Acceleration Down an Incline Lab

i. What quantities could be graphed to yield a straight line that could be used to determine the acceleration of the object? Only indicate quantities that either were measured in part (b) or could be determined from quantities measured in part (b). Vertical axis Horizontal axis

1 point can be earned for choosing appropriate quantities that are related to position and time that will produce a graph that is a straight line. Example responses: x and t^2 x and 1/2 t^2 2x and t^2 sqrt(x) and t

(a) Assume the object moves with a constant acceleration as it rolls down the incline. Write an equation that includes acceleration and quantities that can be measured or obtained from measurements by using the available equipment in the list.

1 point for an equation that includes acceleration and is conceptually relevant to the procedure described in part b 1 part is earned for stating or implying that the initial speed of the object is 0 when released from the top of the incline example response: x = 1/2 at^2

After rolling down the incline, the cylindrical object rolls across a horizontal surface, as shown in Figure 2a2a. The object then hits a vertical wall (Figure 2b2b) and bounces off the wall with the same speed it had before hitting the wall (Figure 2c2c). Note that during the bounce the object is in contact with the wall for a time interval that is very small, but not zero. i. On the dot below, which represents the object during the time it is in contact with the wall, draw an arrow showing the direction of the object's acceleration during the bounce.

1 point is earned for drawing an error to the left. example response: <-------@

How could the graph be used to analyze the data and determine the acceleration?

1 point is earned for indicating that acceleration could be determined from the slope of the line in a graph of the quantities indicated in part (c)(i). 1 point is earned for correctly indicating how acceleration could be determined from the slope of the line in a graph of the quantities indicated in part (c)(i). example responses (in order of above examples) slope = 1/2 a slope = a slope = a slope = sqrt(a/2)

(b) Design an experimental procedure the students could use to measure the quantities required to determine the acceleration of the object. In the table below, list the quantities and associated symbols that would be measured in your experiment and the equipment used to measure them. Also list the equipment that would be used to measure each quantity. You do not need to fill in every row. If you need additional rows, you may add them to the space just below the table. Quantity to be Measured Symbol for Quantity Equipment for Measurement Describe the overall procedure to be used, referring to the table. Provide enough detail so that another student could replicate the experiment, including any steps necessary to reduce experimental uncertainty. As needed, use the symbols defined in the table and/or include a simple diagram of the setup.

1 point is earned for listing relevant/appropriate equipment that matches the measured quantities. 1 point is earned for a plausible/practical way to directly or indirectly determine acceleration of the object. 1 point is earned for measuring the position of the object at equal time intervals. 1 point is earned for attempting to reduce uncertainty with multiple trials/by rolling the object multiple times. example response 1: Mark the position of the object in equal time intervals, as measured by a stopwatch, as it rolls down the incline. Measure the position of the marks using the meter stick. Repeat this procedure for three trials. example response 2: Mark a starting point near the top of the incline where the cylinder is to be released from rest. 2. Use the meter stick to mark off distances of 30cm, 60cm, and 100cm from the starting point. 3. Use the stopwatch to time how long it takes the cylinder to reach the 30cm mark after it is released from rest at the starting point. 4. Repeat step 3 for a total of 3 trials. 5. Repeat steps 3 and 4 for the 60cm and 100cm marks, with a total of 3 trials for each mark.

ii. During the time the object is in contact with the wall, is the magnitude of the acceleration greater than, less than, or the same as it was while it was rolling down the ramp? Briefly explain your reasoning.

1 point is earned for stating that the time of contact is less than the time it took for the object to roll down the ramp 1 point is earned for a statement that relates the acceleration to the time interval example response: Acceleration a is given by the expression (delta v)/(delta t), where delta v is the change in velocity and delta t is the time interval for the change in velocity. When the ball is released from rest at the top of the incline, delta v represents the change in the object's speed from the top of the incline to the bottom of the incline. This change in speed takes place over a time interval delta t. When the ball collides with the wall, the object's change in speed is twice as much as in the first scenario, and the time interval in which the change in speed occurs is much shorter than when the object is released from the top of the inclines. Therefore, the acceleration is greatest for the case in which the object bounces off the wall.