Lab 7: Acceleration on a Ramp Assignment Velocity 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 figure out which is which? (Think carefully about what's graphed on each axis, what's multiplied by what, etc.) Kinematics Equation: Of = Vo + at Trendline Equation: y = mx + b 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 y m/s m x t (time) sec b 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 identified above. And be sure to include the right units! Physics Variable Numerical Value with Units Vo a 2Lab 7: Acceleration on a Ramp Assignment Position vs. time Next, let's find 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 fits data to a second-order polynomial. Again, think carefully about what variables are graphed on each axis, what's multiplied by what, etc. Kinematics Eguation: x, = x0 + 1201: + g at2 Trendline Eguation: y = 6x2 + 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.r For example, what units would the trendline variable C need to have, given that the term 6x2 must have the same units as the trendline variable y? Trendline Variable Physics Variable _-- _-- 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 identified 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 3 Lab 7: Acceleration on a Ramp Assignment Critical Thinking Questions 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 VD. 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 (l9), 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.