Lab 7: Acceleration on a Ramp Assignment In this lab, we will be looking at a set of measurements of the position and velocity of a box as it slides down a frictionless ramp. These measurements are along the x-axis, which is parallel to the surface of the ramp. You won't need to collect the data yourself they can be found in the \"acceleration on a ramp data\" Excel le. In the pre-lab reading, you will have reviewed how to relate the acceleration to the angle of the ramp. Learning Goals: 0 Be able to create a position vs time graph and a velocity vs time graph 0 Create appropriate trendlines for each graph 0 Compare the equations for each trendline with kinematics equations, and determine the initial velocity and the acceleration of the box using the trendline equations. 0 Calculate the angle of the ramp from the horizontal using the acceleration calculated in the lab. Assignment In the le \"acceleration on a ramp data\" you will nd data that was measured of the box as it slid down a frictionless ramp. 1. Using that data, create an XY Scatter graph with time on the x-axis and position on the yaxis. Be sure that your graph has all the relevant information, like axis labels, a title, units. 2. Using Excel, create a trendline for this graph. Do NOT use a linear t, however. Instead, use apolmomial t of order 2. (You'll see it when you open up the trendline menu). Be sure to have Excel display the equation for the trendline. 3. Next, create a second XY Scatter graph with time on the x-axis and veloci on the y-axis. Be sure it has all the relevant information, like axis labels, a title, units. 4. Using Excel, create a trendline for this graph, using a linear t. Be sure to display the equation for the trendline on the graph. 5. Save this le, with graphs, trendlines and equations, with a le name \"yourname_ramp_data_graph.xlsx\". You will submit this as part of the assignment. Yourname only needs to be your last name, although it can be the whole name if you prefer. Lab 7: Acceleration on a Ramp Assignment Velocig; vs time: Now we are going to compare your Excel trendline equations with their corresponding kinematics equations, to determine the initial velocity and acceleration values for the box. First, let's compare the relevant equations for the velocity vs. time graph, which are given below. The kinematics equation is written in terms of physics variables that describe the motion, while the trendline describes the graph itself. Each variable in one equation corresponds directly to a variable in the other, but can you gure out which is which? (Think carefully about what's graphed on each axis, what's multiplied by what, etc.) Kinematics Equation: 1),: = 170 + at Trendline Equation: 3/ = mx + .5 Fill in the empty cells in the following table with the corresponding variable from the kinematics equation and its units, as indicated. The units should make sense for the physics variable you've chosen, but they should also make sense when you think about the graph and its trendline equation. For example, if the slope of the trendline would be calculated as m = Ay/Ax, what would the units for that slope need to be? Trendline Variable Physics Variable Units 3' m f s m x t (time) sec 13 Now, let's interpret what the numerical values shown in the Excel trendline equation actually mean. Write down each numerical value in the correct cell below, according to the connections you identied above. And be sure to include the right units! Physics Variable Numerical Value with Units 170 a Lab 7: Acceleration on a Ramp Assignment Position vs. time Next, let's nd similar connections between the relevant equations for the position vs. time graph, which are given below. The variables C, d and f represent the numerical values that Excel displays when it ts data to a second-order polynomial. Again, think carefully about what variables are graphed on each axis, what's multiplied by what, etc. Kinematics Equation: x); = x0 + vot + iatz Trendline Equation: 3/ = (:12 + dx + f Fill in the empty cells in the following table with the corresponding variable (or algebraic expression) from the kinematics equation and its units, as indicated. Think carefully about the units! For example, what units would the trendline variable c need to have, given that the term 61:2 must have the same units as the trendline variable y? Trendline Variable Physics Variable Units 31 meters x t (time) sec 5 d f Now, let's interpret the meaning of the numerical values shown in Excel's trendline for this graph. Write down each numerical value in the correct cell below, according to the connections you identied above. (Note: You will need to do a tiny bit of math on one of these values.) And be sure to include the right units! Physics Variable Numerical Value with Units a Lab 7: Acceleration on a Ramp Assignment Critical Thinkin uestions On the previous two pages, you have determined two different values for the box's acceleration a. How different are they? Calculate the percent difference between these two values, and show your work below. You have also determined two different values for the box's initial velocity v0. How different are they? Calculate the percent difference between these two values, and show your work below. Are these two methods providing reasonably similar descriptions of the motion of the box? Explain why, or why not. Finally, write down one of the values you found for the acceleration (ax), and the relationship between the acceleration due to gravity (9), the angle of the ramp (6), and the measured acceleration (ax). (This equation was derived previously, and you should have also seen it in the lecture course.) Calculate the angle that the ramp makes with the horizontal, using your value for a. Show your calculations