The strong nuclear force
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
with solution and formula<3
It takes approximately 47 seconds for the sound of thunder to reach you at 20°C temperature.
The time it takes for the sound of thunder to reach you can be determined using the formula:
Time = Distance / Speed
Sound travels at a speed of approximately 343 meters per second at 20°C. Therefore, to calculate the time it takes for the sound to reach you, divide the distance by the speed:
Time = 16,090 meters / 343 meters per second
Time = 46.97 seconds
So, it takes approximately 47 seconds for the sound of thunder to reach you at 20°C temperature.
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photon?
(1) 1.86 × 10^22 J (3) 4.14 × 10^−19 J
(2) 1.44 × 10^2 J (4) 3.18 × 10^−26 J
Taking into account the definition of photon, energy of a photon, wavelength, frecuency and propagation speed, the correct answer is the option (3): The energy of a photon with aa wavelength of 4.80×10⁻⁷ meter is 4.14×10⁻¹⁹ J.
You have to know that electromagnetic radiation carries energy, which can be absorbed or emitted. To explain the processes of emission and absorption, Plank and Einstein proposed that the energy of radiation is composed of indivisible units (quanta). In each elemental process only a quantum of light can be emitted or absorbed. Each of these quanta was called a "photon".
The exchanges of energy between matter and radiation take place not continuously, but by discrete and indivisible quantities or quanta of energy. The quantum of energy is proportional to the frequency of radiation.
The relationship between the amount of energy (E) transported by the photon and its frequency (f) is determined by the following expression, where the energy of a photon is obtained by multiplying Planck's constant h by the frequency f of electromagnetic radiation:
E=h×f
Wavelength is the minimum distance between two successive points on the wave that are in the same state of vibration. It is expressed in units of length (m).
On the other side, frequency is the number of vibrations that occur in a unit of time. Its unit is s⁻¹ or hertz (Hz).
Finally, the propagation speed is the speed with which the wave propagates in the medium, that is, it is the magnitude that measures the speed at which the wave disturbance propagates along its displacement.
The propagation speed relate the wavelength (λ) and the frequency (f) inversely proportional using the following equation:
v = f×λ
All electromagnetic waves propagate in a vacuum at a constant speed of 3×10⁸ m/s, the speed of light.
In this case, you know:
Replacing in the definition of energy of a photon:
E=h× (v÷λ)
E= 6.63×10⁻³⁴ Js× (3×10⁸ m/s ÷4.80×10⁻⁷ m)
Solving:
E= 4.14×10⁻¹⁹ J
Finally, the correct answer is the option (3): The energy of a photon with aa wavelength of 4.80×10⁻⁷ meter is 4.14×10⁻¹⁹ J.
Learn more about
definition of photon and energy of a photon:
wavelength, frecuency and propagation speed:
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