The time period of the spring is 2[tex]\pi[/tex][√(m/k)].
What is meant by spring constant ?The spring constant of a spring is defined as the measurement of ratio of the force that is exerted on the spring to the displacement caused by it.
Here,
The mass of the block = m
Let F be the applied force on the spring and k be the spring constant.
When the mass attached to the spring is pulled to one side then released, it executes SHM.
Therefore we can write that, the applied force,
F = kx
Restoring force = -kx
According to Newton's law, we know that,
F = ma
So,
ma = -kx
Therefore, the acceleration,
a = (-k/m) x
For an SHM, the acceleration is given as,
a = -ω²x
Therefore, we can write that,
-ω²x = (-k/m) x
ω² = k/m
So, the time period of the spring,
T = 2[tex]\pi[/tex]/ω
T = 2[tex]\pi[/tex][√(m/k)]
Hence,
The time period of the spring is 2[tex]\pi[/tex][√(m/k)].
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In these formulas, it is useful to understand which variables are parameters that specify the nature of the wave. The variables E0E0E_0 and B0B0B_0 are the __________ of the electric and magnetic fields. Choose the best answer to fill in the blank.
What is the order of magnitude of the distance of Sun to nearest star in meters?
Answer:
Approximating the Milky Way as a disk and using the density in the solar neighborhood, there are about 100 billion stars in the Milky Way.
Explanation:
Since we are making an order of magnitude estimate, we will make a series of simplifying assumptions to get an answer that is roughly right.
Let's model the Milky Way galaxy as a disk.
The volume of a disk is:
V
=
π
⋅
r
2
⋅
h
Plugging in our numbers (and assuming that
π
≈
3
)
V
=
π
⋅
(
10
21
m
)
2
⋅
(
10
19
m
)
V
=
3
×
10
61
m
3
Is the approximate volume of the Milky Way.
Now, all we need to do is find how many stars per cubic meter (
ρ
) are in the Milky Way and we can find the total number of stars.
Let's look at the neighborhood around the Sun. We know that in a sphere with a radius of
4
×
10
16
m there is exactly one star (the Sun), after that you hit other stars. We can use that to estimate a rough density for the Milky Way.
ρ
=
n
V
Using the volume of a sphere
V
=
4
3
π
r
3
ρ
=
1
4
3
π
(
4
×
10
16
m
)
3
ρ
=
1
256
10
−
48
stars /
m
3
Going back to the density equation:
ρ
=
n
V
n
=
ρ
V
Plugging in the density of the solar neighborhood and the volume of the Milky Way:
n
=
(
1
256
10
−
48
m
−
3
)
⋅
(
3
×
10
61
m
3
)
n
=
3
256
10
13
n
=
1
×
10
11
stars (or 100 billion stars)
Is this reasonable? Other estimates say that there are are 100-400 billion stars in the Milky Way. This is exactly what we found.
Answer:
Mercury, 46,001,272 km from the sun at the nearest point.
Explanation:
Earth’s Moon has a diameter of 3,474 km and orbits at an average distance of 384,000 km. At that distance it subtends and angle just slightly larger than half a degree in Earth’s sky. Pluto’s moon Charon has a diameter of 1,186 km and orbits at a distance of 19,600 km from the dwarf planet. Compare the appearance of Charon in Pluto’s skies with the Moon in Earth’s skies. Describe where in the sky Charon would appear as seen from various locations on Pluto.
