Answer:
The new time period is [tex]T_2 = 3.8 \ s[/tex]
Explanation:
From the question we are told that
The period of oscillation is [tex]T = 5 \ s[/tex]
The new length is [tex]l_2 = 0.76 \ m[/tex]
Let assume the original length was [tex]l_1 = 1 m[/tex]
Generally the time period is mathematically represented as
[tex]T = 2 \pi \sqrt{ \frac{ I }{ mgh } }[/tex]
Now I is the moment of inertia of the stick which is mathematically represented as
[tex]I = \frac{m * l^2 }{12 }[/tex]
So
[tex]T = 2 \pi \sqrt{ \frac{ m * l^2 }{12 * mgh } }[/tex]
Looking at the above equation we see that
[tex]T \ \ \ \alpha \ \ \ l[/tex]
=> [tex]\frac{ T_2 }{T_1} = \frac{l_2}{l_1}[/tex]
=> [tex]\frac{ T_2}{5} = \frac{0.76}{1}[/tex]
=> [tex]T_2 = 3.8 \ s[/tex]
A 50kg block slides down a slope that forms an angle of 54 degrees if it is known that when descending it has a force of 40N and a coefficient of friction of 0.33. What is the acceleration in the block?
Answer:
The acceleration in the block is 2.1 m/s²
Explanation:
Given that,
Mass = 50 kg
Angle = 54°
Force = 40 N
Coefficient of friction = 0.33
We need to calculate the acceleration in the block
Using balance equation
[tex]F_{net}=F_{f}-F\cos\theta[/tex]
[tex]ma=\mu mg\sin\theta-F\cos\theta[/tex]
[tex]a=\dfrac{\mu mg\sin\theta-F\cos\theta}{m}[/tex]
Put the value into the formula
[tex]a=\dfrac{0.33\times50\times9.8\sin54-40\cos54}{50}[/tex]
[tex]a=2.1\ m/s^2[/tex]
Hence, The acceleration in the block is 2.1 m/s²
You need to make a spring scale to measure the mass of objects hung from it. You want each 1.0 cm length along the scale to correspond to a mass difference of 0.10 kg. What should be the value of the spring constant?
Answer:
The spring constant should be:
[tex]k= 98\, \frac{N}{m}[/tex]
Explanation:
Use Hooke's law for this problem, knowing that the magnitude of the force (F) on the spring equals the stretching it experiences [tex]\Delta x[/tex] times the spring constant "k":
[tex]F=k\,\Delta x[/tex]
in our case, since the mass hanging is given in kg, we need to multiply it by "g" to get the force exerted:
Then if we add to the spring in its relaxed state, a mass of 0.10 kg, and we want for that a displacement of 1 cm (0.01 m), then the value of the spring constant should be:
[tex]k=\frac{F}{\Delta x} \\k=\frac{9.8\,(0.1)}{0.01} \, \frac{N}{m} \\k= 98\, \frac{N}{m}[/tex]
What type of tectonic plate boundary exists along the edge of the North American plate near the coast of Northern California, Oregon, and Washington?
A reverse fault, like the Cascadia subduction zone off the coast of Oregon and Northern California (north of Mendocino California), has relatively deep earthquakes—like the 1964 Alaska earthquake and the 2004 Sumatra earthquake that caused the Boxing Day Tsunami.
True
False
Megathrust earthquakes can be strongest in magnitude—stronger than a San Andreas earthquake like 1906
Answer:
-transform plate boundary
- false
A circuit contains a single 220 pF capacitor hooked across a battery. It is desired to store three times as much energy in a combination of two capacitors by adding a single capacitor to this one.
How would you hook it up?
The capacitor is connected in series to the original capacitor
or
The capacitor is connected in parallel to the original capacitor
I believe its parallel
but now What would its value be?
