Answer:
r = 4.747 cm and h = 9.4925 cm
Explanation:
We know that volume of a cylinder is given as:
V = πr²h
Also, surface area is given as;
S = 2πr² + 2πrh
Where r is radius and h is height
Now, we are told that the volume is 672 cm³
Thus, πr²h = 672
Making h the subject gives;
h = 672/πr²
Putting 672/πr² for h in the surface area equation gives;
S = 2πr² + 2πr(672/πr²)
Factorizing gives;
S = 2π[r² + 672/πr]
Differentiating to get first derivative gives;
S' = 2π[2r - (672/πr²)]
Equating to zero gives;
2π[2r - (672/πr²)] = 0
4πr - 1344/r² = 0
4πr = 1344/r²
r³ = 1344/4π
r³ = 106.95212175775
r = ∛106.95212175775
r = 4.747 cm
So, since h = 672/πr²
Then, h = 672/π(4.747)²
h = 9.4925 cm
What should a model of the rock cycle show as the process that changes metamorphic rock to igneous rock?
Answer:
Rock cycle describes the concept in geology that shows the changes in the rock type in the geologic time.
Many processes undergoes in the rock cycle that leads to transition of rocks, the process that changes metamorphic rock to igneous rock is melting and crystallization. The metamorphic rock melts under high pressure and temperature and which crystallizes into a completely different kind of rock, called igneous rock.
Answer:
Melting followed by cooling
When a p-n-p transistor is operated in saturation region, then its ___________
Answer:
Base-emitter and Base-collector junctions are forward biased
The downward pull on an object due to gravity is the object’s ______. A. volume B. mass C. weight D. matter
Answer:
C. Weight
Explanation:
A push or pull is a force. The force caused by gravity is called weight.
Answer:
C: Weight
Explanation:
Suppose that you measure the length of a spaceship, at rest relative to you, to be 400 m. How long will you measure it to be if it flies past you at a speed of v
Answer:
264 m
Explanation:
The complete question is
Suppose that you measure the length of a spaceship, at rest relative to you, to be 400 m. How long will you measure it to be if it flies past you at a speed of v = 0.75c
using the length contraction relationship,
[tex]l = l_{0} \sqrt{1 - \beta ^{2} }[/tex]
where [tex]\beta = \frac{v}{c}[/tex]
[tex]l[/tex] is the relativistic length
[tex]l_{0}[/tex] is the actual length = 400 m
v is the velocity of the spaceship
c is the speed of light
since v = 0.75c
v/c = 0.75
substituting, we have
[tex]l = 400 * \sqrt{1 - 0.75 ^{2} }[/tex] = 400 x 0.66 = 264 m
A sailboat moves north for a distance of 10.00 km when blown by a wind from the exact south with a force of 5.00 x 10^4 N.
How much work was done by the wind?
Answer:
5*10^8Nm
Explanation:
work done= displacement* force
Since the wind blows in the direction that the boats want to travel, all values would be positive.
10*10^3*(5*10^4)=5.00*10^8Nm
Answer:
5 x 10⁸ J
Explanation:
Recall that
Work Done = Force x Distance Traveled in the direction of the force
We are given :
Force = 5.00 x 10⁴ = 50,000 N
Distance Travelled in the direction of the force = 10.00 km = 10,000 m
Hence,
Work Done = 50,000 N x 10,000 m
= 500,000,000 J
= 5 x 10⁸ J
an astronaut is said to be weightless when he/she travells in a satellite . does it mean that the earthdoes not attract him/her ?
