Answer:
0.05cos10t
Explanation:
X(t) = Acos(wt+φ)
The oscillation angular frequency can be calculated using below formula
w = √(k/M)
Where K is the spring constant
But we were given body mass of 5.0 kg
We know acceleration due to gravity as 9.8m)s^2
The lenghth of spring which stretches =10 cm
Then we can calculate the value of K
k = (5.0kg*9.8 m/s^2)/0.10 m
K= 490 N/m
Then if we substitute these values into the formula above we have
w = √(k/M)
w = √(490/5)
= 9.90 rad/s=10rads/s(approximately)
Its position as a function of time can be calculated using the below expresion
X(t) = Acos(wt+φ)
We were given amplitude of 5 cm , if we convert to metre = 0.05m
w=10rads/s
Then if we substitute we have
X(t)=0.05cos(10×t)
X(t)= 0.05cos10t
Therefore,Its position as a function of time=
X(t)= 0.05cos10t
Please help!
Much appreciated!
Answer:
F = 2.7×10¯⁶ N.
Explanation:
From the question given:
F = (9×10⁹ Nm/C²) (3.2×10¯⁹ C × 9.6×10¯⁹ C) /(0.32)²
Thus we can obtain the value value of F by carrying the operation as follow:
F = (9×10⁹) (3.2×10¯⁹ × 9.6×10¯⁹) /(0.32)²
F = 2.7648×10¯⁷ / 0.1024
F = 2.7×10¯⁶ N.
Therefore, the value of F is 2.7×10¯⁶ N.
An aluminum rod 17.400 cm long at 20°C is heated to 100°C. What is its new length? Aluminum has a linear expansion coefficient of 25 × 10-6 C-1.
Answer:
the new length is 17.435cm
Explanation:
the new length is 17.435cm
pls give brainliest
The new length of aluminum rod is 17.435 cm.
The linear expansion coefficient is given as,
[tex]\alpha=\frac{L_{1}-L_{0}}{L_{0}(T_{1}-T_{0})}[/tex]
Given that, An aluminum rod 17.400 cm long at 20°C is heated to 100°C.
and linear expansion coefficient is [tex]25*10^{-6}C^{-1}[/tex]
Substitute, [tex]L_{0}=17.400cm,T_{1}=100,T_{0}=20,\alpha=25*10^{-6}C^{-1}[/tex]
[tex]25*10^{-6}C^{-1} =\frac{L_{1}-17.400}{17.400(100-20)}\\\\25*10^{-6}C^{-1} = \frac{L_{1}-17.400}{1392} \\\\L_{1}=[25*10^{-6}C^{-1} *1392}]+17.400\\\\L_{1}=17.435cm[/tex]
Hence, The new length of aluminum rod is 17.435 cm.
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What is temperature?
O A. The force exerted on an area
B. A measure of mass per unit volume
O C. The net energy transferred between two objects
OD. A measure of the movement of atoms or molecules within an
object
Answer:
The net energy transferred between two objects
Explanation:
The physical property of matter that expresses hot or cold is called temperature. It demonstrates the thermal energy. A thermometer is used to measure temperature. It defines the rate to which the chemical reaction occurs. It tells about the thermal radiation emitted from an object.
The correct option that defines temperature is option C.
Answer:
A measure of the movement of atoms or molecules within an object
Explanation:
Process of elimination
What is the pathway of sound through fluids starting at the oval window through to dissipation of the sound waves at the round window
An ac generator consists of a coil with 40 turns of wire, each with an area of 0.06 m2 . The coil rotates in a uniform magnetic field B = 0.4 T at a constant frequency of 55 Hz. What is the maximum induced emf?
a. 625 V
b. 110 V
c. 421 V
d. 332 V
e. 200 V
Answer:
d. 332 V
Explanation:
Given;
number of turns in the wire, N = 40 turns
area of the coil, A = 0.06 m²
magnitude of the magnetic field, B = 0.4 T
frequency of the wave, f = 55 Hz
The maximum emf induced in the coil is given by;
E = NBAω
Where;
ω is angular velocity = 2πf
E = NBA(2πf)
E = 40 x 0.4 x 0.06 x (2 x π x 55)
E = 332 V
Therefore, the maximum induced emf in the coil is 332 V.
