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Science · Drill 16

Science practice 16

14 questions ~9 min recommended
⏱ 00:00
Score
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I appreciate your detailed instructions, but I need to point out an important issue: the PASSAGE you've provided consists entirely of data tables with no prose text to mark up with underlines and subscripts. The passage shows: - Two tables with numerical data (drop heights, hill heights, horizontal distances across different trials) - No narrative text, sentences, or phrases that could be underlined The QUESTIONS reference concepts like "drop height," "potential energy," "frictional dissipation," etc., but these are analytical questions about the data—they don't correspond to specific underlined phrases in the passage that need HTML formatting. **To proceed, I would need:** 1. A prose passage (sentences/paragraphs with actual text to format), OR 2. Clarification that this is a data table that should be rendered as an HTML table rather than prose with underlines Could you provide the actual text passage that contains underlined portions corresponding to these questions? Or if the task is to convert these data tables to HTML table format, please let me know and I can do that instead.

A rollercoaster car is often used as a model of energy transformations. Resting at its starting point, the car has gravitational potential energy. As it moves along the track, the potential energy is converted to kinetic energy and then back to potential energy as the car approaches the rollercoaster's ending point.

An object's gravitational potential energy can be calculated as the product of the object's mass, acceleration due to gravity, and the object's height above the ground (PEg = m × g × h). In a frictionless system, the amount of potential energy at the beginning and end of the rollercoaster would be equal. However, friction between the car and the track causes frictional dissipation to transform some of the energy to heat and sound. The amount of energy dissipated due to friction can be calculated as the product of the frictional force on an object and the distance traveled by the object (Ffd).

A group of students built a marble rollercoaster out of foam pipe insulation tubing and tried to determine the conditions that would maximize the height of the rollercoaster's hill. The students conducted two experiments to study the effects of gravitational potential energy and frictional dissipation on the marble.

Experiment 1

Figure 5.1 shows the initial setup for the marble rollercoaster. A indicates the starting height (drop height) and C indicates the ending height (hill height) of the marble. B is the lowest point located halfway between A and C.

Figure 5.1

Students started with a drop height of 0.6 m and stretched the rollercoaster tubing out to a horizontal length of 1 m. They then varied the hill height until the marble was able to successfully reach the top of the hill without going over. To study the effects of the marble's initial gravitational potential energy, students conducted three more trials using different drop heights. Table 5.3 shows the results for each trial.

TABLE 5.3 Experiment 1

Experiment 2

Students started with a drop height of 1.2 m and stretched the rollercoaster tubing out to a horizontal length of 1.0 m. Students then varied the hill height until the marble was able to reach the top of the hill successfully without going over. To study the effects of frictional dissipation, students conducted two more trials using different horizontal track lengths. Table 5.4 shows the results for each trial.

TABLE 5.4 Experiment 2

1. When determining the gravitational potential energy of various objects on Earth, which variable would be considered a constant?

2. According to the formula provided in the passage, doubling the height of an object should:

3. In a frictionless environment, with a drop height of A1 the marble should be able to reach a hill height (C in Figure 5.1) of:

4. In Experiment 1, students altered the drop height of the marble to test the effect of which of the following variables on hill height?

5. What was the maximum drop height used in either experiment?

6. Which of the following graphs best represents the relationship between drop height and hill height in Experiment 1?

7. The data in Table 5.4 indicate that lengthening the rollercoaster's track:

8. What was the smallest hill height recorded by the students in Experiment 2?

9. The students used drop height as the dependent variable in:

10. If the students were to carry out a third experiment to study the relationship between marble mass and hill height, how would the data table for this new experiment compare to Table 5.3?

11. Based on the data for the two experiments, at which point in Figure 5.1 does the marble have the greatest gravitational potential energy?

12. Which of the following is a similarity between Experiments 1 and 2?

13. Which of the following energy transformations is not demonstrated by the marble rollercoaster in either Experiment 1 or Experiment 2?

14. In Experiment 2, a fourth trial using a horizontal distance of 1.75 m would most likely result in a hill height:

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