Answer
The capacitor should be connected in parallel as parallel connection gives the arithmetic sum of capacitance which will give a corresponding sum of energy while capacitors in series gives the sum of the reciprocal if the individual capacitance
An ac source of period T and maximum voltage V is connected to a single unknown ideal element that is either a resistor, and inductor, or a capacitor. At time t = 0 the voltage is zero and increasing toward a maximum. At time t = T/4 the current in the unknown element is equal to zero, and at time t = T/2 the current is I = -I max, where Imax is the current amplitude. What is the unknown element?
a. a resistor
b. an inductor or a capacitor
c. an inductor
d. a capacitor
Scientists today learn about the world by _____. 1. using untested hypotheses to revise theories 2. observing, measuring, testing, and explaining their ideas 3. formulating conclusions without testing them 4. changing scientific laws
Answer:
Option 2 (observing, measuring, testing, and explaining their ideas) is the correct choice.
Explanation:
A traditional perception of such a scientist is those of an individual who performs experiments in some kind of a white coat. The reality of the situation is, a researcher can indeed be described as an individual interested in the comprehensive as well as a recorded review of the occurrences occurring in nature but perhaps not severely constrained to physics, chemistry as well as biology alone.The other three choices have no relation to a particular task. So the option given here is just the right one.
a trombone can be modeled like an open closed air tube. the trombone plays a fifth harmonic of 159 hz. the speed of sound is 343 m/s. what is the wavelength of this sound
Answer:
The wavelength is 2.16 m.
Explanation:
Given the speed of the sound = 343 m/s
Trombone generate the frequency = 159 Hz
Now we have to find the wavelength of the sound. Here, we can find the wavelength by dividing the speed of the sound with frequency.
The wavelength of the sound = Speed of sound/frequency
Wavelength of the sound = 343 / 159 = 2.16 m
Describe how you expect the waveform and the sound you hear changes when you hit the tuning fork harder.
Answer:
In a tuning fork, two basic qualities of sound are considered, they are
1) The pitch of the waveform: This pitch depends on the frequency of the wave generated by hitting the tuning fork.
2) The loudness of the waveform: This loudness depends on the intensity of the wave generated by hitting the tuning fork.
Hitting the tuning fork harder will make it vibrate faster, increasing the number of vibrations per second. The number of vibration per second is proportional to the frequency, so hitting the tuning fork harder increase the frequency. From the explanation on the frequency above, we can say that by increasing the frequency the pitch of the tuning fork also increases.
Also, hitting the tuning fork harder also increases the intensity of the wave generated, since the fork now vibrates faster. This increases the loudness of the tuning fork.
A small wave pulse and a large wave pulse approach each other on a string; the large pulse is moving to the right.
Sometime after the pulses have met and passed each other, which of the following statements is correct? (More than one answer may be correct)
- the large pulse continues moving to the right
- the large pulse continues unchanged, moving to the right
- the small pulse is reflected and moves off to the right with a smaller amplitude
- the small pulse is reflected and moves off to the right with its original amplitude
- the two pulses combine into a single pulse moving to the right
Answer:
the large amplitude wave keeps moving to the right
the small amplitude wave continues to move to the left.
When checking the answers, the correct ones are 1, 2
Explanation:
The waves fulfill the principle of superposition, which states that the value of the function at a point is the algebraic sum of the waves at a given instant.
The two waves in this exercise travel in the opposite direction, so when they are close, the resulting wave is the sum of the two waves, having a complicated shape. But when the waves follow their movement, they give in the same way as the initial a,
the large amplitude wave keeps moving to the right
the small amplitude wave continues to move to the left.
When checking the answers, the correct ones are 1, 2
A system of four particles moves along a dimension. The center of mass is at rest, and the particles do not interact with any objects outside of the system. Find the velocity of v4 at t=2.83 seconds given the details for the motion of particles 1,2,3
Answer:
v = - 14.08 m / s
Explanation:
The definition of center of mass is
[tex]x_{cm}[/tex] = 1 /M ∑sun [tex]x_{i} m_{i}[/tex]
where M is the total mass of the system and [tex]x_{i}[/tex] and [tex]m_{i}[/tex] are the position and mass of each component.