The correct option is "D"
d. 332 V
A flatbed truck is supported by its four drive wheels, and is moving with an acceleration of 7.4 m/s2. For what value of the coefficient of static friction between the truck bed and a cabinet will the cabinet slip along the bed surface?
Answer:
The value is [tex]\mu = 0.76[/tex]
Explanation:
From the question we are told that
The acceleration is [tex]a = 7.4 \ m /s^2[/tex]
Generally the force by which the truck bed (truck) is moving with is mathematically represented as
[tex]F = ma[/tex]
Now for the truck cabinet to slip from the truck bed then the frictional force between the truck cabinet is equal the force by which the the truck bed is moving with that is
[tex]F_f = F[/tex]
Here [tex]F_f[/tex] is the frictional force which is mathematically represented as
[tex]F_f = \mu * m * g[/tex]
substituting into above equation
[tex]\mu * m * g = ma[/tex]
=> [tex]\mu = \frac{a}{g}[/tex]
substituting values
[tex]\mu = \frac{ 7.4 }{ 9.8}[/tex]
[tex]\mu = 0.76[/tex]
Select the situation for which the torque is the smallest.
a. A 200 kg piece of silver is placed at the end of a 2.5 m tree branch.
b. A 20 kg piece of marble is placed at the end of a 25 m construction crane arm.
c. A 8 kg quartz rock is placed at the end of a 62.5 m thin titanium rod.
d. The torque is the same for two cases.
e. The torque is the same for all cases.
Answer:
e. The torque is the same for all cases.
Explanation:
The formula for torque is:
τ = Fr
where,
τ = Torque
F = Force = Weight (in this case) = mg
r = perpendicular distance between force an axis of rotation
Therefore,
τ = mgr
a)
Here,
m = 200 kg
r = 2.5 m
Therefore,
τ = (200 kg)(9.8 m/s²)(2.5 m)
τ = 4900 N.m
b)
Here,
m = 20 kg
r = 25 m
Therefore,
τ = (20 kg)(9.8 m/s²)(25 m)
τ = 4900 N.m
c)
Here,
m = 8 kg
r = 62.5 m
Therefore,
τ = (8 kg)(9.8 m/s²)(62.5 m)
τ = 4900 N.m
Hence, the correct answer will be:
e. The torque is the same for all cases.
If mirror M2 in a Michelson interferometer is moved through 0.233 mm, a shift of 792 bright fringes occurs. What is the wavelength of the light producing the fringe pattern?
Answer:
The wavelength is [tex]\lambda = 589 nm[/tex]
Explanation:
From the question we are told that
The distance of the mirror shift is [tex]k = 0.233 \ mm = 0.233*10^{-3} \ m[/tex]
The number of fringe shift is n = 792
Generally the wavelength producing this fringes is mathematically represented as
[tex]\lambda = \frac{ 2 * k }{ n }[/tex]
substituting values
[tex]\lambda = \frac{ 2 * 0.233*10^{-3} }{ 792 }[/tex]
[tex]\lambda = 5.885 *10^{-7} \ m[/tex]
[tex]\lambda = 589 nm[/tex]
Which of the following regions of the electromagnetic spectrum have longer wavelengths than visible light? 1. infrared radiation 2. ultraviolet radiation 3. microwave radiation
Answer:infrared radiation
Explanation:
Infrared radiation and microwave radiation of the electromagnetic spectrum have longer wavelengths than visible light.
What is electromagnetic wave?EM waves are another name for electromagnetic waves. When an electric field interacts with a magnetic field, electromagnetic waves are created. These electromagnetic waves make up electromagnetic radiations. It is also possible to say that electromagnetic waves are made up of magnetic and electric fields that are oscillating. The basic equations of electrodynamics, Maxwell's equations, have an answer in electromagnetic waves.
If we arrange electromagnetic wave with decrease in wavelength, we get:
Radio waves > microwave > Infrared > Visible light > Ultraviolet > X-rays > Gamma radiation.
Hence, Infrared radiation and microwave radiation of the electromagnetic spectrum have longer wavelengths than visible light.
