. In other words, a photon with twice the wavelength has one half of the energy. The question says the wavelength became 1/4 of the original value, so the new energy is 1/(1/4) = 4 times larger than before.Question: The angular size of the Moon is about 30 arcmin. If it were 5 times far away as it is now, how big would its angular diameter be?
Answer: If the Moon is 5 times farther away, its size should look 5 times smaller, or 30/5 = 6 arcmin.
Question: The speed of light is 300,000 km/sec. How long does it take light to travel 60 thousand km?
Answer: Time is distance divided by speed, so (60,000 km)/(300,000 km/s) = 0.2 second.
Question: The speed of light is 300,000 km/sec. How long would it take for a flashlight beam you shine at Mars to reach it when it is at its closest, about 78 million kilometers away from us? Express your answer in minutes.
Answer: Time is distance divided by speed, so (78e6 km)/(300,000 km/s) = 260 seconds = 4.33 minutes.
Question: Suppose you measure 9 Joules (a unit of energy Physicists like to use) for the kinetic energy of a housefly. The housefly speeds up to 3 times faster than it was moving before. How many Joules of kinetic energy does the housefly have now?
Answer: In the textbook, you should have found that kinetic energy is proportional to speed squared, i.e. KE = mv2. So, this means if you double the speed (v), kinetic energy goes up as (2)2 = 2 x 2 = 4 times larger. If the speed becomes 3 times larger, then the kinetic energy becomes (3)2 = 3 x 3 = 9 times larger. So, the new kinetic energy is 9 Joules x 9 = 81 Joules.
Question: Suppose you have a tennis ball tied to one end of a string and the other end tied to a pole. As you swing the ball on the string over you head, the string gets shorter and shorter as it wraps around the pole. When the string is 10 inches long, the ball is traveling at 5 meter per second. How fast would be ball travel when the string has become only 5 inches long?
Answer: Conservation of angular momentum says the quantity "mass x radius x speed" should be constant. In this question, mass is not changing but the radius is. The product of radius and speed has to be the same before and after, and if the radius has become only 1/2 as large as before (5 inches versus 10 inches), then the speed has to increase by a factor of 2 to compensate exactly. Therefore, the ball should be traveling at 10 meter per second (twice the earlier value of 5 meter per second).
Question: Suppose you are living on a planet whose diameter is 4 times smaller than the Earth. It has the same mass as the Earth. How does the escape velocity from that planet compare with the escape velocity from the Earth?
Answer: In the lecture note (also in Math Insight 5.3 of the textbook) you should find that escape velocity is proportional to the square root of the 1/R where R is the radius of the planet. In this case, R is 1/4 of the the radius of the Earth. A square root of 1/4 is 1/2. Escape velocity is inversely proportional to this quantity, so the escape velocity from this hypothetical planet has to be 1/(1/2) = 2 times larger.
Question: Suppose a photon has a wavelength of 8710 nanometers. The photon is Doppler shifted to 1/4 its original wavelength. What is the ratio of the Doppler shifted energy of the photon to its original energy?
Answer: In the lecture (and the textbook), you learned that energy of a photon is inversely proportional to wavelength, i.e. . In other words, a photon with twice the wavelength has one half of the energy. The question says the wavelength became 1/4 of the original value, so the new energy is 1/(1/4) = 4 times larger than before.