Activities for Friday, November 14.
[1] Arrange yourselves into the following 3 groups: (1) Elbrus, (2) Everest + Kilimanjaro, (3) Denali + Aconcagua. Each group should get one Fan Cart, a couple of timers and a few sheets of graph paper, and go to one of the three tape tracks on the floor. Make sure that the angle of your fan blade is set to 0.
[2] You are going to study the motion of the Fan Carts today, with the fan set on the low power setting. Watch your fingers with the Fan Carts. They like fingers.
[3] The main questions to be answered today are (1) "Are the fan carts traveling at constant speed once you release them?", and (2) "If they are not traveling at constant speed, what is their acceleration?".
[4] Notice that the positions 1 meter, 2 meter, etc….are marked off on the tape tracks on the floor. These represent the distances from the window end of the tape. After releasing the cart from the window end of the tape, time how long it takes to get to the 1 meter point. Repeat the process for the 2, 3, 4, and 5 meter points, and use your data to fill in the table below.
Travel Time (seconds)
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Position (meters)
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0
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0
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1
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2
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3
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4
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5
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[5] Graph your results, placing time on the horizontal axis and position on the vertical axis. Is your cart moving at a constant speed as it is moving along the floor? How can you tell from your graph?
[6] Even though your cart doesn't have a well-defined speed [it changes], it does have a well-defined average speed. Determine your cart's average speed for the full 5 meter run.
[7] We have said several times in class that the slope ("steepness") of a position vs. time graph corresponds to the speed of the object. In fact, it represents the speed of the object at one instant in time, and is therefore called the "instantaneous speed". On your plot, sketch in a tangent line at time 2 seconds. The instantaneous speed of your cart at time t = 2 seconds is the slope of this tangent line. Determine your cart's instantaneous speed at 2 seconds.
[8] Repeat the procedure above to determine your cart's instantaneous speed at t = 4 seconds.
[9] An object's average acceleration is defined by:
acceleration = (change in speed)/(time it took the speed to change)
Using your data from 2 seconds and 4 seconds, determine your cart's average acceleration during this time.
[10] Predict what a speed vs. time graph would look like for your cart.
[11] As homework for Tuesday, November 18, do Exercise 6.5 on p. 674 (this was already assigned on Thursday) and Exercise 4.1 on p. 660.