Lab 1  Motion in One dimension


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1 Lab 1  Motion in One dimension In this lab, you will explore motion in one dimension. A computer will aid in acquiring the data, displaying the data and analysis of the data. Theory: If an object is moving at a constant acceleration over a fixed period of time, the rate at which the distance it travels and it s increasing or decreasing velocity during this period of time can be determined from the following equations For position x = x o + v o t + ½at 2 [1] For velocity v = v o + at [2] where x o and v o are the initial starting position and velocity of the object. Equation [1] is in the form of a quadratic equation such that y = Ax 2 + Bx + C. position x = ½at 2 + v o t + x o [1] The value of A, B and C relates to ½ a, v o and x o. In this lab the computer will fit the acquired data for position vs. time to a quadratic fit and from the information box you will be able to determine the acceleration and initial velocity of the cart. One can also have a general idea of what a graph for displacement vs. time. For example an object starting at rest where v o = 0, and setting the displacement, x o,also as zero. Simplifies equation [1] to x=1/2at 2. This is of the form of y=x 2 that yields a parabola when graphed. Equation [2] is in the form of a linear fit y = mx + b velocity v = at + v o [2] The values m and b relates to a and v o. A linear fit applied to data of a graph for velocity vs. time will yield the information need to determined initial velocity and acceleration. If a linear fit is applied to a graph of acceleration vs. time and the object has constant acceleration, the expected output should be a horizontal line whose slope is equal to zero. So if y = mx + b then a = 0(x) + a [3] From equation [2] it can be rationalize that under constant acceleration as time increases linearly the acceleration should remain constant such that a graph of acceleration vs. times yields a straight horizontal line and the yintercept is the constant acceleration
2 PreLab Activity A position vs. time graph for a cart undergoing a positive constant acceleration is expected to be a) an increasing linear line b) an increasing parabolic c) a flat horizontal line A velocity vs. time graph for a cart undergoing a positive constant acceleration is expected to be a) an increasing linear line b) an increasing parabolic c) a flat horizontal line An acceleration vs. time graph for a cart undergoing a positive constant acceleration is expected to be a) an increasing linear line b) an increasing parabolic c) a flat horizontal line
3 The Graph display for this experiment will be divided into three separate portions representing position, velocity and acceleration; each vs. time. Any one of these portions can be made the active portion by clicking the mouse pointer within its area. Once data is acquired it will be retained within the graph display until deleted. Along the yaxis a colored symbol will represent the data for individual data runs for each portion. To perform tasks such as a linear or quadratic fit on the data a data set can be individually selected by clicking the mouse on the appropriate colored symbol next to its corresponding yaxis. Procedure: Setting it up 1. Start the computer; and open the Data Studio program. Select open Activity and from the UB folder open the file motion in one. Place the cart on the track, with the end with the string towards the pulley. Hook the mass hanger through the loop of the string. Pass the string over the pulley. Add 50 grams to the weight hanger for a total of 100 grams. Place a piece of foam on the floor at the point the weight hanger rests on the floor. 1 st Data Run 2. Have a lab partner pull the cart back until the hook of the weight hanger is just below the wheel of the pulley and hold it at this point. Select Start and then have the lab partner release the cart. Once the cart has reached the catcher mechanism at the end of the track select Stop. Evaluating The Data 3. In the appropriate spaces on the data sheet sketch each graph. Position vs. Time Theory predicts that under constant acceleration an object position obeys x = (½a)t 2 + v o t + x o. It is predicted that a position over time data collected for an object undergoing constant acceleration should be able to be fitted to a quadratic function, y = Ax 2 + Bx + C. 4. With the mouse pointer click within the position vs. time graph in order to activate that window. At the top of the graph window there is a button labeled Fit. Select this button and then from the submenu select Quadratic fit. At this time the fit most likely will not be a very good fit as it is trying to fit all of the data within the window. Select the valid data, that which follows a parabola, within the position graph by clicking and dragging the mouse over it. The line of the fit now should lay atop of the data. A box contains the values for y = Ax 2 + Bx + C which resembles x = (½a)t 2 + v o t + x o. From these values, determine the initial velocity and the acceleration. Deselect the quadratic fit from the Fit menu. This will reduce clutter on the screen for the second data run.
4 Velocity vs. Time Theory predicts that under constant acceleration an objects velocity vs. time obeys v = at + v o. It is predicted that a velocity over time data collected for an object undergoing constant acceleration should be able to be fitted to a linear function, y = mx + b 5. With the mouse pointer click within the velocity vs. time graph to activate it. Using the Fit button choose the Linear fit option. Again the fit will try to fit all the data and this may not be what you desire. With the mouse pointer click and drag to select only the data along the increasing linear line. The fit line should now lay atop the data. A box contains the values for y = mx + b which resembles v = at + v o. From these values, determine the initial velocity and the acceleration. Deselect the linear fit from the Fit menu. This will reduce clutter on the screen for the second data run. Acceleration vs. Time If an object is under constant acceleration then an acceleration vs. time graph should be a horizontal line where the y intercept value is the value of the constant acceleration. 6. Activate the acceleration vs. time graph. Select the data and then perform a linear fit on that data. Ideally the slope will be zero and the y intercept the constant acceleration 7. Repeat the procedure step 2 6 using 200 grams.
5 Data Sheet position vs. time with 100g position vs. time with 200g acceleration = acceleration = initial velocity initial velocity = velocity vs. time with 100 g velocity vs. time with 200 g acceleration = acceleration = initial velocity = initial velocity = acceleration vs. time with 100 g acceleration vs. time with 200 g acceleration = acceleration =
6 What can be concluded about the acceleration from those that were determined from each graph for the 100 gram mass? What effect does adding mass to the mass hanger have on the acceleration of the cart? Describe how the experimental results agree with each prediction made in the Prelab Activity.
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