The reason for arriving at the above solutions is as follows:
The given dimensions and distance from the Earth of the Moon are;
The diameter of the Moon, d = 3,474 km
The average distance of the Moon from the Earth, R = 384,000 km
Required:
The comparison between Charon's appearance in Pluto and the Moon's appearance on Earth Earth
Solution:
The distance of the Moon's travels in an orbit, C = 2·π·R
∴ C = 2 × π × 384,000 km
The angle subtended by the Moon, θ = d/C × 360°
∴ θ = 3,474/(2 × π × 384,000) × 360° ≈ 0.518°
Pluto's moon Charon, has the following parameters;
The diameter of the Charon, d₂ = 1,186 km
The average distance of the Charon from Pluto, R₂ = 19,600 km
Therefore, the distance of the Moon's travels in an orbit, C₂ = 2·π·R₂
∴ C₂ = 2 × π × 19,600 km
The angle subtended by the Moon, θ₂ = d₂/C₂ × 360°
∴ θ₂ = 1,186/(2 × π × 19,900) × 360° ≈ 3.415°
The angle subtended by Charon in Pluto's sky ≈ 3.415°
Charon therefore, appears 7 times larger in Pluto's skies than the Moon's appearance in Earth's skies
Required:
The appearance of Charon as seen from different locations on Pluto
Solution:
Charon is gravitationally locked to Pluto, therefore, the same side of Pluto is faced with the same side of Charon
Therefore;
Charon appears constantly overhead from the side of Pluto locked to CharonCharon appears constantly at the horizon from the poles on either side of the axis of rotation of Pluto and CharonLearn more about Pluto's moon Charon here:
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Find out other examples of bodies showing more than one type of motion Tabulate your findings.
Answer:
down below
Explanation:
Image 1- wheels of train showing both translatory motion as well as rotatory motion.
Image 2- rotation of ball shows both rotatory motion as well as translatory motion.
Image 3- the earth rotates about its axis, same time it revolves around the sun thus showing both rotatory motion and curvilinear motion in a fixed time. (perodic motion)
Image 4- while cutting wood, the
carpenter's saw has both
translatory motion and oscillatory
motion, as it moves down while
oscillating.
A race car goes from a complete stop at the start line to 150 miles per hour in 5 seconds. What is its acceleration? Show your work.
Answer:
Explanation:
150/5 = 30
30mph per 1 second
g Light that is incident upon the eye is refracted several times before it reaches the retina. As light passes through the eye, at which boundary does most of the overall refraction occur?
Answer
Explanation
:giác mạc
A cylindrical wire made of an unknown alloy hangs from a support in the ceiling. You measure the relaxed length of the wire to be 16 m long; and the radius of the wire to be 3.5 m. When hang a 5 kg mass from the wire, you measure that it stretches a distance of 4 x 10 m The average bond length between atoms is 2.3 x 10^0 m for th alloy.
Required:
What is the stiffness of a typical interatomic bond in the alloy
Answer: hello some of your values are wrongly written hence I will resolve your question using the right values
answer:
stiffness = 1.09 * 10^-6 N/m
Explanation:
Given data:
Length ( l ) = 16 m
radius of wire ( r ) = 3.5 m
mass ( m ) = 5kg
Distance stretched ( Δl ) = 4 * 10^-3 m ( right value )
average bond length ( between atoms ) = 2.3 * 10^-10 m ( right value)
first step : calculate the area
area ( A ) = πr^2 = π * ( 3.5)^2 = 38.48 m^2
γ = MgL / A Δl
= [ (5 * 9.81 * 16 ) / ( 38.48 * (4.3*10^-3) ) ]
= 784.8 / 0.165 = 4756.36 N/m^2
hence : stiffness = γ * bond length
= 4756.36 * 2.3 * 10^-10 = 1.09 * 10^-6 N/m
A professor of physics cannot see clearly at a distance shorter than 1 m. What should be the focal length of an eyeglass lens that would assist him in reading a newspaper while holding it at a desired distance of 25 cm
Answer:
Explanation:
Two masses of 3 kg and 5 kg are connected by a light string that passes over a smooth polley as shown in the Figure.