Answer:
It does attract
Explanation:
But due to the lack of gravitational pull of the earth he/she feels weightless I hope this helps you
A ruby laser delivers a 16.0-ns pulse of 4.20-MW average power. If the photons have a wavelength of 694.3 nm, how many are contained in the pulse
Answer:
The value is [tex]n = 2.347 *10^{17} \ photons[/tex]
Explanation:
From the question we are told that
The amount of power delivered is [tex]P = 4.20 \ M W = 4.20 *10^{6} \ W[/tex]
The time taken is [tex]t = 16.0ns = 16.0 *10^{-9} \ s[/tex]
The wavelength is [tex]\lambda = 694.3 \ nm = 694.3 *10^{-9} \ m[/tex]
Generally the energy delivered is mathematically represented as
[tex]E = P * t = \frac{n * h * c }{\lambda }[/tex]
Where [tex]h[/tex] is the Planck's constant with value [tex]h = 6.262 *10^{-34} \ J \cdot s[/tex]
c is the speed of light with value [tex]c = 3.0*10^{8} \ m/s[/tex]
So
[tex]4.20 *10^{6} * 16*10^{-9}= \frac{n * 6.626 *10^{-34} * 3.0*10^{8} }{694.3 *10^{-9}}[/tex]
=> [tex]n = 2.347 *10^{17} \ photons[/tex]
Jane is sliding down a slide. What kind of motion is she demonstrating? A. translational motion B. rotational motion C. vibrational motion D. transverse motion
Answer:
Transational Motion
Explanation:
A bar of silicon is 4 cm long with a circular cross section. If the resistance of the bar is 280 Ω at room temperature, what is the cross-sectional radius of the bar?
Answer:
r = 17.05 cm
Explanation:
Given that,
Length of silicon bar is 4 cm or 0.04 m
Resistance of the bar is 280 ohms
We know that the resistivity of the silicon is 640 Ωm
We need to find the cross-sectional radius of the bar. Let it is r.
Using definition of resistance of an object. It is given by :
[tex]R=\rho\dfrac{l}{A}[/tex]
A is area of bar, A = πr²
So,
[tex]R=\rho\dfrac{l}{\pi r^2}\\\\r^2=\dfrac{\rho l}{R\pi}\\\\r^2=\dfrac{640\times 0.04}{280\pi}\\\\r=0.1705\ m\\\\r=17.05\ cm[/tex]
So, the cross-sectional radius of the bar is 17.05 cm.
Please help!
Much appreciated!
Answer:
Ts = 3.0×10¯² sec
Explanation:
From the question given:
Ts = 2π √(4.5×10¯² Kg / 2.0×10³ Kg/s²)
The above expression can be evaluated as follow:
Pi (π) = 3.14
Ts = 2π √(4.5×10¯² / 2.0×10³)
Ts = 2 × 3.14 √(4.5×10¯² / 2.0×10³)
Ts = 6.28 × √(2.25×10¯⁵)
Ts = 6.28 × 4.74×10¯³
Ts = 3.0×10¯² sec
Three identical very dense masses of 3500 kg each are placed on the x axis. One mass is at x1 = -100 cm , one is at the origin, and one is at x2 = 320 cm . Part A What is the magnitude of the net gravitational force Fgrav on the mass at the origin due to the other two masses? Take the gravitational constant to be G = 6.67×10−11 N⋅m2/kg2 . Express your answer in newtons to three significant figures. Part B What is the direction of the net gravitational force on the mass at the origin due to the other two masses? +x direction or -x direction.
Answer:
A) 7.37 x 10^-4 N
B) The resultant force will be towards the -x axis
Explanation:
The three masses have mass = 3500 kg
For the force of attraction between the mass at the origin and the mass -100 cm away:
distance r = 100 cm = 1 m
gravitational constant G= 6.67×10^−11 N⋅m^2/kg^2
Gravitational force of attraction [tex]F_{g}[/tex] = [tex]\frac{Gm^{2} }{r^{2} }[/tex]
where G is the gravitational constant
m is the mass of each of the masses
r is the distance apart = 1 m
substituting, we have
[tex]F_{g}[/tex] = [tex]\frac{6.67*10^{-11}*3500^{2} }{1^{2} }[/tex] = 8.17 x 10^-4 N
For the force of attraction between the mass at the origin and the mass 320 cm away
distance r = 320 cm = 3.2 m
[tex]F_{g}[/tex] = [tex]\frac{Gm^{2} }{r^{2} }[/tex]
substituting, we have
[tex]F_{g}[/tex] = [tex]\frac{6.67*10^{-11}*3500^{2} }{3.2^{2} }[/tex] = 7.98 x 10^-5 N
Resultant force = (8.17 x 10^-4 N) - (7.98 x 10^-5 N) = 7.37 x 10^-4 N
B) The resultant force will be towards the -x axis
what is the percent uncertainty in the volume of a spherical beach ball whose radius is r = .84 plus or minus .04 m?
