Each vertical steel column of an office building supports a weight of 1.30 x 10^5 N and is compressed to 5.90 x 10^-3
A) Find the compression in each column if a wegith of 5.50 x 10^5 N is supported.
B)If the compression of each steel column is 0.0710 cm, what wight is supported by each column?
compression=force*k
k= compression /force
find k from the given.
a) using k, find compression for that force.
b) find force, given k and compression
A) To find the compression in each column when a weight of 5.50 x 10^5 N is supported, we can use the formula for compression:
Compression = Force / Spring Constant
Given that the compression is 5.90 x 10^-3 m and the weight is 5.50 x 10^5 N, we need to find the spring constant.
The spring constant of each column can be calculated using the formula:
Spring Constant = Force / Compression
So, substituting the given values, we get:
Spring Constant = (1.30 x 10^5 N) / (5.90 x 10^-3 m)
= 2.20 x 10^7 N/m
Now, we can find the compression in each column when a weight of 5.50 x 10^5 N is supported:
Compression = Force / Spring Constant
= (5.50 x 10^5 N) / (2.20 x 10^7 N/m)
= 2.50 x 10^-2 m
Therefore, the compression in each column when a weight of 5.50 x 10^5 N is supported is 2.50 x 10^-2 m.
B) To find the weight supported by each column when the compression is 0.0710 cm, we can use the same formula as before:
Compression = Force / Spring Constant
Given that the compression is 0.0710 cm (convert to meters: 0.0710 cm * 10^-2 = 0.0710 m), we need to find the spring constant.
The spring constant of each column can be calculated using the formula:
Spring Constant = Force / Compression
So, substituting the given values, we get:
Spring Constant = Force / Compression
= Force / (0.0710 m)
Now, we need to find the weight supported by each column, which is equal to the force:
Weight = Spring Constant * Compression
Substituting the given values, we get:
Weight = (Spring Constant) * (0.0710 m)
Therefore, to find the weight supported by each column, we need to know the spring constant.