ACT Science Practice Test 19

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 (PE_g = 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 (F_fd).

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

The scientific classification of organisms provides information about the relative level of relatedness between species. Biologists use a hierarchical grouping system to classify organisms into various taxa (groups) based on shared physiological, developmental, and genetic characteristics. Table 5.5 identifies the scientific classification of five common species.

TABLE 5.5 Taxonomic Classification

Biologists use a phylogenetic tree to illustrate the evolutionary history of related species. In a typical tree, currently living species called extant taxa are listed along the right. Moving to the left, the point at which two or more extant taxa meet is called a node. A node indicates an ancestral taxon, or a common ancestor shared by the extant taxa.

Horizontal line length in a phylogenetic tree indicates relative divergence time, an estimation of how long ago the extant taxa are thought to have diverged into separate species. Figure 5.6 shows a phylogenetic tree of the species listed in Table 5.5.

Figure 5.6