Answer:
The percent uncertainty in the volume [tex]\frac{\delta V}{V} * 100 = 14.286\%[/tex]
Explanation:
From the question we are told that
The radius is [tex]r = 0.84 \pm 0.04 \ m[/tex]
From the given value
The uncertainty of radius is [tex]\delta r = 0.04[/tex]
Generally the volume of a spherical beach ball is mathematically represented as
[tex]V = \frac{4\pi }{3}* r^3[/tex]
Now taking the log of both sides
[tex]log V = log [\frac{4\pi}{3} ] * r^3[/tex]
=> [tex]log V = log [\frac{4\pi}{3} ] + log( r^3)[/tex]
=> [tex]log V = log [\frac{4\pi}{3} ] + 3log( r)[/tex]
Differentiating both sides
[tex]\frac{1}{V} \delta V = 0 + 3 [\frac{1}{r} ] \ \delta r[/tex]
Now converting them to percentage by multiplying by 100
[tex]\frac{\delta V}{V} * 100 = [\frac{ 3 \delta r }{r} ] \ * 100[/tex]
=> [tex]\frac{\delta V}{V} * 100 = [\frac{ 3 * 0.04 }{ 0.84} ] \ * 100[/tex]
=> [tex]\frac{\delta V}{V} * 100 = 14.286\%[/tex]
You slide a coin across the floor, and observe that it slows down and eventually stops. A sensitive thermometer shows that its temperature increased. What can we conclude
Answer:
The mechanical energy of the coin has been used up in doing work against friction.
Explanation:
When two bodies in contact move against one another, friction comes to play. Friction converts energy in such a system to heat which raises the temperature of the body, with most lost to the ambient environment. Sliding the coins on the floor transfers energy from your hand into the mechanical energy of the coin as it moves across the floor. Fiction between the coin and the surface of the floor gradually slows the coin down by converting its energy to heat (which raises the temperature of the coin as detected by the thermometer) until the coin comes to a halt.
Two identical balls are thrown directly upward, ball A at speed v and ball B at speed 2v, and they feel no air resistance. Which statement about these balls is correct
Answer:
B) Ball B will go four times as high as ball A because it had four times the initial kinetic energy.
Explanation:
The complete question is
Two identical balls are thrown directly upward, ball A at speed v and boll B at speed 2v. and they feel no air resistance. Which statement about these balls is correct? A) Ball B will go twice as high as ball A because it had twice the initial speed. B) Ball B will go four times as high as ball A because it had four times the initial kinetic energy. C) The balls will reach the same height because they have the same mass and the same acceleration. D) At its highest point, ball B will have twice as much gravitational potential energy as ball A because it started out moving twice as fast. E) At their highest point, the acceleration of each ball is instantaneously equal to zero because they stop for an instant.
According to conservation of energy, the mechanical energy of a ball thrown up is equal to the sum of the potential energy and the kinetic energy. At its highest point, all the mechanical energy will be equal to the potential energy. At the instant when it was thrown, all the mechanical energy is proportional to its kinetic energy, which will be proportional to the potential energy at the highest point. Also, potential energy is proportional to the maximum height reached.
We know that the kinetic energy is given as [tex]\frac{1}{2}mv^{2}[/tex]
where
m is the mass of the balls, which is the same for both ball,
and v is the velocity.
We can see that the kinetic energy is proportional to the square of the initial velocity with which the ball is thrown.