The velocity of the center of mass can be found by deriving this expression with respect to time
[tex]v_{cm}[/tex] = 1 / M ∑ m_{i} [tex]v_{i}[/tex] vi
let's find the total mass
M = m₁ + m₂ + m₃ + m₄
M = 1.45 + 2.81 +3.89 + 5.03
m = 13.18 kg
let us substitute in the velocity of the center of mass [tex]v_{cm}[/tex] = 0
0 = 13.18 (m₁ v₁ + m₂ v₂ + m₃v₃ + m₄v₄)
v₄ = - (m₁ v₁ + m₂ v₂ + m₃v₃) / m₄
let's substitute the given values
v₄ = -[1.45 (6.09 +0.299 t) +2.81 (7.83 + 0.357t) +3.89 (8.09 + 0.405 t)] / 5.03
They ask us for the calculations for a time t = 2.83 s
v₄ = - [8.8305 + 1.227 + 22.00 + 2.839 + 31.47 +4.4585] / 5.03
v = - 14.08 m / s
The velocity of the particle 4 at time, t = 2.83 s, is -14.1 m/s.
The given parameters;
[tex]m_1 = 1.45 \ kg, \ \ v_1(t) = (6.09 \ m/s) + (0.299 \ m/s^2)\times t\\\\m_2 = 2.81 \ kg, \ \ v_2(t) = (7.83 \ m/s) + (0.357 \ m/s^2)\times t \\\\m_3 = 3.89 \ kg, \ \ v_3(t) = (8.09 \ m/s) + (0.405 \ m/s^2)\times t\\\\m_4 = 5.03 \ kg[/tex]
The velocity of the center mass of the particles is calculated as;
[tex]M_{cm}V_{cm} = m_1v_1 + m_2 v_2 + m_3v_3 + m_4v_4\\\\V_{cm} = \frac{m_1v_1 + m_2 v_2 + m_3v_3 + m_4v_4}{M_{cm}} \\\\0 = \frac{m_1v_1 + m_2 v_2 + m_3v_3 + m_4v_4}{M_{cm}}\\\\m_1v_1 + m_2 v_2 + m_3v_3 + m_4v_4 = 0\\\\m_4v_4 = -(m_1v_1 + m_2 v_2 + m_3v_3)\\\\v_4 = \frac{-(m_1v_1 + m_2 v_2 + m_3v_3)}{m_4}[/tex]
The velocity of particle 1 at time, t = 2.83 s;
[tex]v_1 = 6.09 \ + \ 0.299\times 2.83\\\\v_1 = 6.94 \ m/s[/tex]
The velocity of particle 2 at time, t = 2.83 s;
[tex]v_2 = 7.83\ + \ 0.357\times 2.83\\\\v_2 = 8.84 \ m/s[/tex]
The velocity of particle 3 at time, t = 2.83 s;
[tex]v_3 = 8.09\ + \ 0.405 \times 2.83\\\\v_3 = 9.24 \ m/s[/tex]
The velocity of the particle 4 at time, t = 2.83 s;
[tex]v_4 = \frac{-(m_1v_1 + m_2v_2 + m_3v_3)}{m_4} \\\\v_4 = \frac{-(1.45\times 6.94\ + \ 2.81\times 8.84\ + \ 3.89 \times 9.24)}{5.03} \\\\v_4 = -14 .1 \ m/s[/tex]
Thus, the velocity of the particle 4 at time, t = 2.83 s, is -14.1 m/s.
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A bar magnet is dropped from above and falls through the loop of wire. The north pole of the bar magnet points downward towards the page as it falls. Which statement is correct?a. The current in the loop always flows in a clockwise direction. b·The current in the loop always flows in a counterclockwise direction. c. The current in the loop flows first in a clockwise, then in a counterclockwise direction. d. The current in the loop flows first in a counterclockwise, then in a clockwise direction. e. No current flows in the loop because both ends of the magnet move through the loop.
