Experiment #8 Bouncing Ball the ball. Translate this equation into the variables defined for this problem (h, g, vx, d, etc. ) by crossing out any terms in the general equation that are zero and substituting in the variables in appropriate places in the general equation. You should be left with a fairly Big Question: What is the relationship between the maximum height of a bouncing ball and the distance simple equation that includes the at least some of the variables h, g, Vx, and d. that it bounces? (f) The distance between bounces is also important. Select a general equation that includes the horizontal distance. Translate this equation into the variables defined for this Experiment Overview: You will bounce a rubber ball so that it bounces several times while moving horizontally. problem (h, g, Vx, d, etc.). You will measure the maximum height of each bounce and the distance between each (g) You now have two equations. Count how many unknowns there are in your bounce. You will examine this data for a pattern relating the height and the distance, i.e. is the height proportional to the distance, inversely proportional to the distance, equations. Your count should include the height h and any other variables that are not proportional to the distance squared, etc. included in your list of knowns from part (b). If your number of equations is equal to your number of unknowns, the problem may be solved algebraically. Do you have Reading assignment: Read Giancoli sections 3.5-3.6 enough equations to solve the problem? (h) Your equations in parts (e) and (f) likely introduced two extra unknown Prelab questions: variables: time (t) and the vertical component of the initial velocity (Viy). The time can be The prelab assignments for previous experiments have not included any calculations. This prelab will pose a problem requiring calculation. The parts of this problem are found from your equation in part (f). You still need another equation to find Viy. Select intended to guide you through the problem solving process. You should complete each another general equation that involves vertical velocity. Translate this equation into the part and answer the overall problem. variables defined for this problem (h, g, Vx, d, etc.). 1. A bouncing ball lands at one point and another point a distance d away. In between (i) At this point, you should have 3 equations from parts (e), (f), and (h). There these points, the ball rises to a maximum height h before falling down again. Derive an should be 3 unknown variables: d, t, and Viy. Use your 3 equations to solve for h in terms equation for the height h in terms of the distance (d), the acceleration due to gravity (g), and the horizontal component of the ball's velocity (Vx). No other variables should appear of only d, g, and Vx, eliminating the unwanted unknowns t and Viy. in your equation. (j) Check that your equation for h makes sense. If the height is larger, is the (a) Draw a diagram for this situation. Label the distance d and the height h on distance larger? If the horizontal velocity is larger, is the distance larger? Check that your your diagram. Draw vectors for the velocity and acceleration of the ball at the highest point. Choose a coordinate system and draw the origin of your coordinate system and the equation has correct units. direction of the x and y axes. 2. (Multiple choice) According to the equation that you have derived, the maximum (b) What variable are you trying to solve for in this problem? What variables can you treat as known in this problem, i.e. what variables may be in your final answer? height of a bounce is (c) Describe the ball's motion in physics terms. What direction is the ball's (a) unrelated to the distance between bounces. velocity? What direction is the ball's acceleration? How does the velocity change over (b) proportional to the distance between bounces. the ball's trajectory? How does the acceleration change? Is there anything constant in this situation? (c) inversely proportional to the distance between bounces. (d) The assigned reading contained a set of equations in the yellow box 3.25. Do (d) proportional to the square root of the distance between bounces. these equations apply to this situation? (e) The height is important in this problem. Since this variable must be included at (e) proportional to the distance between bounces squared. some point, it is a good place to start. Select a general equation that includes the height of (f) inversely proportional to the square root of the distance between bounces. (g) inversely proportional to the distance between bounces squared