For the ball A thrown with velocity v, the kinetic energy is proportional to [tex]v^{2}[/tex],
and for the ball B with velocity 2v, kinetic energy is proportional to [tex]4v^{2}[/tex]
comparing the two, we'll see that the ball B will had 4 times the energy of ball A. Therefore ball B will go four times as high as ball A because it had four times the initial kinetic energy
A woman rides a carnival Ferris wheel at radius 16 m, completing 4.5 turns about its horizontal axis every minute. What are (a) the period of the motion, and the magnitude of her centripetal acceleration at (b) the highest point and (c) the lowest point
Answer:
a)13.33s
b)at highest point, the centripetal acceleration has its direction at downward path towards the center of the circular path, and the radius vector has its direction upward. Then acceleration=3.555m/s^2
c)c)at lowest point the centripetal acceleration has its direction upward towards the center of the circular path, and the radius vector has its direction downward Then acceleration=3.555m/s^2
Explanation
a)number of turns= 4.5
radius= 16m
We know that the period is the time taken by the wheel to complete one turn which can be calculated using below expresion
T= t/n
Where T= period of motion
t= Time taken by the wheel to finish n turns where our n= 4.5
T= (1×60)/4.5= 13.33s
Hence the period is 13.33s
Then the speed of the woman v= 2πr/T
v= (2×π×16)/13.33
v=7.5417m/s
b)at highest point, the centripetal acceleration has its direction at downward path towards the center of the circular path, and the radius vector has its direction upward.
a= v^2/r
Where r= radius
v= speed of the woman= 7.5417m/s
a=(7.5417m/s)^2/16
a=3.555m/s^2
The centripetal acceleration and radius vector are in opposite direction
c)at lowest point the centripetal acceleration has its direction upward towards the center of the circular path, and the radius vector has its direction downward
The magnitude of the acceleration is calculated below
a= v^2/r
Where r= radius
v= speed of the woman= 7.5417m/s
a=(7.5417m/s)^2/16
a=3.555m/s^2
Your bedroom has a rectangular shape and you want to measure its size. You use a tape that is precise to 0.001 m and find that the shortest wall in the room is 3.547 m long. The tape, however, is too short to measure the length of the second wall, so you use a second tape, which is longer but only precise to 0.01 m. You measure the second wall to be 4.79 m long. Which of the following numbers is the most precise estimate that you can obtain from your measurements for the area of your bedroom?
a) 30 m^2.
b) 31.4 m^2.
c) 31.37 m^2.
d) 31.371 m^2.
Your bedroom has a rectangular shape, and you want to measure its area. You use a tape that is precise to 0.001 and find that the shortest wall in the room is 3.547 long. The tape, however, is too short to measure the length of the second wall, so you use a second tape, which is longer but only precise to 0.01 . You measure the second wall to be 4.79 long. Which of the following numbers is the most precise estimate that you can obtain from your measurements for the area of your bedroom?
b)If your bedroom has a circular shape, and its diameter measured 6.32 , which of the following numbers would be the most precise value for its area?
a)30 m^2
b) 31.4 m^2
c)31.37 m^2
d)31.371 m^2
Answer:
Part A
[tex]A = 16.99 \ m^2[/tex]
Part B
[tex]A_r =31.37 \ m^2[/tex]
Explanation:
From the question we are told that
The shortest wall is [tex]x = 3.547 \ m[/tex]
The length of the second wall is [tex]y = 4.79 \ m[/tex]
Generally the area is mathematically evaluated as
[tex]A = x * y[/tex]
=> [tex]A = 3.547 * 4.79[/tex]
=> [tex]A = 16.99 \ m^2[/tex]
Given that the diameter is d = 6.32
Then the area is
[tex]A_r = \pi \frac{d^2}{4}[/tex]
[tex]A_r =3.142 * \frac{6.32^2}{4}[/tex]
[tex]A_r =31.37 \ m^2[/tex]
An air-filled capacitor consists of two parallel plates, each with an area of 8 cm^2 , separated by a distance 2.9 mm. A 22 V potential difference is applied to these plates.
What is the magnitude of the surface charge density on each plate?
Answer:
The magnitude of the surface charge density on each plate is 6.714 x 10⁻⁸ C/m²
Explanation:
Given;
area of the parallel plates, A = 8 cm² = 8 x 10⁻⁴ m²
distance between the plates, d = 2.9 mm = 0.0029 m
potential difference applied to the plates, V = 22 V
The electric field between the plates is given by;
[tex]E = \frac{V}{d} \\\\E = \frac{22}{2.9*10^{-3}}\\\\E = 7586.207 \ V/m[/tex]
The surface charge density is given by;
σ = ε₀E
σ = (8.85 x 10⁻¹²)(7586.207)
σ = 6.714 x 10⁻⁸ C/m²
Therefore, the magnitude of the surface charge density on each plate is 6.714 x 10⁻⁸ C/m²
A tank 20 m deep and 7m wide is layered with 8m of oil,6m of water and 5m of mercury.complete total hydroatatic force.(density of oil and mercury is 800 and 13600kg/m respectively ).