QL
Determine:
i. the tension in the string,
ii. the acceleration of each mass, and
iii. the distance each mass moves in the first second of motion if they start from rest
i. [tex]T = 36.8\:\text{N}[/tex]
ii. [tex]a = 2.45\:\text{m/s}^2[/tex]
iii. [tex]x = 1.23\:\text{m}[/tex]
Explanation:
Let's write Newton's 2nd law for each object. We will use the sign convention assigned for each as indicated in the figure. Let T be the tension on the string and assume that the string is inextensible so that the two tensions on the strings are equal. Also, let a be the acceleration of the two masses. And [tex]m_1 = 3\:\text{kg}[/tex] and [tex]m_2 = 5\:\text{kg}[/tex]
Forces acting on m1:
[tex]T - m_1g = m_1a\:\:\:\:\:\:\:(1)[/tex]
Forces acting on m2:
[tex]m_2g - T = m_2a\:\:\:\:\:\:\:(2)[/tex]
Combining Eqn(1) and Eqn(2) together, the tensions will cancel out, giving us
[tex]m_2g - m_1g = m_2a + m_1a[/tex]
or
[tex](m_2 - m_1)g = (m2 + m_1)a[/tex]
Solving for a,
[tex]a = \left(\dfrac{m_2 - m_1}{m_2 + m_1}\right)g[/tex]
[tex]\:\:\:\:= \left(\dfrac{5\:\text{kg} - 3\:\text{kg}}{5\:\text{kg} + 3\:\text{kg}}\right)(9.8\:\text{m/s}^2)[/tex]
[tex]\:\:\:\:= 2.45\:\text{m/s}^2[/tex]
We can solve for the tension by using this value of acceleration on either Eqn(1) or Eqn(2). Let's use Eqn(1).
[tex]T - (3\:\text{kg})(9.8\:\text{m/s}^2) = (3\:\text{kg})(2.45\:\text{m/s}^2)[/tex]
[tex]T = (3\:\text{kg})(9.8\:\text{m/s}^2) + (3\:\text{kg})(2.45\:\text{m/s}^2)[/tex]
[tex]\:\:\:\:= 29.4\:\text{m/s}^2 + 7.35\:\text{m/s}^2 = 36.8\:\text{N}[/tex]
Assuming that the two objects start from rest, the distance that they travel after one second is given by
[tex]x = \frac{1}{2}at^2 = \frac{1}{2}(2.45\:\text{m/s}^2)(1\:\text{s})^2 = 1.23\:\text{m}[/tex]
A proposed communication satellite would revolve around the earth in a circular orbit in the equatorial plane at a height of 35880Km above the earth surface. Find the period of revolution of the satellite. (Take the mass of earth =5.98×10²⁴kg, the radius of the earth 6370km and G=6.6×10–¹¹Nm²/kg2)
Answer:
Period is 86811.5 seconds.
Explanation:
[tex]{ \boxed{ \bf{T {}^{2} = (\frac{4 {\pi}^{2} }{GM}) {r}^{3} }}}[/tex]
[tex]{ \tt{T {}^{2} = \frac{4 {(3.14)}^{2} }{(6.6 \times {10}^{ - 11} ) \times (5.98 \times {10}^{24} )} \times {((35880\times {10}^{3}) } + (6370 \times {10}^{3} )) {}^{3} }} \\ \\ { \tt{T {}^{2} = 7.54 \times {10}^{9} }} \\ { \tt{T = \sqrt{7.54 \times {10}^{9} } }} \\ { \tt{T = 86811.5 \: seconds}}[/tex]
Monochromatic light is incident on a metal surface and electrons are ejected. If the intensity of the light is increased, what will happen to the ejection rate and maximum energy of the electrons
Answer:
Increase the rate and the same maximum energy of the electrons
Explanation:
According to the photoelectric effect we can say:
The number of electrons, or the electric current, has a linear behaviour with the intensity of the light and a constant behaviour whit the frequency. Therefore, the rate of electrons increases.The kinetic energy of the ejected electrons has a linear dependence on the frequency of the light and has a constant behaviour with the intensity. So, we can say there is the same maximum energy.I hope it helps you!
A rod of length L and electrical resistance R moves through a constant uniform magnetic field ; both the magnetic field and the direction of motion are parallel to the rod. The force that must be applied by a person to keep the rod moving with constant velocity is:
Answer:
don't know what class are you you are using which mobile or laptop
Electron A is fired horizontally with speed 1.00 Mm/s into a region where a vertical magnetic field exists. Electron B is fired along the same path with speed 2.00 Mm/s. (i) Which electron has a larger magnetic force exerted on it
B will have the greater force
Fc=MV2 /R=Fm
The A particle has less centipetal force and larger radius so larger curve
Two divers, G and H, are at depths 20 m and 40 m respectively
below the water surface in lake. The pressure on G is P, while
the pressure on H is P2 if the atmospheric pressure is equivalent
to 10 m of water, then the value of P2/P1 is.