Learn more about electromagnetic wave here:
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Coherent light that contains two wavelengths, 660 nm (red) and 470 nm (blue), passes through two narrow slits that are separated by 0.310 mm. Their interference pattern is observed on a screen 4.40 m from the slits. What is the disatnce on the screen between the first order bright fringe for each wavelength?
Answer:
0.002699 m or 2.699 mm
Explanation:
y = Fringe distance
d= Distance between slits = 0.310mm
L = Screen distance = 4.40m
λ= Wavelength
Given from question
λ₁= 660 nm = 6.6 x 10^-9 m
λ₂= 470 nm = 4.7 x 10^-9 m
d = 0.340 mm = 3.4 x 10^-3 m
L = 4.40 m
In the case of constructive interference, we use below formula
y/L = mλ/d
For first order wavelength
(y₁/4.40) =(1×660x10⁻⁹)/(0.310*10⁻³)
y₁= (0.310*10⁻³)×(4.40)/(0.310*10⁻³)
y₁=0.00937m
(y2/4.40) =(1×470x10⁻⁹)/(0.310*10⁻³)
y2= =(1×470x10⁻⁹)×(4.40)/(0.310*10⁻³)
y2=0.00667m
distance between the fringes is given by (y₁ -y2)
=0.00937-0.00667=0.002699m
Therefore, distance on the screen between the first-order bright fringes for the two wavelengths is 0.002699 m or 2.699 mm
The only force acting on a 3.4 kg canister that is moving in an xy plane has a magnitude of 3.0 N. The canister initially has a velocity of 2.5 m/s in the positive x direction, and some time later has a velocity of 4.8 m/s in the positive y direction. How much work is done on the canister by the 3.0 N force during this time
Answer:
16.79JExplanation:
Given data
mass of canister= 3.4 kg
force acting on canister= 3 N
initial velocity u= 2.5 m/s
final velocity v= 4.8 m/s
The work done on the canister is the change in kinetic energy on the canister
change in [tex]KE= Kfinal- Kinitial[/tex]
K.E initial
[tex]Kintial= \frac{1}{2} mv^2\\\\Kintial= \frac{1}{2}*2*2.5^2\\\\KInitial= \frac{1}{2} *2*6.25\\\\Kinitial= 6.25J[/tex]
K.E final
[tex]Kfinal= \frac{1}{2} mv^2\\\\ Kfinal= \frac{1}{2}*2*4.8^2\\\\ Kfinal= \frac{1}{2} *2*23.04\\\\ Kfinal= 23.04J[/tex]
The net work done is [tex]KE= Kfinal- Kinitial[/tex]
[tex]W net= 23.04-6.25= 16.79J[/tex]
A skull believed to belong to an ancient human being has a carbon-14 decay rate of 5.4 disintegrations per minute per gram of carbon (5.4 dis/min*gC). If living organisms have a decay rate of 15.3 dis/min*gC, how old is this skull
Answer:
9.43*10^3 year
Explanation:
For this question, we ought to remember, or know that the half life of carbon 14 is 5730, and that would be vital in completing the calculation
To start with, we use the formula
t(half) = In 2/k,
if we make k the subject of formula, we have
k = in 2/t(half), now we substitute for the values
k = in 2 / 5730
k = 1.21*10^-4 yr^-1
In(A/A•) = -kt, on rearranging, we find out that
t = -1/k * In(A/A•)
The next step is to substitite the values for each into the equation, giving us
t = -1/1.21*10^-4 * In(5.4/15.3)
t = -1/1.21*10^-4 * -1.1041
t = 0.943*10^4 year
help... Please help!!!!!!!!!!!
Answer:
a) 6.8--5.10 thats equal 11.9
b) m=ris/run +10 equal 0.06/8 =7.5*10^-3
You simultaneously shine two light beams, each of intensity I0, on an ideal polarizer. One beam is unpolarized, and the other beam is polarized at an angle of exactly 30.0∘ to the polarizing axis of the polarizer. Find the intensity of the light that emerges from the polarizer. Express your answer in term of I0 .