Answer:
F = 3.03 10⁷ N
Explanation:
We will eat by calculating the pressure in the tank
P = ρ g h
the pressure totals the sum of the pressure of each liquid
P_total = P_oil + P_water + P_Hg
P_total = ρ_oil g h_oil + ρ_water g h_water + ρ_Hg g h_Hg
P_total = g (ρ_oil h_oil + ρ_water h_water + ρ_Hg h_Hg)
P_total = 9.8 (800 8 + 1000 6 + 13 600 5)
P_total = 7,879 10⁵ Pa
The definition of Pressure is
P = F / A
F = P A
The area of a tank is the area of a circle
A = π r² = π d² / 4
F = P π d² / 4
let's calculate
F = 7,879 10⁵ π 7²/4
F = 3.03 10⁷ N
In this calculation the atmospheric pressure was not taken into account because they ask the hydrostatic pressure
A very long straight current-carrying wire produces a magnetic field of 20 mT at a distance d from the wire. To measure a field of 5 mT due to this wire, you would have to go to a distance from the wire of
A- 4d.
B - 16d.
C - d sqrt2
D- 8d.
E- 2d.
Answer:
A. 4d
Explanation:
Magnetic field strength is inversely proportional to distance. So in order to have a smaller magnetic field, we need to move further out from the wire. How far we go exactly can be determined from the formula: B=(μ₀I)/(2πr)
(That is derived from Ampere's Law, which states ∫B•dl=μ₀I)
With that you can set up a ratio between the magnetic fields in both cases. Because the current is the same for both instances, everything reduces out on one side of the equation and leaves you with something that relates the two distances by a ratio of each magnetic field value.
My work is in the attachment, comment for questions.
A cruise started its trip 8:00. Its average speed was 100 km/h.
When it travelled 2/5 of its journey by 12:00, the boat changed
its speed. If the boat was required to arrive at the destination at
17:00, what average speed must the boat travel at for the
remaining journey?
Answer:
120 k/m
Explanation:
Answer: 120
Explanation:
A person speed walking down a street covers 20m in 5s. What is the
speed of the individual? *
Answer:
4 m/s.
Explanation:
The following data were obtained from the question:
Distance travalled (d) = 20 m
Time (t) = 5 secs
Speed (S) =?
Speed is defined as the rate of change of distance moved with time. Mathematically, it is expressed as:
Speed (S) = Distance (d) /time (t)
S = d/t
With the above formula, we can easily calculate the speed of the individual as follow:
Distance travalled (d) = 20 m
Time (t) = 5 secs
Speed (S) =?
S = d/t
S = 20/5
S = 4 m/s
Therefore, the speed of the individual is 4 m/s
An 8-hour exposure to a sound intensity level of 90.0 dB may cause hearing damage. What energy in joules falls on a 0.800-cm-diameter eardrum so exposed?
Answer:
1.4E-3J
Explanation:
Given that
Time = 8hrs = 28.8E3 seconds
Intensity= 90dB
D= 0.008m
Radius= 0.004m
So intensity is sound level Bis
10dBlog(I/Io)
I= 10 (B/10dB)Io
= 10( 90/10) x 10^-12
=0.001W/m²
But we know that
I = P/A
P= I πr²
= 5.02 x10^-8W
But energy is power x time
So E= 5.02E-8 x 28.8E3
= 1.4E-3J
Answer:
1.44x10⁻³J
Explanation:
Given :
Time = 8hrs *(3600secs/1hr)= 28.8*10³seconds
Intensity= 90dB
D= 0.008m
Radius=0.008m/2
=0.004m
the sound level in decibel can be expressed below as
I=10dBlog[I/I₀]
where I₀=10⁻¹²/m² which is the refrence intensity
90=10log[I/10⁻¹²]
I=0.001W/m²
we know that intensity of the wave which id the average rate per unit area which energy is transfered can be calculated using below formular
I = P/A
where P= powerr which is renergy transfer at a time
A= area= πr²
making P subject of formular we have
P= I πr²
= 5.02 x10⁻⁸W
Energy =power x time
E=28800*5*10⁻⁸
=0.001443J
therefore,the energy in joules is 1.44x10⁻³J
An inductor has inductance of 0.260 H and carries a current that is decreasing at a uniform rate of 18.0 mA/s.
