A lamp has a mass of 18.5 kg and is suspended by two cables attached to the ceiling. The cable on the right makes an angle of 42.2° with the ceiling and the cable on the left makes an angle of 54.4° with the ceiling. Find the tension in each cable? Why is the sum of the two tensions greater than the weight of the lamp fixture?
weight = mass * gravity
The Attempt at a Solution
So for the tension...(after drawing a sketch of what it would look like)...i ended up with the weight being 181.3kg. There's 2 cables so 181.3/2 = 90.65N. Since each cable needs to support 90.65N, it looks like 2 right triangles, with 90.65N being the opposite side, and us wanting to know the hypotenuse.
so i did sin(42.2°) 90.65/t and sin(54.4°) 90.65/t (where t is tension)
and got 135.0N and 111.5N respectively.
The sum of these 2 tensions is 246.5
Now I just can't understand why exactly they are greater than the weight of the lamp. I don't think it has anything to do with gravity because we already took that into account when figuring out the weight with respect to gravity.