Wrecking Ball Hoist
In the below diagram, two cables merge together at point A to hoist up a 200 kg wrecking ball. What is the tension in the right cable?
Expand Hint
Free Body Diagram:
Hint 2
First, evaluate the sum of forces about Point A. Keep in mind that
$$Force=mass\times acceleration$$
and
$$Tension_{left}=Tension_{right}$$
.
Free Body Diagram:
Keep in mind that
$$Force=mass\times acceleration$$
and
$$Tension_{left}=Tension_{right}$$
. Let's first evaluate the sum of forces about Point A:
$$$\sum F_y=0=2Tsin(60)-mg$$$
$$$mg=2Tsin(60)\rightarrow T=\frac{mg}{2sin(60)}$$$
$$$T=\frac{(200kg)(9.8m/s^2)}{2sin(60)}=\frac{1960}{1.732}N=1,132\:N$$$
Since the load is equally shared between the two cables, the right cable's tension is 1,132 N.
1,132 N
Time Analysis
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