A. 1.67.
B. 2.00.
C. 0.50.
D. 0.60.
Answer:
B
Explanation:
P1/P1 = 40/20
=2
Which of the following statements about magnetism is TRUE?
a) The direction of the magnetic force on a current-carrying wire is parallel to the wire.
b) Magnetic poles always occur in pairs (N and S).
c) Magnetic field lines begin at south poles and end on north poles.
d) Moving charges do not experience a force in magnetic fields.
1. Estimate the buoyant force that air exerts on a man. (To do this, you can estimate his volume by knowing his weight and by assuming that his weight density is about equal to that of water. Assume his weight is 940 N.) answer in N
2.On a perfect fall day, you are hovering at low altitude in a hot-air balloon, accelerated neither upward nor downward. The total weight of the balloon, including its load and the hot air in it, is 17000 N.
(a) What is the weight of the displaced air?
answer in N
(b) What is the volume of the displaced air?
answer in m^3
Solution :
1. We know that : Buoyant force = weight of the liquid displace
= volume displaced x density of the fluid
Now volume of the man = [tex]$\frac{\text{mass}}{\text{density}}$[/tex]
Mass = weight / g
[tex]$=\frac{940}{9.8}$[/tex]
= 95.92 kg
And density = 1000 [tex]kg/m^3[/tex]
Therefore,
[tex]$\text{volume} = \frac{\text{mass}}{\text{density}}$[/tex]
[tex]$=\frac{95.92}{1000}$[/tex]
= 0.0959 [tex]m^3[/tex]
We know density of air = 1.225 [tex]kg/m^3[/tex]
∴ Mass of air displaced = 0.0959 x 1.225
= 0.1175 kg
Weight of the air displaced = 1.1515 N
Therefore, the buoyant force = 1.1515 N
2). As the balloon is not accelerated, the net force acting on it is zero.
Thus the weight that acts downwards = buoyant force upwards
So, the weight of the air displaced = weight of the balloon
= 17000 N
Therefore, the mass of the air displaced = volume of the air displaced (volume of the balloon) x density of air
[tex]$\frac{17000}{9.8} = \text{volume of air} \times 1.225$[/tex]
[tex]$\text{Volume of air displaced} = \frac{1700}{9.8 \times 1.225}$[/tex]
= 1416.0766 [tex]m^3[/tex]
What is hydroelectric power ?
Answer quickly..!
Answer:
It's electricity produced from hydropower. It's also a form of energy that controls the power of water motion.
Explanation:
One pro about hydroelectric power is that it's renewable energy. But one con about hydroelectric power is that it can impact the environment in a negative way.
a standard bathroom scale is placed on an elevator. A 34 kg boy enters the elevator on the first floor and steps on the scale. What will the scale read (in newtons) when the elevator begins to accelerate upward at 0.4 m/s2
Answer:F = 255 N
Explanation:
It is given that,
Mass of the boy, m = 25 kg
Acceleration of the elevator,
The elevator is accelerating in upward direction. The net force acting on the boy is given by :
g is the acceleration due to gravity
F = 255 N
The scale reading is 255 N as it begins to accelerate upward. hence, this is the required solution.
Question 3 of 10
What has the same value no matter where it is located in the universe?
A. Volume
B. Weight
C. Mass
D. Density
Reset Selection
Answer:
C. Mass
Explanation:
Light of a given wavelength is used to illuminate the surface of a metal, however, no photoelectrons are emitted. In order to cause electrons to be ejected from the surface of this metal you should: ___________
a. use light of the same wavelength but increase its intensity.
b. use light of a shorter wavelength.
c. use light of the same wavelength but decrease its intensity.
d. use light of a longer wavelength.