Answer:
b. The current in the loop always flows in a counterclockwise direction.
Explanation:
When a magnet falls through a loop of wire, it induces an induced current on the loop of wire. This induced current is due to the motion of the magnet through the loop, which cause a change in the flux linkage of the magnet. According to Lenz law, the induced current acts in such a way as to repel the force or action that produces it. For this magnet, the only opposition possible is to stop its fall by inducing a like pole on the wire loop to repel its motion down. An induced current that flows counterclockwise in the wire loop has a polarity that is equivalent to a north pole on a magnet, and this will try to repel the motion of the magnet through the coil. Also, when the magnet goes pass the wire loop, this induced north pole will try to attract the south end of the magnet, all in a bid to stop its motion downwards.
The current in the loop always flows in a counterclockwise direction. Hence, option (b) is correct.
The given problem is based on the concept and fundamentals of magnetic bars. When a magnet falls through a loop of wire, it induces an induced current on the loop of wire. There is some magnitude of current induced in the wire.
This induced current is due to the motion of the magnet through the loop, which cause a change in the flux linkage of the magnet. According to Lenz law, the induced current acts in such a way as to repel the force or action that produces it. For this magnet, the only opposition possible is to stop its fall by inducing a like pole on the wire loop to repel its motion down. An induced current that flows counterclockwise in the wire loop has a polarity that is equivalent to a north pole on a magnet, and this will try to repel the motion of the magnet through the coil. Also, when the magnet goes pass the wire loop, this induced north pole will try to attract the south end of the magnet, all in a bid to stop its motion downwards.Thus, we can say that the current in the loop always flows in a counterclockwise direction. Hence, option (b) is correct.
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Define the following, and give the letter which we will abbreviate them by:
Center of curvature:
Vertex:
Focal Point:
Radius of curvature:
Focal length:
Answer:
As in explanation.
Explanation:
A) Centre of Curvature: This is defined as the point in the center of the sphere from which the mirror was sliced. It is represented by the letter "C"
B) Vertex: It is defined as the point on the mirror's surface where the principal axis meets the mirror. It is represented by the letter A.
C) Focal Point: This is defined as the Midway point between the vertex and the center of curvature. It is represented by the letter "F"
D) Radius of Curvature: This is defined as the distance from the vertex to the center of curvature. It is represented by the letter "R"
E) Focal Length: This is defined as the distance from the mirror to the focal point. It's represented by the letter "f"
6)the speed of light is approximately 186,000 mi/sec. It takes light from a particular star approximately 9 yrs to reach Earth. How many miles away is the star from Earth? Express the answer in scientific notation. Use 365 days in 1 year. The star is nothing miles away from Earth.
Answer:
5.2791264*10¹³
Explanation:
Convert the 9 years to seconds and then multiple it by 186000
The star is 4.62 x 10¹⁶ miles away from Earth.
The speed of light is 186,000 miles per second. It takes light from a particular star approximately 9 years to reach Earth. There are 365 days in 1 year, so it takes 9 x 365 = 3285 days for light from the star to reach Earth.
The distance between the star and Earth is 3285 x 186,000 = 608,810,000 miles. In scientific notation, this is 4.62 x 10¹⁶ miles.
Here is the calculation:
distance = speed * time
distance = 186,000 miles/second * 3285 days * 24 hours/day * 60 minutes/hour * 60 seconds/minute
distance = 608,810,000 miles
distance = 4.62 x 10¹⁶ miles
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6. If you wanted to develop a telescope, what kind of lenses would you use for the objective lens (the lens that collects the light) and the eyepiece? Explain your reasoning. Draw a picture with ray tracing of your setup.
Answer:
objetive: a converging lens for large diameter lenses
eyepiece you must select a lens with a small focal length and the diameter is not important
The selected lenses should decrease chromatic aberration.
