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In your physics lab you release a small glider from rest
Chapter 2, Problem 2.84(choose chapter or problem)
In your physics lab you release a small glider from rest at various points on a long, frictionless air track that is inclined at an angle \(\theta\) above the horizontal. With an electronic photocell, you measure the time t it takes the glider to slide a distance x from the release point to the bottom of the track. Your measurements are given in Fig. P2.84, which shows a second-order polynomial (quadratic) fit to the plotted data. You are asked to find the glider’s acceleration, which is assumed to be constant. There is some error in each measurement, so instead of using a single set of x and t values, you can be more accurate if you use graphical methods and obtain your measured value of the acceleration from the graph. (a) How can you re-graph the data so that the data points fall close to a straight line? (Hint: You might want to plot x or t, or both, raised to some power.) (b) Construct the graph you described in part (a) and find the equation for the straight line that is the best fit to the data points. (c) Use the straight-line fit from part (b) to calculate the acceleration of the glider. (d) The glider is released at a distance x = 1.35 m from the bottom of the track. Use the acceleration value you obtained in part (c) to calculate the speed of the glider when it reaches the bottom of the track.
Questions & Answers
QUESTION:
In your physics lab you release a small glider from rest at various points on a long, frictionless air track that is inclined at an angle \(\theta\) above the horizontal. With an electronic photocell, you measure the time t it takes the glider to slide a distance x from the release point to the bottom of the track. Your measurements are given in Fig. P2.84, which shows a second-order polynomial (quadratic) fit to the plotted data. You are asked to find the glider’s acceleration, which is assumed to be constant. There is some error in each measurement, so instead of using a single set of x and t values, you can be more accurate if you use graphical methods and obtain your measured value of the acceleration from the graph. (a) How can you re-graph the data so that the data points fall close to a straight line? (Hint: You might want to plot x or t, or both, raised to some power.) (b) Construct the graph you described in part (a) and find the equation for the straight line that is the best fit to the data points. (c) Use the straight-line fit from part (b) to calculate the acceleration of the glider. (d) The glider is released at a distance x = 1.35 m from the bottom of the track. Use the acceleration value you obtained in part (c) to calculate the speed of the glider when it reaches the bottom of the track.
Step 1 of 4
(a)
The equation for the distance traveled by the glider is,
\(x = ut + \frac{1}{2}a{t^2}\)
Here, x, u, a, and tare the distance, initial speed, acceleration, and time, respectively.
Since the glider is starting from rest, therefore the initial speed of the glider is u is 0 m/s.
Substitute 0 for u in the above equation, and we get,
\(x = \frac{1}{2}a{t^2}\)
From the above equation, it is clear that the distance traveled by the glider is proportional to the square of the time. Therefore, the graph of x versus \({t^2}\) is a straight line.