ACT science practice test 75

Directions: Each passage is followed by several questions. After reading a passage, choose the best answer to each question and fill in the corresponding oval on your answer document. You may refer to the passages as often as necessary.

You are NOT permitted to use a calculator on this test.


Students studying mirrors and reflection were given the following information:

There is a definite relationship between image characteristics and the distance an object is placed with regard to a concave mirror (see Figure 1). If an object is located beyond the center of curvature (C), its reflected image will be inverted (upside down) and smaller than the object itself. If an object is located precisely at C, the image will also be located at C; it will appear inverted and true to the object’s actual size. When the object is placed between C and the focal length (F), the image will be inverted and larger than the object. When the object is located precisely at F, no image is formed whatsoever. Lastly, if an object is placed between F and the mirror, its image will appear upright and larger than the object.

image

Figure 1

Given no further information, the students were asked to explain how the following magic trick is performed:

A famous Chinese magician conducts a classic magic trick utilizing a concave mirror with a focal length (F) of 1.6 m and a center of curvature (C) of 2.2 m. He is able to utilize the mirror in such a manner as to produce an image of a light bulb at the same location and of the same size as the actual light bulb itself.

Student 1

The light bulb must have been placed exactly 1.6 m in front of the mirror, creating a perfect reflection. The image would thus be in the same location as the light bulb, have the same dimensions as the light bulb, and be an upright image.

Student 2

The light bulb must have been placed exactly 2.2 m in front of the mirror. The image would then be in the same location and have the same dimensions as the actual light bulb, although it would be inverted.

1. The students disagreed about which aspect of the light bulb’s image?

F. Its size
G. Its location
H. Its orientation
J. Its shape

2. The two explanations were similar to each other in that both explanations:

A. assumed that the image was upright.
B. assumed that the exact positioning of the light bulb was important.
C. correctly interpreted the information provided by the teacher.
D. incorrectly interpreted the information provided by the teacher.

3. Placing the light bulb in front of the mirror at which of the following distances would have resulted in an upright image?

F. 1.0 m
G. 1.6 m
H. 2.2 m
J. 2.6 m

4. Did Student 2 provide an adequate explanation of the magic trick?

A. No. Student 2’s explanation included an image that was upside down.
B. No. if the light bulb were placed at 2.2 m, it would not have produced an image.
C. Yes. 2.2 m is the center of curvature. Placing an object at C results in an image of the same size in the same place.
D. Yes. The magician specified that the image was inverted; Student 2 was the only student to account for this.

5. All of the following statements concerning concave mirror reflections are true EXCEPT:

F. an object placed anywhere in front of C (closer to the mirror) will produce a reflected image that is larger than the actual object.
G. an object placed anywhere in front of F (closer to the mirror) will produce an upright reflection.
H. an object placed anywhere beyond F (farther from the mirror) will produce an inverted reflection.
J. the only possible way to produce a reflected image equal in size to the actual object is to place the object precisely at C.

6. The teacher posed another question to the students. The students were told that the magician performed another trick in which he relocated the light bulb so as to create the illusion that it had disappeared completely. How far in front of the mirror must the light bulb have been placed in order to NOT produce a reflection?

A. 1.3 m
B. 1.6 m
C. 2.0 m
D. 2.2 m

7. Assume that Student 2’s explanation is correct. If the magician wanted to create an image of the light bulb that was smaller than the light bulb itself, at which of the following distances in front of the mirror could he place the light bulb?

F. 1.6 m
G. 2.0 m
H. 2.2 m
J. 2.5 m

Friction is the force that resists movement when two surfaces are in contact and is represented by Ff. The coefficient of friction (COF, symbolized by μ) is a quantity used to measure the force of friction based on the normal force (FN). There are two COF’s for a given surface-to-surface contact: static COF (μs) and kinetic COF (μk). μs is used for objects at rest and μk is used for objects in motion. The normal force is an upward force, perpendicular to the surface the object is either resting on or moving on.

The basic equation for calculating the coefficient of friction is:

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Figure 1 is a diagram of a block resting on an inclined plane. The forces shown are defined above. FG represents the force of gravity.

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Figure 1

Scientists performed an experiment using several different materials to determine μs and μk for each pair of materials. Figures 2 and 3 show the results.

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Figure 2

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Figure 3

8. Based on the results of the experiment, which combination of materials has the largest static COF?

A. Plastic on plastic
B. Plastic on steel
C. Rubber on concrete
D. Rubber on asphalt

9. A comparison of the COFs given in Figure 2 shows that, relative to the COF for rubber on concrete, the COF for plastic on plastic is approximately:

F. 1/100 as high.
G. 1/2 as high.
H. 2 times as high.
J. 10 times as high.

10. Which of the following ranks the materials used in the experiment from lowest static COF to highest static COF?

A. Plastic on plastic, steel on steel, plastic on steel, rubber on asphalt, rubber on concrete
B. Rubber on concrete, rubber on asphalt, steel on steel, plastic on steel, plastic on plastic
C. Plastic on steel, plastic on plastic, rubber on asphalt, rubber on concrete, steel on steel
D. Plastic on plastic, plastic on steel, steel on steel, rubber on asphalt, rubber on concrete

11. A student theorized that the higher the static COF for a material, the higher the kinetic COF would be. Do the results of the experiment support this theory?

F. Yes. The materials with the highest static COF also had the highest kinetic COF.
G. Yes. Plastic on steel had both the highest static COF and the highest kinetic COF.
H. No. Plastic on plastic had both the lowest static COF and the lowest kinetic COF.
J. No. There is no relationship between static COF and kinetic COF for any of the materials.

12. According to Figures 1, 2, and 3, which block would most likely slide down the incline the fastest?

A. A steel block on a steel incline
B. A plastic block on a plastic incline
C. A rubber block on a concrete incline
D. A plastic block on a steel incline