Explanation:
A telescope is an instrument that collects light from very distant objects, therefore very weak.
Therefore you should select a converging lens for large diameter lenses, to collect magnanimous light and with a large focal length.
For the eyepiece you must select a lens with a small focal length and the diameter is not important
the telescope magnification is
m = f_objective / F_ocular
The selected lenses should decrease chromatic aberration.
In general, these lenses are heavy, so refractory telescopes were imposed, so it uses a concave mirror instead of an objective lens.
Answer: this the real answer try it objetive: a converging lens for large diameter lenseseyepiece you must select a lens with a small focal length and the diameter is not importantThe selected lenses should decrease chromatic aberration.Explanation:A telescope is an instrument that collects light from very distant objects, therefore very weak.Therefore you should select a converging lens for large diameter lenses, to collect magnanimous light and with a large focal length.For the eyepiece you must select a lens with a small focal length and the diameter is not importantthe telescope magnification is m = f_objective / F_ocularThe selected lenses should decrease chromatic aberration.In general, these lenses are heavy, so refractory telescopes were imposed, so it uses a concave mirror instead of an objective lens.
Explanation:
Two identical trucks have mass 5500 kg when empty, and the maximum permissible load for each is 8000 kg. The first truck, carrying a 3900 kg, is at rest. The second truck plows into it at 64 km/h, and the pair moves away at 44 km/h. As an expert witnes, you're asked to determine whether the second truck was overloaded. What do you report? Yes the truck is overloaded, or no, the truck is not overloaded?
Answer:
no, the truck is not overloaded
Explanation:
The computation is shown below;
Let us assume the mass of the loan in the second truck be M
So, the equation is as follows
{(Mass + M) × second truck × 1000 ÷ 3,600} = {(Mass + M + mass + first truck) × Pair moves away × 1,000 ÷ 3,600}
{(5500 + M) × 64 × 1,000 ÷ 3,600 = {(5,500 + M + 5,500 + 3,900) × 44 × 1,000 ÷ 3,600}
(5500 + M) × 64 = (14,900 + M) × 44
352,000 + 64 M = 655,600 + 44 M
After solving this
M = 15,180 kg
Therefore the second truck is not overloaded
Suppose, we have a parallel plate capacitor and we know the following about it: Area of each plate = $0.0012m^2$ Distance between the two plates = $0.002m$ Charge on each plate after fully charging the capacitor = $2\times10^{-6}C$ Potential difference between the plates after fully charging the capacitor = $4\times 10^{-3}V$ My solution: We know that the electric field intensity at a point between two equally and oppositely charged plates is $\LARGE\frac{\sigma}{\epsilon_0}$. So, for the above case, $$\large E = \frac{\sigma}{\epsilon_0}$$ $$\large\implies E = \frac{\frac{2\times10^{-6}}{0.0012}}{8.85\times10^{-12}}{NC^{-1}}$$ $$\large\implies E =188323917.1NC^{-1}$$ My book's solution: $$E = \frac{V}{d}$$ $$\implies E=\frac{4\times 10^{-3}V}{0.002m}NC^{-1}$$ $$\implies E = 2NC^{-1}$$ If the books solution is correct, could you please explain why my answer is wrong and the book's is correct? Thanks in advance!
Answer:
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A rod of length L is hinged at one end. The moment of inertia as the rod rotates around that hinge is ML2/3. Suppose a 2.50 m rod with a mass of 3.00 kg is hinged at one end and is held in a horizontal position. The rod is released as the free end is allowed to fall. What is the angular acceleration as it is released?
Answer:
6 rad/s²
Explanation:
Sum the torques about the hinge.
∑τ = Iα
mg(L/2) = mL²/3 α
g/2 = L/3 α
α = 3g/(2L)
α = 3 (10 m/s²) / (2 × 2.50 m)
α = 6 rad/s²
Question 5 of 25
Which of the following means that a mirror is convex?
