Question

Plot the following data, then find the slope and intercept. F = 1/K(x + a) F = force x = position m (slope) = (intercept) = From the value of slope and intercept found in problem #5, find the following constants.(Do not find them by solving the equation and plugging in values.) K = force coefficient = a = initial position = For the data of problem #1, find a change of variable substitution that will transform the data to a linear form. Plot the "new" data set and find the slope and intercept. From those find the values of a and v_0. Plot the following data. Then make a change of variable substitution that will transform the data to a linear form. Plot the "new" data set and find the value of k from the slope and/or intercept of the graph. M = k/f + 1 M = magnification f = focal length m = b = k =

Answer 1

5. The plot is given by,

If the straight line is denoted by,

The slope of the straight line is given by, m = 0.214 N/m and the interception is b = 0.567 N.

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6. If we compare the equation with the given one,

$F(x) = \frac{x}{K} + \frac{a}{K}$

we get the values of K and a.

$K = \frac{1}{m} = 4.66 \hspace{2mm} m/N$

$a = Kb = 4.66 \times 0.567 = 2.64 \hspace{2mm} m$

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7. No data found

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8. If we just plot the data it will look like,

It is clear that the plot is not linear. Look at the equation,

$M = \frac{k}{f} +1$

if we take a new variable as x = 1/f, then the equation would be linear, as,

The new data set will be,

x = 1/f    -----------------    M       

1        13.1
0.67                                 9.1
0.5    7.0
0.25 4.0
0.2                                   3.3
0.143 2.6

We plot this set of data and get,

The slope of the curve is m = 12.26 m and the intercept is b = 0.88

Clearly the plot is linear now. From the equation,

we can easily say that the slope is k = m = 12.26 m.