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FromTheMoon [43]
3 years ago
10

Your lab instructor has asked you to measure a spring constant using a dynamic method—letting it oscillate—rather than a sta

tic method of stretching it. You and your lab partner suspend the spring from a hook, hang different masses, m, on the lower end, and start them oscillating. One of you uses a meter stick to measure the amplitude, A, and the other uses a stopwatch to time 10 oscillations, t. Your data are as follows:Mass, m(g) Amplitude, A(cm) Time, T(s) 100 6.5 7.8150 5.5 9.8200 6.0 10.9250 3.5 12.4Use the best-fit line of an appropriate graph to determine the spring constant.

Physics
1 answer:
yuradex [85]3 years ago
7 0

Answer:

  k = 6,547 N / m

Explanation:

This laboratory experiment is a simple harmonic motion experiment, where the angular velocity of the oscillation is

         w = √ (k / m)

angular velocity and rel period are  related

         w = 2π / T

substitution

         T = 2π √(m / K)

in Experimental measurements give us the following data

  m (g)     A (cm)    t (s)   T (s)

  100        6.5         7.8    0.78

  150        5.5          9.8   0.98

   200      6.0        10.9    1.09

   250       3.5        12.4    1.24

we look for the period that is the time it takes to give a series of oscillations, the results are in the last column

        T = t / 10

To find the spring constant we linearize the equation

        T² = (4π²/K)    m

therefore we see that if we make a graph of T² against the mass, we obtain a line, whose slope is

         m ’= 4π² / k

where m’ is the slope

           k = 4π² / m'

the equation of the line of the attached graph is

       T² = 0.00603 m + 0.0183

therefore the slope

       m ’= 0.00603  s²/g

    we calculate

         k = 4 π² / 0.00603

          k = 6547 g / s²

we reduce the mass to the SI system

         k = 6547 g / s² (1kg / 1000 g)

         k = 6,547 kg / s² =

         k = 6,547 N / m

let's reduce the uniqueness

         [N / m] = [(kg m / s²) m] = [kg / s²]

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In the following diagrams the larger vector has a magnitude of 10, and the smaller
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the sum of vectors with the Pythagorean theorem allows us to find that the maximum magnitude occurs for the case:

d) the two vectors are parallel

Vectors are physical quantities that have modulus and direction, for example: force, velocity, acceleration, etc.

Vector algebra has defined the sum, the product by a scalar and by a vector.  The modulus and the direction of the resulting vector must be encoded.

The sum of two quantities is done using the Pythagorean theorem

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Let's apply this expression to the present case

a, b) perpendicular vectors

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the magnitude is the same in both cases, changing the direction of the vector

c) Antiparallel vectors

             

For this case the vectors are collinear, so the sum reduces to the algebraic addition

             c = a-b

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We can see that the vectors addition gives their maximum and minimum values ​​when the vectors are collinear.

In conclusion using the vectors addition we find that the correct answer is

d) the two vectors are parallel

learn more about vector addition here:

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