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Chapter 2: Problem 37

An object has a mass of 57.6 \(\mathrm{g} .\) Find the object's density, given that its volume is 40.25 \(\mathrm{cm}^{3} .\)

Short Answer

Expert verified
The density of the object is \(1431.60 \space kg/m³\).

Step by step solution

01

Understand the Concept of Density

Density is a measure of how much mass is contained in a given volume. It is computed as the mass divided by the volume ([Density = Mass / Volume])
02

Convert The Given Mass to Kilograms

In most physical science contexts, density is typically expressed in units of grams per cubic centimeter (g/cm³). However, in this case, the mass of the object is given in grams and should be converted to kilograms because the standard unit of mass in Physics is kilograms (kg). Therefore, to convert grams to kg, we divide the mass by 1000. So, \( mass = \frac{57.6 \space g}{1000} = 0.0576 \space kg \)
03

Convert Volume to Cubic Meters

The given volume is in cubic centimeters (cm³). But in Physics, the standard unit for volume is cubic meters (m³). To convert cm³ to m³, we multiply the volume by \( \frac{1}{1,000,000} \). So, \( volume = 40.25 \space cm³ * \frac{1}{1,000,000} = 0.00004025 \space m³ \)
04

Substitute The Values and Solve

Substitute the mass and volume values into the density equation to solve. So, \( Density = \frac{mass}{volume} = \frac{0.0576 \space kg}{0.00004025 \space m³} = 1431.60 \space kg/m³ \)

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Most popular questions from this chapter

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