Answer:
The emerging intensity is equal to 0.75[tex]I_{o}[/tex]
Explanation:
The initial intensity of the light = [tex]I_{o}[/tex]
The angle of polarization β = 30°
We know that the polarized light intensity is related to the initial light intensity by
[tex]I[/tex] = [tex]I_{0} cos^{2}\beta[/tex]
where [tex]I[/tex] is the emerging polarized light intensity
inserting values gives
[tex]I[/tex] = [tex]I_{0} cos^{2}[/tex] 30°
[tex]cos^{2}[/tex] 30° = [tex](cos 30)^{2}[/tex] = [tex](\frac{\sqrt{3} }{2} )^{2}[/tex] = 0.75
[tex]I[/tex] = 0.75[tex]I_{o}[/tex]
Please help!
Much appreciated!
Answer:
Rp = 3.04×10² Ω.
Explanation:
From the question given:
1/Rp = 1/4.5×10² Ω + 1/ 9.4×10² Ω
Rp =?
We can obtain the value of Rp as follow:
1/Rp = 1/4.5×10² + 1/ 9.4×10²
Find the least common multiple (lcm) of 4.5×10² and 9.4×10².
The result is 4.5×10² × 9.4×10²
Next, divide the result of the lcm by each denominator and multiply the result obtained with the numerator as shown below:
1/Rp = (9.4×10² + 4.5×10²) /(4.5×10²) (9.4×10²)
1/Rp = 13.9×10²/4.23×10⁵
Cross multiply
Rp × 13.9×10² = 4.23×10⁵
Divide both side by 13.9×10²
Rp = 4.23×10⁵ / 13.9×10²
Rp = 3.04×10² Ω.
A 1.2-m length of wire centered on the origin carries a 20-A current directed in the positive y direction. Determine the magnetic field at the point x= 5.0m on x-axis.
a. 1.6 nt in the negative z direction
b. 1.6 nt in the positive z direction
c. 2.4 T in the positive z direction
d. 2.4 nt in the negative z direction
e. None of the above
Answer:
None of the above
Explanation:
The formula of the magnetic field of a point next to a wire with current is:
B = 2×10^(-7) × ( I /d)
I is the intensity of the current.
d is the distance between the wire and the point.
● B = 2*10^(-7) × (20/5) = 8 ×10^(-7) T
The Milky Way has a diameter (proper length) of about 1.2×105 light-years. According to an astronaut, how many years would it take to cross the Milky Way if the speed of the spacecraft is 0.890 c?
Answer:
t = 134834.31 years
Explanation:
First we find the speed of the ship:
v = 0.890 c
where,
v = speed of the ship = ?
c = speed of light = 3 x 10⁸ m/s
Therefore, using the values, we get:
v = (0.89)(3 x 10⁸ m/s)
v = 2.67 x 10⁸ m/s
Now, we find the distance in meters:
Distance = s = (1.2 x 10⁵ light years)(9.461 x 10¹⁵/1 light year)
s = 11.35 x 10²⁰ m
Now, for the time we use the following equation:
s = vt
t = s/v
t = (11.35 x 10²⁰ m)/(2.67 x 10⁸ m/s)
t = (4.25 x 10¹² s)(1 h/3600 s)(1 day/24 h)(1 year/365 days)
t = 134834.31 years
the charge density in an insulateed solid sphere of radius find the electric field at a distance of from the center of the solid
Answer:
Assuming the charged density in the insulated solid sphere of radius 3.1m is 8.8e-9, the electric field at 5.2 meters is 73.1256 [tex]i[/tex].
Explanation:
The electric charge linear density is equal to 8.8 x[tex]10^{-9}[/tex]
the radius of the sphere is 3.1m
The magnitude of the electric field at the radius of the sphere equal to 5.2 meters can be calculated with the formula ;
- E = λ / 4πε₀ [ r / α ( α + r ) ] [tex]i[/tex]
Solution:
E = 8.8 x[tex]10^{-9}[/tex] / 4πε₀ [ 3.1/ 5.2( 5.2 + 3.1) ] [tex]i[/tex]
= 1018.0995 [0.07183] [tex]i[/tex]
= 73.1256 [tex]i[/tex]
Suppose a 1300 kg car is traveling around a circular curve in a road at a constant
9.0 m/sec. If the curve in the road has a radius of 25 m, then what is the
magnitude of the unbalanced force that steers the car out of its natural straight-
line path?