Answer:
use light of the same wavelength but decrease it's intensity
elastic wire extend by 1.ocm when a load on 20g range from It, what additional load will it be required Cause the futher extension of 2.0cm
Answer:
40g
Explanation:
20g range > 1.0cm
Therefore,
40g range > 2.0cm
A mountain biker takes a jump in a race and goes airborne. The mountain bike is travelling at 10.0 m/s before it goes airborne. If the mass of the front wheel on the bike is 750 g and has radius 35 cm, what is the angular momentum of the spinning wheel in the air the moment the bike leaves the ground?
Answer:
Explanation:
The formula for angular momentum is
L = mvr where L is the angular momentum, m is the mass of the object, v is the velocity of the object, and r is the radius of the object. The problem we have that prevents us from just throwing those numbers in there is that mass has to be in kg and it's not, and radius has to be in meters and it's not.
Changing the mass to kg:
750 g = .750 kg
Changing the radius to m:
35 cm = .35 m
Now we can fill in the variables with their respective values:
L = .750(10.0)(.35) gives us
[tex]L=2.625\frac{kg*m^2}{s}[/tex]
Two long straight wires are suspended vertically. The wires are connected in series, and a current from a battery is maintained in them. What happens to the wires? What happens if the battery is replaced by an a-c source?
Answer:
(i) When a battery is connected inseries to two long parallel wires, the currents in the two wires will be in opposite directions. Due to which a force of repulsion will be acting between them and they are moving further apart.
(ii) When a battery is connected in parallel to two long parallel wires, the currents in the two wires will be in same direction. Due to it, a force of attraction will be acting between them and they are coming closer to each other.
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Explanation:
Hope it will helps you lot!
A roller coaster has a total track length of 500 yards. A complete ride on the roller coaster is considered two times around the track. The start and stop places for the ride are virtually the same. What are the distance and displacement for a ride on the roller coaster? Explain your answers.
Answer:
Explanation:
its 1000 yards if its going around the track 2 times and that if one whole around the track is 500 its 500 x 2
Uuse Lenz's law to explore what happens when an electromagnet is activated a short distance from a wire loop. You will need to use the right-hand rule to find the direction of the induced current.
Answer:
Explanation:
According to the Fleming's right hand rule, if we spread our right hand such that the thumb, fore finger and the middle finger are mutually perpendicular to each other, then the thumb indicates the direction of force, fore finger indicates the direction of magnetic field, then the middle finger indicates the direction of induced current.
According to the Lenz's law, the direction of induced emf is such that it always opposes the cause due to which it is produced.
Two circular coils are concentric and lie in the same plane.The inner coil contains 120 turns of wire, has a radius of 0.012m,and carries a current of 6.0A. The outer coil contains 150turns and has a radius of 0.017 m. What must be the magnitudeand direction (relative to the current in the inner coil) ofthe current in the outer coil, such that the net magnetic field atthe common center of the two coils is zero?
Answer:
[tex]I_2=6.8A[/tex]
Explanation:
From the question we are told that:
Turns of inner coil [tex]N_1=120[/tex]
Radius of inner coil [tex]r_1=0.012m[/tex]
Current of inner coil [tex]I_1=6.0A[/tex]
Turns of Outer coil [tex]N_2=150[/tex]
Radius of Outer coil [tex]r_2=0.017m[/tex]
Generally the equation for Magnetic Field is mathematically given by
[tex]B =\frac{ \mu N I}{2R}[/tex]
Therefore
Condition for the net Magnetic field to be zero
[tex]\frac{N_1* I_1}{( 2 * r_1 )}=\frac{N_2 * I_2}{2 * r_2}[/tex]
