Nursing Elites

1. A 5-cm candle is placed 20 cm away from a concave mirror with a focal length of 15 cm. About what is the image height of the candle in the mirror?

• A. 30.5 cm
• B. 15.625 cm
• C. −15 cm
• D. −30.5 cm

Correct answer: B

Rationale: The magnification formula for a mirror is given by M = -f / (f - d), where f is the focal length of the mirror, and d is the object distance from the mirror. Using the mirror equation and magnification formula, the image height is found to be negative because it is inverted. Plugging in the values (f = 15 cm, d = 20 cm) into the formula gives M = -15 / (15 - 20) = -15 / -5 = 3. The negative sign indicates that the image is inverted. The image height is then calculated by multiplying the magnification by the object height: 3 * 5 cm = 15 cm. Therefore, the correct image height is approximately -15 cm. Choice A (30.5 cm) and Choice D (-30.5 cm) are incorrect as they do not consider the inversion of the image. Choice C (-15 cm) is also incorrect because it neglects the negative sign, which indicates the inversion of the image.

2. The efficiency (η) of a heat engine is defined as the ratio of the net work done (Wnet) by the engine to the heat input (Qh) from the hot reservoir. The relationship is expressed as:

• A. η = Wnet / Qh
• B. η = Qh / Wnet
• C. η = Wnet x Qh
• D. η = (Wnet + Qh) / 2

Correct answer: A

Rationale: The correct formula for efficiency (η) of a heat engine is η = Wnet / Qh. Efficiency is defined as the ratio of the net work done by the engine (Wnet) to the heat input from the hot reservoir (Qh). This formula shows how effectively the engine converts heat into useful work, making choice A the correct answer. Choices B, C, and D present incorrect relationships between efficiency, net work done, and heat input, leading to their incorrectness.

3. Marilyn is driving to a wedding. She drives 4 miles south before realizing that she left the gift at home. She makes a U-turn, returns home to pick up the gift, and sets out again driving south. This time, she drives 1 mile out of her way to pick up a friend. From there, they continue 5 miles more to the wedding. Which of these statements is true about Marilyn’s trip?

• A. The displacement of her trip is 6 miles, and the distance traveled is 6 miles.
• B. The displacement of her trip is 14 miles, and the distance traveled is 14 miles.
• C. The displacement of her trip is 8 miles, and the distance traveled is 14 miles.
• D. The displacement of her trip is 6 miles, and the distance traveled is 14 miles.

Correct answer: C

Rationale: Marilyn’s displacement is calculated based on her final position relative to the starting point. She drives 1 mile to pick up her friend, then 5 miles more to the wedding, totaling 6 miles after returning to her home. So, the correct displacement is 8 miles south from her starting point (4 miles to the gift + 4 miles return + 1 mile to the friend + 5 miles to the wedding). The total distance traveled is 14 miles (adding all the distances). Choice A is incorrect because it miscalculates the displacement. Choice B is incorrect as it overestimates both the displacement and distance traveled. Choice D is incorrect as it underestimates the displacement.

4. What is the kinetic energy of a 500-kg wagon moving at 10 m/s?

• A. 50 J
• B. 250 J
• C. 2.5 × 10^4 J
• D. 5.0 × 10^5 J

Correct answer: C

Rationale: The formula for calculating kinetic energy is KE = 0.5 × mass × velocity². Given the mass of the wagon is 500 kg and the velocity is 10 m/s, we can substitute these values into the formula: KE = 0.5 × 500 kg × (10 m/s)² = 0.5 × 500 kg × 100 m²/s² = 25,000 J or 2.5 × 10⁴ J. Therefore, the kinetic energy of the 500-kg wagon moving at 10 m/s is 2.5 × 10⁴ J. Choice A (50 J) is incorrect because it is too low; Choice B (250 J) is incorrect as it does not match the correct calculation; Choice D (5.0 × 10^5 J) is incorrect as it is too high. The correct answer is C (2.5 × 10^4 J).

5. An electromagnet is holding a 1,500-kg car at a height of 25 m above the ground. The magnet then experiences a power outage, and the car falls to the ground. Which of the following is false?

• A. The car had a potential energy of 367.5 kJ.
• B. 367.5 kJ of potential energy is converted to kinetic energy.
• C. The car retains potential energy of 367.5 kJ when it hits the ground.
• D. The car’s potential energy converts to kinetic energy and then to sound energy.

Correct answer: C

Rationale: When the car falls to the ground, its potential energy is converted to kinetic energy as it accelerates downwards. Upon impact with the ground, the car's kinetic energy is dissipated in various forms, such as sound energy, heat, and deformation energy. Therefore, the car does not retain its initial potential energy of 367.5 kJ when it hits the ground. Choice A is true because the potential energy of the car can be calculated as mgh = 1500 kg * 9.8 m/s^2 * 25 m = 367,500 J = 367.5 kJ. Choice B is true because as the car falls, its potential energy is converted to kinetic energy. Choice D is true as the kinetic energy is eventually dissipated into other forms upon impact.

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