Question

1. an accepted value for free - fall acceleration is 9.8 m/s². in an experiment with pendulums, you calculate that the value is 9.4 m/s². should the accepted value be tossed out to accommodate your new finding? explain.

Explanation:

Step1: Calculate the percentage - error

The formula for percentage - error is $\text{Percentage Error}=\frac{\vert\text{Experimental Value}-\text{Accepted Value}\vert}{\text{Accepted Value}}\times100\%$. Here, the experimental value is $9.4\ m/s^{2}$ and the accepted value is $9.8\ m/s^{2}$.
$\text{Percentage Error}=\frac{\vert9.4 - 9.8\vert}{9.8}\times100\%=\frac{\vert- 0.4\vert}{9.8}\times100\%=\frac{0.4}{9.8}\times100\%\approx4.08\%$

Step2: Evaluate the result

In scientific experiments, a percentage - error of around $4.08\%$ is relatively small. Usually, errors up to a few percent are considered acceptable depending on the nature of the experiment and the precision of the measuring instruments. So, the accepted value should not be tossed out.

Answer:

The accepted value should not be tossed out because the percentage - error between the experimental value of $9.4\ m/s^{2}$ and the accepted value of $9.8\ m/s^{2}$ is approximately $4.08\%$, which is relatively small and within an acceptable range for many scientific experiments.