[tex]I_2=\frac{(N_1* I_1)*(( 2 * r_2)}{( 2 * r_1)*N_2}[/tex]
[tex]I_2=\frac{(120*6.0)*(( 2 * 0.017)}{( 2 * 0.012)*150}[/tex]
[tex]I_2=6.8A[/tex]
A light spectrum is formed on the screen using a diffraction grating. The entire apparatus made up of laser, grating and the screen is now immersed in a liquid with refractive index 1.33. Do the bright spots on the screen get closer together, farther apart, remain the same or disappear entirely? Explain
Answer:
the points are closer to each other
Explanation:
The expression for the diffraction of a grating is
d sin θ = m λ
sin θ = m λ / d (1)
where d is the distance between slits and m is the order of diffraction, the most general is to work in the order m = 1, the angle te is the angle of diffraction
When we immerse the apparatus in a medium with refractive index n = 1.33, the light emitted by the laser must comply
v = λ f
where v is the speed of light in the medium, the frequency remains constant
velocity and refractive index are related
n = c / v
v = c / n
we substitute
c / n = λf
λ = [tex]\frac{c}{f} \ \frac{1}{n}[/tex]
λ = λ₀ / m
where λ₀ is the wavelength in vacuum
we substitute is equation 1
d sin θ = m λ₀ / n
sin θ = λ₀/ n d
sin θ = [tex]\frac{1}{n}[/tex] sin θ₀
we can see that the value of the sine is redueced since the refractive index is greater than 1,
consequently the points are closer to each other
1. There is a famous intersection in Kuala Lumpur, Malaysia, where thousands of vehicles pass each hour. A 750 kg Tesla Model S traveling south crashes into a 1250 kg Ford F-150 traveling east. What are the initial speeds of each vehicle before collision if they stick together after crashing into each other and move at an angle of 320 and a common velocity of 18 m/s.
Solution :
Let the positive [tex]x-axis[/tex] is along the East and the positive [tex]y[/tex] direction is along the north.
Given :
Mass of the Tesla car, [tex]m_1[/tex] = [tex]750 \ kg[/tex]
Mass of the Ford car, [tex]m_2 = 1250 \ kg[/tex]
Now let the initial velocity of Tesla car in the south direction be = [tex]-v_1j[/tex]
The initial momentum of Tesla car, [tex]p_1 = -750 \ v_1[/tex]
Let the initial velocity of Ford car in the east direction be = [tex]v_2 \ i[/tex]
So the initial momentum of the Ford car is [tex]p_2=1250\ v_2 \ i[/tex]
Therefore, the initial velocity of both the cars is [tex]p_i = p_1+p_2[/tex]
[tex]=1250 \ v_2 \ i - 750\ v_1 \ j[/tex]
Now the final velocity of both the cars is [tex]v = 18 \ m/s[/tex]
So the vector form is :
[tex]v = 18\cos 32\ i-18 \sin 32 \ j[/tex]
[tex]= 15.26 \ i - 9.54 \ j[/tex]
Therefore the momentum after the accident is
[tex]p_f=(m_1+m_2) \times v[/tex]
[tex]=(750+1250) \times (15.26 \ i - 9.54 \ j)[/tex]
[tex]= 30520\ i -19080\ j[/tex]
According to the law of conservation of momentum, we know
[tex]p_i = p_f[/tex]
[tex]1250 \ v_2 \ i - 750\ v_1 \ j[/tex] [tex]= 30520\ i -19080\ j[/tex]
[tex]1250 \ v_2 = 30520[/tex]
[tex]v_2=24.4 \ m/s[/tex]
From, [tex]750\ v_1 = 19080[/tex]
We get, [tex]v_1=25.4 \ m/s[/tex]
Therefore the speed of Tesla car before collision = 25.4 m/s
The speed of ford car before collision = 24.4 m/s
Ayudaaa :(
Calcula la resistencia total del siguiente circuito eléctrico.
A large metal sphere has three times the diameter of a smaller sphere and carries three times the charge. Both spheres are isolated, so their surface charge densities are uniform. Compare (a) the potentials (relative to infinity) and (b) the electric field strengths at their surfaces.
Answer:
A. Equals to that of the smaller sphere
B. 3 times less than that of the smaller sphere
Explanation:
(a) Equals to that of the smaller sphere
The potential of an isolated metal sphere, with charge Q and radius R, is kQ=R, so a sphere with charge 3Q and radius 3R has the same potential
b) 3 times less than that of the smaller sphere
However, the electric field at the surface of the smaller sphere is ?=? 0 = kQ=R2 , so tripling Q and R reduces the surface field by a factor of 1/3
