagram is suspending a 40 kg payload. What is the tension in the diagonal cable that is supporting the load? Assume the crane arm is weightless.

##
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__**Hint**

**Hint**

The problem is asking to solve for the y-component of
$$F_{tension}$$
in the free body diagram below:

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__**Hint 2**

**Hint 2**

To find
$$F_y$$
, we can multiply the mass by gravity (Newton's 2nd law):

$$$F_y=mass\times acceleration$$$

The problem is asking to solve for the y-component of
$$F_{tension}$$
in the free body diagram below:

To find
$$F_y$$
, we can multiply the mass by gravity (Newton's 2nd law):

$$$F_y=mass\times acceleration=40kg\times 9.8m/s^2=392\:N$$$

Because there is only one upward pulling cable in the vertical direction, it will counteract the entire downward force. Thus:

$$$F_y=F_{tension}\cdot sin(30)=392N$$$

$$$F_{tension}=\frac{392N}{sin(30)}=\frac{392N}{0.5}=784\:N$$$

Despite the payload only causing a 392 N downward force, the cable has to work twice as hard to suspend the object due to its diagonal positioning.

784 N