Many physical quantities are connected by inverse square laws, that is, by power functions of the form f(x)=kx^(-2). In particular, the illumination of an object by a light source is inversely proportional to the square of the distance from the source. Suppose that after dark you are in a room with just one lamp and you are trying to read a book. The light is too dim and so you move halfway to the lamp. How much brighter is the light?
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Answer:
- 4 times
Explanation:
Since the equation for the illumination of an object, i.e. the brightness of the light, is inversely proportional to the square of the distance from the light source, the form of the function is:
- f(x) = k.x⁻²
Where x is the distance between the object and the light force, k is the constant of proportionality, and f(x) is the brightness.
Then, if you move halfway to the lamp the new distance is x/2 and the new brightness (call if F) is :
Then, you have found that the light is 4 times as bright as it originally was.
Related Questions
Someone please help me
If you walk across a nylon rug and then touch a large metal object such as a doorknob you may get a spark and a shock. Why does this tend to happen more on dry days than on humid days (Hint: it has to do with the electric dipole of water molecules). Why are you less likely to get a shock if you touch a small metal object, such as a paper clip?
A170 g hockey puck sliding at 25 m/s slows to a speed of 10 m/s in a distance of 7.5 m. Determine the force of friction causing the puck to slow.
This time, William Tell is shooting at an apple that hangs on a tree (Fig. 3.32). The apple is a horizontal distance of 20.0 m away and at a height of 4.00 m above the ground. If the arrow is released from a height of 1.00 m above the ground and hits the apple 0.500 s later, what is the arrow’s initial velocity?
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You're going to have to give me the choices.
I'm pretty sketchy on that subject.
B. Friction is a nonconservative force.
C. Kinetic energy can be transformed into thermal energy.
D. The total energy of all types remains the same in a closed system.
Answers
Answer: The correct option A.
Explanation:
- Law of conservation of energy states that energy can neither be created nor be destroyed. But it can be transformed from one form to another.
- Law of conservation of Mechanical energy states that mechanical energy of the closed system remain constant until dissipative forces are absent. This means that potential energy gets converted in kinetic energy or vice versa.
Mechanical energy is defined as the sum of the both potential and kinetic energies.
M.E = P.E + K.E
So, from the given options the correct answer is option A.
Answers
Let's rank the atoms A (Gold), B (Copper), C (Carbon), and D (Silver) based on:
a. Mass (atomic mass or atomic weight)
b. Number of electrons
c. Number of protons
a. Mass (Atomic Mass or Atomic Weight):
1. Gold (A) has an atomic mass of approximately 196.97 atomic mass units (u).
2. Silver (D) has an atomic mass of approximately 107.87 u.
3. Copper (B) has an atomic mass of approximately 63.55 u.
4. Carbon (C) has an atomic mass of approximately 12.01 u.
Ranking by mass from most to least:
1. Gold (A) - 196.97 u
2. Silver (D) - 107.87 u
3. Copper (B) - 63.55 u
4. Carbon (C) - 12.01 u
b. Number of Electrons:
The number of electrons in an atom is equal to the number of protons, which is also the atomic number.
1. Gold (A) has an atomic number of 79, so it has 79 electrons.
2. Silver (D) has an atomic number of 47, so it has 47 electrons.
3. Copper (B) has an atomic number of 29, so it has 29 electrons.
4. Carbon (C) has an atomic number of 6, so it has 6 electrons.
Ranking by the number of electrons from most to least:
1. Gold (A) - 79 electrons
2. Silver (D) - 47 electrons
3. Copper (B) - 29 electrons
4. Carbon (C) - 6 electrons
c. Number of Protons:
The number of protons in an atom is equal to the atomic number.
1. Gold (A) has an atomic number of 79, so it has 79 protons.
2. Silver (D) has an atomic number of 47, so it has 47 protons.
3. Copper (B) has an atomic number of 29, so it has 29 protons.
4. Carbon (C) has an atomic number of 6, so it has 6 protons.
Ranking by the number of protons (which is the same as the ranking by the number of electrons):
1. Gold (A) - 79 protons
2. Silver (D) - 47 protons
3. Copper (B) - 29 protons
4. Carbon (C) - 6 protons
Final answer:
To rank the given atoms by mass, D. Silver has the most mass, followed by A. Gold, B. Copper, and C. Carbon. For number of electrons, B. Copper has the most, followed by A. Gold, C. Carbon, and D. Silver. For number of protons, B. Copper has the most, followed by A. Gold, D. Silver, and C. Carbon.
Explanation:
To rank the given atoms based on their mass, we can refer to the atomic mass or atomic weight of each element. The atomic mass of an element is the sum of the number of protons and neutrons in the nucleus. The element with the highest atomic mass will have the most mass. In this case, the ordering would be D. Silver, A. Gold, B. Copper, and C. Carbon.
To rank the atoms based on the number of electrons, we can refer to the atomic number of each element. The atomic number represents the number of protons, which is equal to the number of electrons in a neutral atom. The element with the highest atomic number will have the most electrons. In this case, the ordering would be B. Copper, A. Gold, C. Carbon, and D. Silver.
To rank the atoms based on the number of protons, we can again refer to the atomic number of each element. The atomic number represents the number of protons in the nucleus. The element with the highest atomic number will have the most protons. In this case, the ordering would be B. Copper, A. Gold, D. Silver, and C. Carbon.
Learn more about Ranking atoms by mass, number of electrons, and number of protons here:
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per second. What is the absolute index of
refraction of the second medium?
(1) 1.00 (3) 1.75
(2) 0.570 (4) 1.94
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Your answer is (2) 0.570
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Answer:
False
Explanation:
NOT due to their kinetic energy