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A pitcher throws a 45-g baseball at a velocity of 42 meters per second. What is the ball's momentum?
- A. 0.189 kgâ‹…m/s
- B. 1.89 kgâ‹…m/s
- C. 1.07 kgâ‹…m/s
- D. 0.93 kgâ‹…m/s
Correct Answer: B
Rationale: Momentum is calculated by multiplying mass (in kg) by velocity (in m/s). The mass of the baseball is 0.045 kg (45 grams converted to kg), and the velocity is 42 m/s. Momentum = 0.045 kg 42 m/s = 1.89 kgâ‹…m/s. Therefore, the correct answer is 1.89 kgâ‹…m/s. Choice A is incorrect as it incorrectly converts the mass from grams to kg. Choice C and D are incorrect due to calculation errors.
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At which point on a roller coaster does the car have the greatest potential energy?
- A. The start of the ride
- B. The highest peak
- C. The lowest trough
- D. The end of the ride
Correct Answer: B
Rationale: The correct answer is B, the highest peak. At the highest peak of the roller coaster, the car reaches its maximum height above the ground. This point represents the car's greatest potential energy because it has the highest potential to do work due to its elevated position. The potential energy is directly proportional to the height of an object, so the highest point on the roller coaster track corresponds to the car's greatest potential energy. Choices A, C, and D are incorrect because potential energy is highest at the peak due to its elevated position, not at the start of the ride, the lowest trough, or the end of the ride.
As the frequency of a sound wave increases, what else is true?
- A. Its wavelength decreases.
- B. Its wavelength increases.
- C. Its amplitude decreases.
- D. Its amplitude increases.
Correct Answer: A
Rationale: The correct answer is A: 'Its wavelength decreases.' The frequency and wavelength of a sound wave are inversely proportional. As the frequency of a sound wave increases (more oscillations per second), its wavelength decreases. This relationship is described by the formula: Speed of Sound = Frequency x Wavelength. Therefore, to maintain the speed of sound constant, when the frequency increases, the wavelength must decrease. Choices B, C, and D are incorrect because an increase in frequency does not lead to an increase in wavelength or changes in amplitude.
Power (P) represents the rate of work done. Which formula accurately depicts power?
- A. P = W / F
- B. P = d / t
- C. P = W x t
- D. P = F / t
Correct Answer: D
Rationale: Power (P) is defined as the rate of work done over time. The correct formula for power is P = W/t, where W is the work done, and t is the time taken. Therefore, option D, P = F / t, correctly represents power as work divided by time. Option A, P = W / F, is incorrect as it represents work divided by force, not power. Option B, P = d / t, is incorrect as it represents distance divided by time, not power. Option C, P = W x t, is incorrect as it represents work multiplied by time, not power. It's important to understand the distinction between work, power, force, time, and other related concepts to solve physics problems accurately.
A rock has a volume of 6 cm3 and a mass of 24 g. What is its density?
- A. 4 g/cm3
- B. 4 cm3/g
- C. 144 g/cm3
- D. 144 cm3/g
Correct Answer: A
Rationale: Density is calculated by dividing the mass of an object by its volume. In this case, the mass of the rock is 24 g and its volume is 6 cm3. By dividing 24 g by 6 cm3, we find that the density of the rock is 4 g/cm3. Choice A is the correct answer because density is expressed in units of mass per unit volume (g/cm3). Choice B is incorrect as it represents the reciprocal of density. Choices C and D are significantly higher values and do not match the calculated density of the rock.
An object with a mass of 45 kg has momentum equal to 180 kgâ‹…m/s. What is the object's velocity?
- A. 4 m/s
- B. 8.1 km/s
- C. 17.4 km/h
- D. 135 m/s
Correct Answer: A
Rationale: The momentum of an object is calculated by multiplying its mass and velocity. Mathematically, momentum = mass x velocity. Given that the mass is 45 kg and the momentum is 180 kgâ‹…m/s, we can rearrange the formula to solve for velocity: velocity = momentum / mass. Plugging in the values, velocity = 180 kgâ‹…m/s / 45 kg = 4 m/s. Therefore, the object's velocity is 4 m/s. Choices B, C, and D are incorrect because they do not align with the correct calculation based on the given mass and momentum values.