The data in the following table represent measurements of the masses and dimensions of solid cylinders of aluminum, copper, brass, tin, and iron. (a) Use these data to calculate the densities of these substances. (b) State how your results compare with those given in Table 14.1.
(a)
The densities of each substance.
Answer to Problem 1.61AP
The density of aluminum solid cylinders is
Explanation of Solution
Given info: The mass, diameter and length of each substance are given below,
Substance | Mass
| Diameter
| Length
|
Aluminum |
|
|
|
Copper |
|
|
|
Brass |
|
|
|
Tin |
|
|
|
Iron |
|
|
|
Formula to calculate the density of substance is,
Here,
Write the expression for the volume of solid cylinder,
Here,
Substitute
For aluminum:
Substitute
Thus, the density of aluminum solid cylinders is
For copper:
Substitute
Thus, the density of copper solid cylinders is
For brass:
Substitute
Thus, the density of brass solid cylinders is
For tin:
Substitute
Thus, the density of tin solid cylinders is
For iron:
Substitute
Thus, the density of iron solid cylinders is
Conclusion:
Therefore, the density of aluminum solid cylinders is
(b)
The comparison between results of part (a) and table
Answer to Problem 1.61AP
The density of aluminum from table is
Explanation of Solution
Given info:
Formula to calculate the percentage error is,
Here,
For aluminum:
From part (a), the density of the aluminum is
Substitute
Thus, the density of aluminum from table is
For copper:
From part (a), the density of the copper is
Substitute
Thus, the density of copper from table is
For brass:
From part (a), the density of the brass is
Substitute
Thus, the density of brass from table is
For tin:
From part (a), the density of the tin is
Substitute
Thus, the density of tin from table is
For iron:
From part (a), the density of the iron is
Substitute
Thus, the density of iron from table is
Conclusion:
Therefore, the density of aluminum from table is
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