excectaican of abe springs. (b) By least-opmares frtings, deterphece part (8) do you wamt to use all the data points, or Showal you iscrove some of them? Explain. (d) From the sloge of the beotrit line, find the spring constamt k. (c) If the springs is extended to 105 mma, what force does it exert on the sampended object?
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When different weights are hung on a spring, the spring stretches to different lengths as shown in the following table. (a) Make a graph of the applied force versus the extension of the spring. By least-squares fitting, determine the straight line that best fits the data. (You may not want to use all the data points.) (b) From the slope of the best-fit line, find the spring constant $k$. (c) If the spring is extended to $105 \mathrm{~mm}$, what force does it exert on the suspended weight? $$ \begin{array}{lccccccrrr} F(\mathrm{~N}) & 2.0 & 4.0 & 6.0 & 8.0 & 10 & 12 & 14 & 16 & 18 \\ L(\mathrm{~mm}) & 15 & 32 & 49 & 64 & 79 & 98 & 112 & 126 & 149 \end{array} $$
When different loads hang on a spring, the spring stretches to different lengths as shown in the following table. (a) Make a graph of the applied force versus the extension of the spring. (b) By least-squares fitting, determine the straight line that best fits the data. (c) To complete part (b), do you want to use all the data points, or should you ignore some of them? Explain. (d) From the slope of the best-fit line, find the spring constant $k$ (e) If the spring is extended to $105 \mathrm{mm},$ what force does it exert on the suspended object? $$\begin{array}{llllllllllll} \hline {F(\mathbf{N})} & {2.0} & {4.0} & {6.0} & {8.0} & {10} & {12} & {14} & {16} & {18} & {20} & {22} \\ {L(\mathrm{mm})} & {15} & {32} & {49} & {64} & {79} & {98} & {112} & {126} & {149} & {175} & {190} \\ \hline \end{array}$$
Question 5: The Relation Between Force and Displacement of a Spring Here, we can see that the force (F) varies linearly with the displacement (x) of the spring. Therefore, the slope of the graph of F versus x gives us the magnitude of the force constant (k). (a) Plot of F versus x: (b) The slope of the graph is found to be 38.82944 N/m, which is the average value of the spring constant. As the mass increases, the spring stretches due to the gravitational force. Thus, the spring moves downwards.
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