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# Physics and Mass Help (page 2)

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By McGraw-Hill Professional
Updated on Sep 4, 2011

## Mass Practice Problems

#### Problem 1

Suppose that you place an object in a “mass meter” similar to the one shown in Fig. 7-1 . Also suppose that the mass-versus-frequency calibration curve for this device has been determined and looks like the graph of Fig. 7-2 . The object oscillates with a frequency of 5 complete cycles per second (that is, 5 hertz or 5 Hz). What is the approximate mass of this object?

Fig. 7.1 . Mass can be measured by setting an object to oscillate between a pair of springs in a weightless environment.

Fig. 7.2 . Graph of mass versus oscillation frequency for a hypothetical “mass meter” such as the one shown in Fig. 7-1 .

#### Solution 1

Locate the frequency on the horizontal scale. Draw a vertical line (or place a ruler) parallel to the vertical (mass) axis. Note where this straight line intersects the curve. Draw a horizontal line from this point toward the left until it intersects the mass scale. Read the mass off the scale. It is approximately 0.8 kg, as shown in Fig. 7-3.

Fig. 7.3 . Solution to Problem 1.

#### Problem 2

What will the “mass meter” shown in Fig. 7-1 , and whose mass-versus-frequency function is graphed in Figs. 7-2 and 7-3 , do if a mass of only 0.000001 kg (that is, 1 milligram or 1 mg) is placed in between the springs?

#### Solution 2

The scale will oscillate at essentially the frequency corresponding to zero mass. This is off the graph scale in this example. You might be tempted at first to suppose that the oscillation frequency would be extremely high, but in fact, any practical “mass meter” will oscillate at a certain maximum frequency even with no mass placed in between the springs. This happens because the springs and the clamps themselves have mass.

#### Problem 3

Wouldn’t it be easier and more accurate in real life to program the mass-versus-frequency function into a computer instead of using graphs like the ones shown here? In this way, we could simply input frequency data into the computer and read the mass on the computer display.

#### Solution 3

Yes, such a method would be easier, and in a real-life situation, this is exactly what a physicist would do. In fact, we might expect the scale to have its own built-in microcomputer and a numerical display to tell us the mass directly.

Practice problems of these concepts can be found at: Mass, Force, And Motion Practice Test

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