Answer:
F = 4212 N
Explanation:
Given that,
Mass of a car, m = 1300 kg
Speed of car on the road is 9 m/s
Radius of curve, r = 25 m
We need to find the magnitude of the unbalanced force that steers the car out of its natural straight- line path. The force is called centripetal force. It can be given by :
[tex]F=\dfrac{mv^2}{r}\\\\F=\dfrac{1300\times 9^2}{25}\\\\F=4212\ N[/tex]
So, the force has a magnitude of 4212 N
Which examination technique is the visualization of body parts in motion by projecting x-ray images on a luminous fluorescent screen?
Answer:
Fluoroscopy
Explanation:
A Fluoroscopy is an imaging technique that uses X-rays to obtain real-time moving images of the interior of an object. In its primary application of medical imaging, a fluoroscope allows a physician to see the internal structure and function of a patient, so that the pumping action of the heart or the motion of swallowing, for example, can be watched.
A charge of 15 is moving with velocity of 6.2 x17 which makes an angle of 48 degrees with respect to the magnetic field. If the force on the particle is 4838 N, find the magnitude of the magnetic field.
a. 06.0T.
b. 08.0T.
c. 07.0T.
d. 05.0 T.
Complete question:
A charge of 15C is moving with velocity of 6.2 x 10³ m/s which makes an angle of 48 degrees with respect to the magnetic field. If the force on the particle is 4838 N, find the magnitude of the magnetic field.
a. 0.06 T
b. 0.08 T
c. 0.07 T
d. 0.05 T
Answer:
The magnitude of the magnetic field is 0.07 T.
Explanation:
Given;
magnitude of the charge, q = 15C
velocity of the charge, v = 6.2 x 10³ m/s
angle between the charge and the magnetic field, θ = 48°
the force on the particle, F = 4838 N
The magnitude of the magnetic field can be calculated by applying Lorentz force formula;
F = qvBsinθ
where;
B is the magnitude of the magnetic field
B = F / vqsinθ
B = (4838) / (6.2 x 10³ x 15 x sin48)
B = 0.07 T
Therefore, the magnitude of the magnetic field is 0.07 T.
Does the moon light originate from the moon only
Answer:
No
Explanation:
Moon has no light of its own. It just shines because its surface reflects light from the sun and that's what we see.
:-)
Radar is used to determine distances to various objects by measuring the round-trip time for an echo from the object. (a) How far away (in m) is the planet Venus if the echo time is 900 s? m (b) What is the echo time (in µs) for a car 80.0 m from a Highway Patrol radar unit? µs (c) How accurately (in nanoseconds) must you be able to measure the echo time to an airplane 12.0 km away to determine its distance within 11.5 m? ns
Answer:
a) 1.35 x 10^11 m
b) 0.53 µs
c) 8 ns
Explanation:
Radar involves the use of radio wave which has speed c = 3 x 10^8 m/s
a) for 900 s,
The distance for a round trip = v x t
==> (3 x 10^8) x 900 = 2.7 x 10^11 m
The distance of Venus is half this round trip distance = (2.7 x 10^11)/2 = 1.35 x 10^11 m
b) for a 80.0 m distance of the car from the radar source, the radar will travel a total distance of
d = 2 x 80 = 160 m
the time taken = d/c = 160/(3 x 10^8) = 5.3 x 10^-7 s = 0.53 µs
c) accuracy in distance Δd = 11.5 m
Δt = accuracy in time = Δd/c = 11.5/(3 x 10^8) = 3.8 x 10^-8 = 38 ns
If the intensity of an electromagnetic wave is 80 MW/m2, what is the amplitude of the magnetic field of this wave
CHECK THE COMPLETE QUESTION BELOW;
the intensity of an electromagnetic wave is 80 MW/m2, what is the amplitude of the magnetic field of this wave? (c=3.0×108m/s, μ0=4π×10−7T⋅m/A, ε0=8.85×10−12C2/N⋅m2)
Answer:
2.4×10^5 N/C
Explanation:
the amplitude can be explained as the maximum field strength of the electric and magnetic fields. Wave energy is proportional to its amplitude squared (E2 or B2).