A. +d;
B. -d;
O C. +f
O D. -f
The sign that represents a convex mirror is +f (option C). Details about convex mirror can be found below.
What is a convex mirror?A convex mirror is that which is curved or bowed outward like the outside of a bowl or sphere or circle.
The focal length is the distance at which a lens or mirror is in focus. The focal length (f) is usually positive (+) for a convex mirror.
Therefore, the sign that represents a convex mirror is +f.
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Light with an intensity of 1 kW/m2 falls normally on a surface with an area of 1 cm2 and is completely absorbed. The force of the radiation on the surface is
Answer:
The force of the radiation on the surface is 3.33 x 10⁻¹⁰ N
Explanation:
Given;
intensity of light, I = 1kw/m² = 1000 W/m²
area of the surface, A = 1 cm² = 1 x 10⁻⁴ m²
Since the light is completely absorbed, the force of the radiation is given by;
F = P/c
where;
c is the speed of light = 3 x 10⁸ m/s
But P = IA
F = IA /c
F = (1000 X 1 X 10⁻⁴) / 3 x 10⁸
F = 3.33 x 10⁻¹⁰ N
Therefore, the force of the radiation on the surface is 3.33 x 10⁻¹⁰ N
The force of radiation will be "3.33 × 10⁻¹⁰ N"
Intensity and ForceAccording to the question,
Intensity of force, I = 1 kW/m² or,
= 1000 W/m²
Area of surface, A = 1 cm² or,
= 1 × 10⁻⁴ m²
Speed of light, c = 3 × 10³ m/s
As we know the relation,
→ F = [tex]\frac{P}{c}[/tex]
or,
P = IA
or,
F = [tex]\frac{IA}{c}[/tex]
By substituting the values, we get
= [tex]\frac{1000\times 1\times 10^{-4}}{3\times 10^3}[/tex]
= 3.33 × 10⁻¹⁰ N
Thus the response above is correct.
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PLEASE ANSWER ASAP
What happens to the ocean water before the precipitation part of the water cycle? ANSWERS; A.The ocean water condenses into the clouds. B.The ocean water collects back in the ocean. C.The ocean water falls back to Earth's surface. D. The ocean water runs off Earth's surface.
Answer:
B.
Explanation:
The water collects in the ocean; it is then evaporated by the sun. After evaporation the water turns into water vapor, it then condenses to form clouds.
The ocean water prior to the part of the water cycle should be option B.
Ocean water:The ocean water should be collected back in the ocean prior to the part of the water cycle.
Because this should be done when it is evaporated by the sun. When the evaporation is done so the water should be transformed into water vapor.
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If two firecrackers produce a sound level of 81 dBdB when fired simultaneously at a certain place, what will be the sound level if only one is exploded?
Answer:
77.96dB
Explanation:
Recall that decibels are a unit of measuring intensity of sound, and depend on the logarithm of the intensity
the intensity, measured in decibels is given by:
I(db)=10log(I/I0)
I is the intensity in MKS units; I0 is the threshold intensity for human hearing (10^-12 W/m^2)
Thus, if the two sounds together have a dB of 81, we know:
81=10log(I/I0)
using the data above, we can find the intensity of the two sounds to be
0.000125 W/m^2
therefore, one firecracker has an intensity half of that, or 0.0000625W/m^2
now use this value to find the dB of one firecracker:
I(dB0=10log(0.0000625/10^-12)=77.96dB
"When red light in vacuum is incident at the Brewster angle on a certain glass slab, the angle of refraction is"
Complete Question
When red light in vacuum is incident at the Brewster angle on a certain glass slab, the angle of refraction is [tex]36.0 ^o[/tex] . What are
(a) the index of refraction of the glass and
(b) the Brewster angle?
