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It's All Uphill Interactive Background: In this Interactive, you will analyze the motion of a cart being pulled up an inclined plane at a constant speed. The angle of the incline can be modified by 10° increments between the values of 30° and 90°. Three different masses can be selected - 2.0 kg, 3.0 kg, and 4.0 kg. In each simulation, the cart is pulled to the same height -1.0 meter above the original starting position. For each simulation, the force that must be applied is reported on the screen. The displacement of the cart can be measured using the cm ruler that is displayed for each trial. Purpose: To determine the effect of the angle of an inclined plane upon the amount of force and the amount of work done when pulling a cart up an inclined plane at a constant speed and to the same height. Discussion of Procedure: Select a mass from one of the three choices. Tap the Run Trial button. The force required to pull the cart at a constant speed is displayed on the screen; record in the Data Table. The displacement from the starting position to the final position can be measured using the cm ruler; record in the Data Table. (Note that the table lists meters as the unit.) The force and the displacement vectors are both directed parallel to the inclined plane. Use the force and displacement to calculate the work done. Repeat the procedure for all angles. Data tables are provided for a single cart mass. Additional tables can be made if necessary. Data: Mass: kg Angle ( ° ) Force (N) Displacement (m) Work (J) 30.0 40.0 50.0 60.0 70.0 80.0 90.0
For the function involving the variables listed, use your intuition or additional research, if necessary, to complete parts (a) through (c) below. (day of year, average high temperature) over a 2-year period for a town a. Describe an appropriate domain and range for the function. Choose the appropriate domain for the function below. A. The domain is all daily average high temperatures over 2 years or -20°F to 120°F. B. The domain is all days over a 2-year period or 1 to 365, where day 1 is July 1st. C. The domain is all days over a 2-year period or 1 to 730, where day 1 is July 1st. D. The domain is all daily average high temperatures over 2 years or 50°F to 90°F. Choose the appropriate range for the function below. A. The range is all days over a 2-year period or 1 to 365, where day 1 is July 1st. B. The range is all daily average high temperatures over 2 years or 50°F to 90°F. C. The range is all daily average high temperatures over 2 years or -20°F to 120°F. D. The range is all days over a 2-year period or 1 to 730, where day 1 is July 1st. b. Make a rough sketch of a graph of the function. Choose the correct graph below. Let t represent time in days and F represent temperature in degrees Fahrenheit. c. Briefly discuss the validity of the graph as a model of the true function. Choose the correct answer below. A. The graph is a valid model of the function because time in days fluctuates as temperature in degrees Fahrenheit increases. B. The validity of the graph as a model of the true function can never be known. C. The graph is not a valid model of the true function. D. The graph is a valid model of the function because temperature in degrees Fahrenheit fluctuates as time in days go through seasons.