We were told to calculate the amplitude of the magnetic field, which can be done using expresion below
S=ε²/2cμ
Where S is the intensity intensity of an electromagnetic wave given as 80 MW/m2
ε² is the Amplitude which we are looking for
c= speed of light given as 3×10^8m/s
Substitute the values into above formula we have,
S=ε²/2cμ
Making Amplitude subject of formula
ε²=S×2cμ
ε²=[80×10^6)(2×3×10^8)(4Π×10^-7)
= 245598.44
ε²=2.4×10^5 N/C
Therefore, amplitude of the magnetic field of this wave is S=2.4×10^5 N/C
Seismic attenuation and how spherical spreading affect amplitude, can anyone explain this please!
Answer:
Hey there!
This can be a confusing topic, so it's totally fine if you get confused...
First, Seismic Attenuation is how seismic waves lose energy as they expand and spread.
Secondly, when distance increases, amplitude decreases. This is because the distance (spherical spreading would mean radius) is inversely proportional to amplitude.
Let me know if this helps :)
The roller coaster car reaches point A of the loop with speed of 20 m/s, which is increasing at the rate of 5 m/s2. Determine the magnitude of the acceleration at A if pA
Answer and Explanation:
Data provided as per the question is as follows
Speed at point A = 20 m/s
Acceleration at point C = [tex]5 m/s^2[/tex]
[tex]r_A = 25 m[/tex]
The calculation of the magnitude of the acceleration at A is shown below:-
Centripetal acceleration is
[tex]a_c = \frac{v^2}{r}[/tex]
now we will put the values into the above formula
= [tex]\frac{20^2}{25}[/tex]
After solving the above equation we will get
[tex]= 16 m/s^2[/tex]
Tangential acceleration is
[tex]= \sqrt{ac^2 + at^2} \\\\ = \sqrt{16^2 + 5^2}\\\\ = 16.703 m/s^2[/tex]
g To decrease the intensity of the sound you are hearing from your speaker system by a factor of 36, you can
Answer:
Increase the distance by a factor of 6.
Explanation:
The intensity at a distance r is given by :
[tex]I=\dfrac{P}{4\pi r^2}[/tex]
Here,
P is power emitted
r is distance from source
It means that the intensity is inversely proportional to the distance from the source.
To decrease the intensity of the sound you are hearing from your speaker system by a factor of 36, we can increase the distance by a factor of 6. Hence, this is the required solution.
A current of 5 A is flowing in a 20 mH inductor. The energy stored in the magnetic field of this inductor is:_______
a. 1J.
b. 0.50J.
c. 0.25J.
d. 0.
e. dependent upon the resistance of the inductor.
Answer:
C. 0.25J
Explanation:
Energy stored in the magnetic field of the inductor is expressed as E = 1/2LI² where;
L is the inductance
I is the current flowing in the inductor
Given parameters
L = 20mH = 20×10^-3H
I = 5A
Required
Energy stored in the magnetic field.
E = 1/2 × 20×10^-3 × 5²
E = 1/2 × 20×10^-3 × 25
E = 10×10^-3 × 25
E = 0.01 × 25
E = 0.25Joules.
Hence the energy stored in the magnetic field of this inductor is 0.25Joules
Suppose a certain laser can provide 82 TW of power in 1.1 ns pulses at a wavelength of 0.24 μm. How much energy is contained in a single pulse?
Answer:
The energy contained in a single pulse is 90,200 J.
Explanation:
Given;
power of the laser, P = 82 TW = 82 x 10¹² W
time taken by the laser to provide the power, t = 1.1 ns = 1.1 x 10⁻⁹ s
the wavelength of the laser, λ = 0.24 μm = 0.24 x 10⁻⁶ m
The energy contained in a single pulse is calculated as;
E = Pt
where;
P is the power of each laser
t is the time to generate the power
E = (82 x 10¹²)(1.1 x 10⁻⁹)
E = 90,200 J
Therefore, the energy contained in a single pulse is 90,200 J
"A light beam incident on a diffraction grating consists of waves with two different wavelengths. The separation of the two first order lines is great if"
Answer:
A light beam incident on a diffraction grating consists of waves with two different wavelengths. The separation of the two first order lines is great if
the dispersion is great
