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At an outdoor market, a bunch of bananas is set on a spring scale to measure the weight. The spring sets the full bunch of bananas into vertical oscillatory motion, which is harmonic with an amplitude 0.14 m. The maximum speed of the bananas is observed to be 2 m/s. What is the mass of the bananas

Respuesta :

Answer:

Mass of banana is [tex]1.12[/tex] Kg

Explanation:

Step 1: Determine the equation of speed of an object moving in an harmonic motion

Speed of moving in an harmonic motion is given by

[tex]v = \sqrt{\frac{k}{m} (A^2 -x^2)} \\[/tex]

Here, v represents the speed of the object in harmonic motion, k is the springs constant, m is the mass of the object, A is the amplitude, and x is the position.

In this question , [tex]x = 0[/tex] because only at this position maximum speed occurs

So the simplified equation becomes -

[tex]v = \sqrt{(\frac{k}{m} * A)}[/tex]

OR

[tex]m = \frac{kA^2}{v_(max)^2}[/tex]

Substituting the given values in above equation we get -

Assume spring constant is [tex]16[/tex]N/m

[tex]m = \frac{16 * 0.14}{2} \\m = 1.12[/tex]

Mass of banana is [tex]1.12[/tex] Kg

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