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In lab, you propel a cart with four known forces while
Chapter 5, Problem 42P(choose chapter or problem)
In lab, you propel a cart with four known forces while using an ultrasonic motion detector to measure the cart’s acceleration. Your data are as follows:
\(\begin{array}{cc} \text { Force }(\mathrm{N}) & \text { Acceleration }\left(\mathrm{m} / \mathrm{s}^{2}\right) \\ \hline 0.25 & 0.5 \\ 0.50 & 0.8 \\ 0.75 & 1.3 \\ 1.00 & 1.8 \\ \hline \end{array}\)
a. How should you graph these data so as to determine the mass of the cart from the slope of the Une? That is, what values should you graph on the horizontal axis and what on the vertical axis?
b. Is there another data point that would be reasonable to add, even though you made no measurements? If so, what is it?
c. What is your best determination of the cart’s mass?
Questions & Answers
QUESTION:
In lab, you propel a cart with four known forces while using an ultrasonic motion detector to measure the cart’s acceleration. Your data are as follows:
\(\begin{array}{cc} \text { Force }(\mathrm{N}) & \text { Acceleration }\left(\mathrm{m} / \mathrm{s}^{2}\right) \\ \hline 0.25 & 0.5 \\ 0.50 & 0.8 \\ 0.75 & 1.3 \\ 1.00 & 1.8 \\ \hline \end{array}\)
a. How should you graph these data so as to determine the mass of the cart from the slope of the Une? That is, what values should you graph on the horizontal axis and what on the vertical axis?
b. Is there another data point that would be reasonable to add, even though you made no measurements? If so, what is it?
c. What is your best determination of the cart’s mass?
ANSWER:
Step 1 of 3
a.) We have to explain how one should graph the given data so as to determine the mass of the cart from the slope of the line. The data for the acceleration and Force acting on the cart are given as follows.
\(\begin{array}{|l|l|} \hline \text { Force }(\mathrm{N}) & \text { Acceleration }\left(\mathrm{m} / \mathrm{s}^{2}\right) \\ \hline 0.25 & 0.5 \\ \hline 0.50 & 0.8 \\ \hline 0.75 & 1.3 \\ \hline 1.0 & 1.8 \\ \hline \end{array}\)
The mass of the cart is related to acceleration and force acting on it by Newton’s second law.
\(F=m a\)
Thus,
\(m=\frac{F}{a}\)
Now, by graphing the values of acceleration on the horizontal axis and force values on the vertical axis, the mass of the cart can be determined.
The slope of the line gives the ratio of Force to acceleration and hence the value of mass.
\(\text { Slope }=\frac{F}{a}=m\)
Therefore, by graphing the values of acceleration on the horizontal axis and force values on the vertical axis, the mass of the cart can be determined.