Answer:Density = 7.5 g/ml (By putting the given values.) [ The ratio of the mass to volume is the density, that's why the unit of the density is also the ratio of the unit of mass to the unit of volume. ] Hence, the density of the object is 7
Explanation: Google
The box has 3 forces acting on it:
• its own weight (magnitude w, pointing downward)
• the normal force of the incline on the box (mag. n, pointing upward perpendicular to the incline)
• friction (mag. f, opposing the box's slide down the incline and parallel to the incline)
Decompose each force into components acting parallel or perpendicular to the incline. (Consult the attached free body diagram.) The normal and friction forces are ready to be used, so that just leaves the weight. If we take the direction in which the box is sliding to be the positive parallel direction, then by Newton's second law, we have
• net parallel force:
∑ F = -f + w sin(35°) = m a
• net perpendicular force:
∑ F = n - w cos(35°) = 0
Solve the net perpendicular force equation for the normal force:
n = w cos(35°)
n = (15 kg) (9.8 m/s²) cos(35°)
n ≈ 120 N
Solve for the mag. of friction:
f = µn
f = 0.25 (120 N)
f ≈ 30 N
Solve the net parallel force equation for the acceleration:
-30 N + (15 kg) (9.8 m/s²) sin(35°) = (15 kg) a
a ≈ (54.3157 N) / (15 kg)
a ≈ 3.6 m/s²
Now solve for the block's speed v given that it starts at rest, with v₀ = 0, and slides down the incline a distance of ∆x = 3 m:
v² - v₀² = 2 a ∆x
v² = 2 (3.6 m/s²) (3 m)
v = √(21.7263 m²/s²)
v ≈ 4.7 m/s
B. 1.2 m/s
C. 21.3 m/s
D. 12.8 m/s
The impact speed of the backpack is approximately 12.8 m/s.
To calculate the impact speed of the backpack, we can use the principle of conservation of energy. The potential energy of the backpack at the top of the window is converted into kinetic energy at the bottom. Assuming no air resistance, we can equate the potential energy to the kinetic energy:
mgh = 1/2mv^2
Here, m is the mass of the backpack, g is the acceleration due to gravity (9.8 m/s^2), and h is the height of the window (8.3 m). By rearranging the equation and solving for v, we can find the impact speed of the backpack.
Using the given values:
v = sqrt(2gh) = sqrt(2 * 9.8 * 8.3) ≈ 12.8 m/s
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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
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.
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.
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