Answer:
a
[tex]n_r = 1.376[/tex]
b
[tex]i = 54^o[/tex]
Explanation:
From the question we are told that
The angle of refraction is [tex]r = 36.0 ^o[/tex]
Generally according Brewster law
[tex]i + r = 90[/tex]
Here [tex]i[/tex] is the angle of incidence which is also the Brewster angle
So
[tex]i + 36.0 = 90[/tex]
[tex]i = 54^o[/tex]
Now the refractive index is mathematically represented as
[tex]n_r = tan (i)[/tex]
substituting values
[tex]n_r = tan (54)[/tex]
[tex]n_r = 1.376[/tex]
A toroidal solenoid with 400 turns of wire and a mean radius of 6.0 cm carries a current of 0.25 A. The relative permeability of the core is 80.
(a) What is the magnetic field in the core?
(b) What part of the magnetic field is due to atomic currents?
Answer:
A) 0.0267 T
B) 0.0263 T
Explanation:
Given that
The number of turns, N = 400
Radius of the wire, r = 6 cm = 0.06 m
Current in the wire, I = 0.25 A
Relative permeability, K(m) = 80
See the attached picture for the calculation
The mass (M) of a piece of metal is directly proportional to its volume (V), where the proportionality constant is the density (D) of the metal. (1) Write an equation that represents this direct proportion, in which D is the proportionality constant. The density of lead metal is 11.3 g/cm3. (2) What is the mass of a piece of lead metal that has a volume of 17.3 cm3
Answer:
1) M = 11.3V2) 195.49 gramsExplanation:
1) If the mass (M) of a piece of metal is directly proportional to its volume (V), where the proportionality constant is the density (D) of the metal, this is expressed mathematically as shown;
M ∝ V
M = kV
For every proportionality sign, there will always be a proportionality constant 'k'
Since the proportionality constant is the density (D) of the metal, the equation will become;
M = DV
Given the density to be 11.3 g/cm3, the equation will become;
M = 11.3V
Hence, the equation that represents this direct proportion, in which D is the proportionality constant with metal density of 11.3g/cm³ is M = 11.3V
2) If the volume of the metal is 17.3cm³, on substituting this values into the equation in (1) to get the mass of the metal, we will have;
M = 11.3V
M = 11.3 * 17.3
M = 195.49 grams
Hence, the mass of a piece of lead metal that has a volume of 17.3 cm³ is 195.49 grams.
NASA is giving serious consideration to the concept of solar sailing. A solar sailcraft uses a large, low- mass sail and the energy and momentum of sunlight for propulsion.
Should the sail be absorbing or reflective? Why?
a. The sail should be reflective because in this case the momentum transferred to the sail per unit area per unit time is smaller than for absorbing sail, therefore the radiation pressure is larger for the reflective sail
b. The sail should be absorbing because in this case the momentum transferred to the sail per unit area per unit time is larger than for reflective sail, therefore the radiation pressure is larger for the absorbing sail
c. The sail should be absorbing because in this case the momentum transferred to the sail per unit area per unit time is smaller than for reflective sail, therefore the radiation pressure is larger for the absorbing sail.
d. The sail should be reflective because in this case the momentum transferred to the sail per unit area per unit time is larger than for absorbing sail, therefore the radiation pressure is larger for the reflective sail
Answer:
d. The sail should be reflective because in this case the momentum transferred to the sail per unit area per unit time is larger than for absorbing sail, therefore the radiation pressure is larger for the reflective sail.
Explanation:
Let us take the momentum of a photon unit as u
we know that the rate of change of momentum is proportional to the force exerted.
For a absorbing surface, the photon is absorbed, therefore the final momentum is zero. From this we can say that
F = (u - 0)/t = u/t
for a unit time, the force is proportional to the momentum of the wave due to its energy density. Therefore,
F = u
For a reflecting surface, the momentum of the wave strikes the sail and changes direction. Since we know that the speed of light does not change, then the force is proportional to
F = (u - (-u))/t = 2u/t
just as the we did above, it becomes
F = 2u.