Required:
Find the self-induced emf in this inductor.
Answer:
The self-induced emf in this inductor is 4.68 mV.
Explanation:
The emf in the inductor is given by:
[tex] \epsilon = -L\frac{dI}{dt} [/tex]
Where:
dI/dt: is the decreasing current's rate change = -18.0 mA/s (the minus sign is because the current is decreasing)
L: is the inductance = 0.260 H
So, the emf is:
[tex] \epsilon = -L\frac{dI}{dt} = -0.260 H*(-18.0 \cdot 10^{-3} A/s) = 4.68 \cdot 10^{-3} V [/tex]
Therefore, the self-induced emf in this inductor is 4.68 mV.
I hope it helps you!
The self-induced emf in this inductor is 4.68 mv.
Calculation of the emf in the inductor:Here
E = -LdI/dt
here
dI/dt represents the the decreasing current's rate change = -18.0 mA/s
the minus sign is due to the current is decreasing
L represents the inductance = 0.260 H
Now the emf should be
= -0260H * (-18.0.10^-3)
= 4.68 mv
hence, The self-induced emf in this inductor is 4.68 mv.
Learn more about current here: https://brainly.com/question/17080022
Given 1ft = 12in, how many feet are in 36 inches?
Answer:
Hey there!
1 ft= 12 inches
3 ft= 36 inches.
Let me know if this helps :)
Answer: 3
The formula is to divide by 12
36÷12=3
1ft = 12in
What Is experimental
design?
Can someone solve the blank questions? I am really having trouble solving them. Thank you!
Answer:
<In the attachment>
Explanation:
There's not really much for me to say here I feel. On 7)b) you appear to let y=0 for some reason, so I redid that one without doing that just in case. Just look at what I did and take notes for the future.
To initiate a nuclear reaction, an experimental nuclear physicist wants to shoot a proton into a 5.50-fm-diameter 12C nucleus. The proton must impact the nucleus with a kinetic energy of 1.80 MeV. Assume the nucleus remains at rest.
Required:
a. With what speed must the proton be fired toward the target?
b. Through what potential difference must the proton be accelerated from rest to acquire this speed?
Answer:
Explanation:
kinetic energy required = 1.80 MeV
= 1.8 x 10⁶ x 1.6 x 10⁻¹⁹ J
= 2.88 x 10⁻¹³ J
If v be the velocity of proton
1/2 x mass of proton x v² = 2.88 x 10⁻¹³
= .5 x 1.67 x 10⁻²⁷ x v² = 2.88 x 10⁻¹³
v² = 3.45 x 10¹⁴
v = 1.86 x 10⁷ m /s
If V be the potential difference required
V x e = kinetic energy . where e is charge on proton .
V x 1.6 x 10⁻¹⁹ = 2.88 x 10⁻¹³
V = 1.8 x 10⁶ volt .
What is a property of “normal force”? a. It always points perpendicular to the contact surface. b. It always points parallel to the contact surface. c. It always points up. d. It always completely counters gravity.
Answer:
a. It always points perpendicular to the contact surface.
Explanation:
"Normal" means perpendicular. Normal forces are always perpendicular to the contact surface.
What magnetic field strength will allow the electrons to pass through without being deflected?
Answer:
Explanation:
If magnetic field exists parallel to the direction of motion of electron , no force will act on the electrons and hence there will be no deflection in them .
In such cases , the magnitude of magnetic field is immaterial . No matter how high or low magnitude of magnetic field be , if it is parallel to the velocity of electron , it will not be deflected as the force created on them will be zero.
Only in case magnetic field makes some angle with the direction of velocity , force will be created and electron will be deflected .
What is solar physics?