From this we can see that the force for a reflective sail is twice of that for an absorbing sail, and we know that the pressure is proportional to the force for a given area. From these, we conclude that the sail should be reflective because in this case the momentum transferred to the sail per unit area per unit time is larger than for absorbing sail, therefore the radiation pressure is larger for the reflective sail.
Sunlight strikes a piece of crown glass at an angle of incidence of 37.4o. Calculate the difference in the angle of refraction between a red (660 nm) and a blue (470 nm) ray within the glass. The index of refraction is n
Answer:
The difference in angle of refraction between the red and blue light is 0.2°
Explanation:
Here is the complete question
Sunlight strikes a piece of crown glass at an angle of incidence of 37.4°. Calculate the difference in the angle of refraction between a red (660 nm) and a blue (470 nm) ray within the glass. The index of refraction is n=1.520 for red and n=1.531 for blue light.
Solution
From Snell's law refractive index n = sini/sinr where i = angle of incidence and r = angle of refraction.
Now for the red light n₁ = 1.520, i = 37.4° and r₁ = angle of refraction of red light
So, n₁ = sini/sinr₁
n₁sinr₁ = sini
sinr₁ = sini/n₁
r₁ = sin⁻¹(sini/n₁) = sin⁻¹(sin37.4°/1.52) = sin⁻¹(0.6074/1.52) = sin⁻¹(0.3996) = 23.55°
Now for the blue light n₂ = 1.531, i = 37.4° and r₂ = angle of refraction of blue light
So, n₂ = sini/sinr₂
n₂sinr₂ = sini
sinr₂ = sini/n₂
r₂ = sin⁻¹(sini/n₂) = sin⁻¹(sin37.4°/1.531) = sin⁻¹(0.6074/1.531) = sin⁻¹(0.3967) = 23.37°
So the difference in angle of refraction between the red and blue light is r₁ - r₂ = 23.55° - 23.37° = 0.18° ≅ 0.2°
A dentist uses a concave mirror (focal length 2 cm) to examine some teeth. If the distance from the object to the mirror is 1 cm, what is the magnification of the tooth
Answer: 2
Explanation:
1/2=1/1 +1/x
x=-2
magnification= 2/1
magnification=2
A cyclist moves effortlessly at a constant speed of 12 m / s, but enters a muddy area where the coefficient of kinetic friction is 0.60. Will the rider leave the muddy area without having to pedal if the mud extends 11m? If so, how fast will it emerge?
Answer:
3.5 m/s
Explanation:
There are 3 forces on the cyclist:
Weight force mg pulling down,
Normal force N pushing up,
and friction force Nμ pushing left.
Sum of forces in the y direction:
∑F = ma
N − mg = 0
N = mg
∑F = ma
-Nμ = ma
-mgμ = ma
a = -gμ
a = -(10 m/s²)(0.60)
a = -6 m/s²
Velocity reached at end of 11 m:
v² = v₀² + 2aΔx
v² = (12 m/s)² + 2 (-6 m/s²) (11 m)
v = √12 m/s
v ≈ 3.5 m/s
Mary had 21 plants when she went on vacation. When she got back , she only had 14 left alive. What is the percent of decrease in the number of plants?
Explanation:
Mary had 21 plants when she went on vacation.
When she got back, she only had 14 left alive.
We need to find the percent decrease in the number of plants.
Decrease in plants = 21 - 14 = 7
Percent decrease is given by :
[tex]\%=\dfrac{7}{21}\times 100\\\\\%=33.33\%[/tex]
So, there is 33% pf decrease in the number of plants.
When a battery is connected to a lightbulb properly, current flows through the lightbulb and makes it glow. How much current flows through the battery compared with the lightbulb
Answer:
The same amount of current flows through the battery and light bulb
Explanation:
Because for a single loop, the current is the same at every point in the loop. Thus, the amount of current that flows through the lightbulb is the same as the amount that flows through the battery
Answer:
The same amount of current flows through the battery and light bulb
Explanation:
