Answer: (b) Approximately 32 years .
Explanation:
Moves = 2n-1 .
It takes (224-1) are the minimum number of moves required to move 24 disks, which is 16777216.
Now each move takes 1 minute, therefore total time in (mintes) = 16777216 .
Now in one year we have 525600 minutes.
Therefore time in years = 16777216/525600 = 31.920121765601217656012176560122 = 32 years (approx)
A uniform disk, a thin hoop, and a uniform sphere, all with the same mass and same outer radius, are each free to rotate about a fixed axis through its center. Assume the hoop is connected to the rotational axis by light spokes. With the objects starting from rest, identical forces are simultaneously applied to the rims, as shown. Rank the objects according to their angular acceleration, least to greatest.1. disk, hoop, sphere2. disk, sphere, hoop3. hoop, sphere, disk4. hoop, disk, shpere5. sphere, disk, hoop6. sphere, hoop, disk
Answer:
4 hoop, disk, sphere
Explanation:
Because
We are given data that
Hoop, disk, sphere have Same mass and radius
So let
And Initial angular velocity, = 0
The Force on each be F
And Time = t
Also let
Radius of each = r
So let's find the inertia shall we!!
I1 = m r² /2
= 0.5 mr² the his is for dis
I2 = m r² for hoop
And
Moment of inertia of sphere wiil be
I3 = (2/5) mr²
= 0.4 mr²
So
ωf = ωi + α t
= 0 + ( τ / I ) t
= ( F r / I ) t
So we can see that
ωf is inversely proportional to moment of inertia.
And so we take the
Order of I ( least to greatest ) :
I3 (sphere) , I1 (disk) , I2 (hoop) , ,
Order of ωf: ( least to greatest)
That of omega xf is the reverse of inertial so
hoop, disk, sphere
Option - 4
The ranking of the objects according to their angular acceleration is option 4 hoop, disk, sphere.
Ranking of the objects:Since
Hoop, disk, sphere contain Same mass and radius
So here
Initial angular velocity, = 0
The Force on each be F
And Time = t
Radius of each = r
Now
I1 = m r² /2
= 0.5 mr² his is for dis
I2 = m r² for hoop
And
Moment of inertia of sphere should be
I3 = (2/5) mr²
= 0.4 mr²
Now
ωf = ωi + α t
= 0 + ( τ / I ) t
= ( F r / I ) t
here,
ωf is inversely proportional to moment of inertia.
Now
Order of I ( least to greatest ) :
I3 (sphere) , I1 (disk) , I2 (hoop) , ,
Order of ωf: ( least to greatest)
That of omega xf is the reverse of inertial so
Therefore, the fourth option is correct.
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A small uniform disk and a small uniform sphere are released simultaneously at the top of a high inclined plane, and they roll down without slipping. Which one will reach the bottom first?
Answer:
the sphere
Explanation:
From the given information,
A free flow body diagrammatic expression for the small uniform disk and a small uniform sphere which are released simultaneously at the top of a high inclined plane can be seen in the image attached below.
From the diagram;
The Normal force mgsinθ - Friction force F = mass m × acceleration a
Meanwhile; the frictional force
[tex]F = \dfrac{I \alpha }{R}[/tex]
where
[tex]\alpha = \dfrac{a}{R}[/tex] in a rolling motion
Then;
[tex]F = \dfrac{I a }{R^2}[/tex]
∴
The Normal force mgsinθ - F = m × a can be re-written as:
[tex]\mathtt{mg sin \ \theta- \dfrac{Ia}{R^2} = ma}[/tex]
making a the subject of the formula, we have:
[tex]a = (\dfrac{mg \ sin \theta}{m + \dfrac{I}{R^2}})[/tex]
Similarly;
I = mk² in which k is the radius of gyration
∴
replacing I = mk² into the above equation , we have:
[tex]a = (\dfrac{mg \ sin \theta}{m + \dfrac{mk^2}{R^2}})[/tex]
where;
the uniform disk [tex]\dfrac{k^2}{R^2 }= \dfrac{1}{2}[/tex]
the uniform sphere [tex]\dfrac{k^2}{R^2 }= \dfrac{2}{5}[/tex]
∴
[tex]a = \dfrac{2}{3} \ g sin \theta \ for \ the \ uniform \ disk[/tex]
[tex]a = \dfrac{5}{7} \ g sin \theta \ for \ the \ uniform \ sphere[/tex]
We can now see that the uniform sphere is greater than the disk as such the sphere will reach the bottom first.
The period of a simple pendulum is 8 s. If the same pendulum experiment is repeated on a plant of g = 1/4 gE, the new period is
Answer:
16 secs.
Explanation:
Data obtained from the question include the following:
Period on earth (T) = 8 secs
Next period (Tn) =?
Next, we shall determine the length of the string. This can be obtained as follow:
Period on earth (T) = 8 secs
Acceleration due to gravity on earth (gE) = 9.8 m/s²
Pi (π) = 3.14
Length of string (L) =?
T = 2π√(L/gE)
8 = 2 × 3.14 ×√(L/9.8)
8 = 6.28 × √(L/9.8)
Divide both side by 6.28
8/6.28 = √(L/9.8)
Take the square of both side
(8/6.28)² = L/9.8
Cross multiply
L = (8/6.28)² × 9.8
L = 15.9 m
Therefore the length of string is 15.9 m
Next, we shall determine the new period of the pendulum as follow:
Length (L) = constant = 15.9 m
Pi (π) = 3.14
Acceleration due to gravity on earth (gE) = 9.8 m/s²
Acceleration due to gravity on the planet (g) = 1/4 gE = 1/4 × 9.8 m/s²
= 2.45 m/s²
New period (Tn) =?
Tn = 2π√(L/g)
Tn = 2 × 3.14 × √(15.9/2.45)
Tn = 6.28 × √(15.9/2.45)
Tn = 16 secs.
Therefore, the new period of the pendulum is 16 secs.
If the diameter of the low-power field is 1.5 mm, an object that occupies approximately a third of that field has an estimated diameter of
Answer:
d' = 0.86 mm
Explanation:
First we need to find the area of low power field:
A = πd²/4
where,
A = Area = ?
d = diameter = 1.5 mm
Therefore, using the value of diameter, we get:
A = π(1.5 mm)²/4
A = 1.767 mm²
Now, the new object occupies 1/3rd of this area:
A' = (1/3)A
πd'²/4 = (1/3)A
d'² = (4/3π) A
d'² = (4/3π)(1.767 mm²)
d' = √(0.75 mm²)
d' = 0.86 mm
Marcus is teaching a lesson on energy transformations to his class. He cracks a glow stick to teach this practice and states that the energy in the glow stick is transformed. Assuming that the glowstick is a closed system and all of the energy gets transfomred, explain how the chemical energy of the glow stick compares to the light energy after he cracks it.
Answer:
this occurs because the energy of the constituents is greater than the energy of the material formed and this excess is what we can appreciate in the form of ligh
Explanation:
When the light stick breaks, it allows substances to mix, produced by a chemical reaction, which releases light into the environment.
The energy released is the energy energy of the excess when the transformation takes place, this occurs because the energy of the constituents is greater than the energy of the material formed and this excess is what we can appreciate in the form of light,
A hollow sphere has a mass of 15 kg, an inner radius of 12 cm and an outer radius of 18 cm. What is the rotational inertia (moment of inertia) of the sphere about an axis passing through its center
Answer:
0.2396
Explanation:
Given that
Mass of the hollow sphere, m = 15 kg
Inner radius, r = 12 cm = 0.12 m
Outer radius, R = 18 cm = 0.18 m
Volume of a sphere is expressed as
V = 4/3.π.R³
Density ρ = mass / volume, therefore
Mass = ρ * v
Mass of the hollow sphere is given as
Mass of the outer sphere - mass of the inner sphere
M = ρV(o) - ρV(i)
V(o) = 4/3 * 3.142 * 0.18³
V(o) = 0.0244
V(i) = 4/3 * 3.142 * 0.12³
V(i) = 0.00724
15 = ρ (0.0244 - 0.00724)
15 = ρ (0.01716)
ρ = 15 / 0.01716
ρ = 874 kg/m³
moment of inertia about its centroidal axis is
I = 2/5 ρVR²
I(h) = I(o) - I(i)
I(h) = (2/5 * 874 * 0.0244 * 0.18²) - (2/5 * 874 * 0.00724 * 0.12²)
I(h) = 0.276 - 0.0364
I(h) = 0.2396
A 0.250-kg rubber ball is dropped from a height of 2.00 m. It hits the floor and rebounds to a height of 1.80 m. What is the magnitude of impulse the floor applies to the ball
Answer:
The magnitude of impulse the floor applies to the ball is 3.05 kg.m/s.
Explanation:
Given;
mass of the rubber ball, m = 0.25 kg
height of drop, h₁ = 2 m
height of rebounds, h₂ = 1.8 m
Determine the initial velocity of the ball as it moves downwards;
[tex]v_i = \sqrt{2gh}\\\\ v_i = \sqrt{2*9.8*2}\\\\v_i = 6.26 \ m/s[/tex]this initial velocity is acting downwards = - 6.26 m/s
Determine the final velocity of the ball as it rebounds
[tex]v_f = \sqrt{2gh} \\\\v_f = \sqrt{2*9.8*1.8}\\\\ v_f = 5.94 \ m/s[/tex]this final velocity is acting upwards = 5.94 m/s
Impulse is given by;
J = mΔv
[tex]J = m(v_f-v_i)[/tex]
J = 0.25(5.94 - (6.26))
J = 0.25(5.94 + 6.26)
J = 3.05 kgm/s
Therefore, the magnitude of impulse the floor applies to the ball is 3.05 kg.m/s.
You travel east for 20 miles and then west for 10 miles. What is your average speed and velocity if the entire
trip takes 1 hour. Answer in mile/hour.
Answer:
30 miles/hour, and 2.24 miles/hourExplanation:
What is average speed?
It is the total distance traveled divided by the time taken to cover the total distance traveled
Given that the various distances are
20 miles and 10 miles
the total distance traveled is 20+10= 30 miles
the average speed is expressed as
average speed= total distance/time taken
average speed= 30/1
average speed= 30 miles/hour
The average velocity is a vector quantity
the velocity is the average displacement divided by time taken
[tex]displacement= \sqrt{1^2+2^2} \\\\displacement= \sqrt{1+4} \\\\displacement=2.24 miles[/tex]
average velocity= displacement / time
average velocity= 2.24 /1
average velocity= 2.24 miles/hour
Below is a car. The car's engine is providing a driving force of 10N. The parachute is creating air resistance of 7N. What is going to happen to the car? Explain.
Answer:
The car is going to slow down to 3N.
Explanation:You have a force going 10N to the left and if you put an opposing force of 7N you get 3N of total force.
The variables n1 and n2 in Snell’s Law of Refraction depend upon
Answer:
It depends on the materials of the medium in involved
You ride your bike at 12.1 m/s directly away from your neighbor's trumpet sound and toward the sound of another neighbor's trombone and find that you hear both instruments at exactly the same pitch. The trumpeter is practicing her middle C at a frequency of 262 Hz . What frequency is the trombonist producing? The speed of sound in air is 337 m/s .
Answer:
243.83 Hz
Explanation:
Given the following :
Recall :
When source is stationary and observe is in motion:
Moving away from the source :
Observed frequency f₀ = f(v-v₀/v)
Moving towards the source :
f₀ = f(v+v₀/v)
Hence ;
v₀ = 12.1 m/s ; f of trumpeter = 262 Hz ; speed of sound (v) = 337m/s
f(v+v₀/v) = 262(v-v₀/v)
f = 262(v-v₀/v) / (v+v₀/v)
f = 262(v-v₀/v) * (v / v+v₀)
f = 262 (v-v₀ / v+v₀)
f = 262 ((337 - 12.1) / (337 + 12.1))
f = 262 (324.9 / 349.1)
f = 262 (0.93067888857)
f = 243.83
f = 244Hz
What are different ways to describe speed and velocity
A sprinter can accelerate with constant acceleration for 4.00 s before reaching top speed. He can run the 100 m dash in 10 s. What is his speed as he crosses the finish line?
Answer:
12.5 m/s
Explanation:
If the avg speed is 10 m/s we assume that the speed is constant and not fluctuating
If VT (Velocity*Time) is equal to speed at the end of the 4 seconds of accel. it is the top speed at the finish line
since the speed is 0 at the beginning of races, we will use V0= 0 m/s
So the avg velocity for those 4 seconds is (VT+V0) /2 = or 1/2 VT (for 40% of the race)
The avg velocity for the last 6 seconds is, of course, VT (for 60% of the race
hence
(1/2VT)(.4) + VT(.6) = 10 m/s
VT = 10/.8 = 12.5 m/s
On planet Q the standard unit of volume is called guppi. Space travelers from Earth have determined that one liter = 38.2 guppies. How many guppies are in 150 liters?
Answer:
5730 guppies
Explanation:
1 liter= 38.2 guppies
150 liters= 150×38.2
On planet Q the standard unit of volume is called guppi. Space travelers from Earth have determined that one liter = 38.2 guppies. Guppies in 150 liters is 5730 guppies.
What are units of volume?Volume, which is measured in cubic units, is the 3-dimensional space occupied by matter or encircled by a surface. The cubic meter (m³), a derived unit, is the SI unit of volume. A addition new nickname for the cubic (dm³) is a liter (L).
Given that in the question on planet Q the standard unit of volume is called guppi, the conversion of different volume unit,
1 liter = 38.2 guppies, so
150 litre = 5730 guppies
Guppies in the given 150 liters of volume is 5730 guppies.
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What is the rotational inertia (moment of inertia) of a 12-kg uniform rod, 0.30 m long, rotating about an axis perpendicular to the rod and passing through the center of the rod
Answer:
[tex]I=0.54\ kg-m^2[/tex]
Explanation:
Given that,
Mass of a uniform rod, m = 12 kg
Length of the rod, l = 0.3 m
The moment of inertia rotating about an axis perpendicular to the rod and passing through the center of the rod is given by :
[tex]I=\dfrac{ml^2}{2}\\\\I=\dfrac{12\times (0.3)^2}{2}\\\\I=0.54\ kg-m^2[/tex]
So, the moment of inertia of the rod is [tex]0.54\ kg-m^2[/tex]
At what distance will a 80 W lightbulb have the same apparent brightness as a 120 W bulb viewed from a distance of 40 m
Answer:
32.6mm
Explanation:
Using area of a sphere(bulb) = 4πr²
So A is proportional to radius²
So the Energy will be proportional to r²
But 120/80 = 1.5 is the energy factor so
Using
1.5/d² = 1/r²
1.5/40²= 1/r^2
r = √( 40²/ 1.5)
r = 32.6m
Discuss the characteristics of the waves in the visible portion of the electromagnetic spectrum
Explanation:
The electromagnetic spectrum consists of series of waves that are arranged from longest wavelength to shortest.
In the electromagnetic spectrum, between infrared and ultraviolet, visible light falls.The frequency of visible light is of the order of 10¹⁴ Hz.Its wavelength is about 740 nm.Visible light spectrum is visible to humans. It consists of colors like violet, blue, green, yellow etc.A passenger train travels 295 miles in the same amount of time it takes a freight train to travel 225 miles. The rate of the passenger train is 14 mph greater than the rate of the freight train. Find the rate of each train.
Answer:
9.3
Explanatin:
Answer:
4.5
Explanation:
100 hectometer =_______ nanometers
Answer:
Hey!
Your answer is 10^12 nanometers!
Explanation:
AKA
1,000,000,000,000 nm
HOPE THIS HELPS!!
A class contains 9 boys and 11 girls. In how
many
ways
can a committee of two boys
and two
girls be formed
in the class?
Monochromatic light with wavelength 588 nm is incident on a slit with width 0.0351 mm. The distance from the slit to a screen is 2.7 m. Consider a point on the screen 1.3 cm from the central maximum. Calculate (a) θ for that point, (b) α, and (c) the ratio of the intensity at that point to the intensity at the central maximum.
Answer:
Explanation:
A. Using
Sinစ= y/ L = 0.013/2.7= 0.00481
စ=0.28°
B.here we use
Alpha= πsinစa/lambda
= π x (0.0351)sin(0.28)/588E-9m
= 9.1*10^-2rad
C.we use
I(စ)/Im= (sin alpha/alpha) ²
So
{= (sin0.091/0.091)²
= 3*10^-4
Unless indicated otherwise, assume the speed of sound in air to be v = 344 m/s.A violinist is tuning her instrument to concert A (440 Hz). She plays the note while listening to an electronically generated tone of exactly that frequency and hears a beat of frequency 6.00 Hz, which increases to 7.00 Hz when she tightens her violin string slightly.
(a) What was the frequency of the note played by her violin when she heard the 3-Hz beats?
(b) To get her violin perfectly tuned to concert A, should she tighten or loosen her string from what it was when she heard the 3-Hz beats?
Answer:
A) 443 Hz
B) She has to loosen the string
Explanation:
A) Given;
Beat frequency;f_beat = 3 Hz
Frequency of electronically generated tone; f_e = 440 Hz
We know that formula for beat frequency is given by;
f_beat = |f1 - f2|
Now, applying it to this question, we have;
f_beat = f_v - f_e
Where f_v is frequency of the note played by the violinist
Thus, plugging in the relevant values;
3 = f_v - 440
f_v = 3 + 440
f_v = 443 Hz
B) In the concept of wave travelling in a string, the frequency is directly proportional to the square root of the force acting on the string.
Now, for the violinist to get her violin perfectly tuned to concert A from what it was when she heard the 3-Hz beats, the beat frequency will have to be zero. Which means it has to decrease by 3 Hz. For it to decrease, it means that the force applied has to decrease as we have seen that frequency is directly proportional to the square root of the force acting on the string.
Thus, she would have to loosen the string.
Is the sinusoidal pattern on a string longer or shorter when there is a greater propagation velocity?
Answer:
We know that
Velocity= wavelength x frequency
And f= 1/2π√T/u
So we also know that
The frequency of nth harmonic standing wave is
fn=nv/2L
So from the relationships above
We can see that as propagational velocity increases, the frequency increases and the wavelength decreases. So finally we can say that sinusoidal pattern on a string is shorter when there is a greater propagation velocity
An object is at rest on a table. The gravitational force is 10 N down, and the normal force is 10 N up. What is the net force?
Fnormal
Fgravity
10 N up
OON
10 N down
20 N up
Answer:
0N
Explanation:
When trying to figure out opposing forces, you have to add them together,
10 + -10 = 0,
so your answer is 0N
Answer:the answer is 0 N
To calculate an answer to the correct number of significant figures, you must complete all calculations first and then round your final answer as the very last step. In Part C, you are asked to calculate the volume of a rectangular prism that has a length of 5.6 cm, a width of 2.1 cm, and a height of 6.6 cm. You can calculate the volume of a prism by multiplying the area of the base times the height. You already calculated the area of the base as 2.1cm×5.6cm in Part A. Part B What value should you use as the area of the base when calculating the answer to Part C? What value should you use as the area of the base when calculating the answer to Part C?
Answer:
B) We should use the complete value of 11.76 cm², because the rounding off is done at the end of all calculations. Until then exact and complete values should be used.
C) Volume of Prism = 78 cm³
Explanation:
PART C:
Since, the volume of prism s given by the following formula:
Volume of Prism = (Area of Base of Prism)(Height of Prism)
Therefore,
Height of Prism = 6.6 cm
Area of Base of Prism = Length x Width
Area of Base of Prism = 5.6 cm x 2.1 cm
Area of Base of Prism = 11.76 cm²
Hence, the equation gives:
Volume of Prism = (11.76 cm²)(6.6 cm)
Volume of Prism = 77.616 cm³
Since, the initial values had 2 significant figures, so rounding off to two significant figures:
Volume of Prism = 78 cm²
PART B:
We should use the complete value of 11.76 cm², because the rounding off is done at the end of all calculations. Until then exact and complete values should be used.
dolphin swims due east for 1.90 km, then swims 7.20 km in the direction south of west. What are the magnitude and direction of the vector that will take the dolphin back to its starting point? (Enter the magnitude in km and the direction in degrees north of east.) Hint
Answer:
Explanation:
We shall represent all the displacement in terms of vector . We shall consider east as i , and north as j . south of west direction will be represented by - i - j .
displacement of 1.9 km due east
D₁ = 1.9 i
vector representing south of west = - i - j
unit vector = - i - j / √ 2
7.2 km south of west = 7.2 ( - i - j ) / √ 2
D₂ = - 5.09 ( i + j )
Total displacement
= D₁ + D₂
= 1.9 i - 5.09 ( I + J )
D = - 3.19 i - 5.09 j .
magnitude of D = √ ( 3.19² + 5.09² )
= 6 km .
Direction of D
Tanθ = 5.09 / 3.19 = 1.59
θ = 58°
So direction will be 58° south of west .
To reach the starting point , he shall have to go in opposite direction .
So he shall have to go in the direction of north of east at angle 58° by a displacement of 6 km .
Interstellar space is filled with radiation of frequency 160.23 GHz.
This radiation is considered to be a remnant of the "big bang." What is the corresponding blackbody temperature of this radiation?
Answer:
1.548K
Explanation:
Given that f= 160.23GHz
c= 3E8m/s
b= 2.898*10^-3mk
So using
(Lambda)m x T= b
So T = b/ lambda
But wavelength ( lambda) = c/f
So T = bf/c
= 2.898E-3x 160.23E9/3E8
=1.548K
The feature that characterizes simple columnar epithelium of the digestive tract is the presence of dense microvilli.
Simple columnar epithelium is a type of tissue that lines the digestive tract, including the stomach and intestines. It is composed of a single layer of column-shaped cells that are tightly packed together. One distinguishing feature of this epithelium is the presence of dense microvilli on the apical surface of the cells. Microvilli are tiny finger-like projections that increase the surface area of the cells, facilitating absorption and secretion processes. These dense microvilli help in the absorption of nutrients and the secretion of digestive enzymes, allowing for efficient digestion and absorption of nutrients in the digestive tract. The microvilli significantly increase the surface area available for these functions, enabling more efficient nutrient absorption. Therefore, the correct answer is (d) dense microvilli.
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A star has a declination of approximately 45°. Which of these statements is correct about the star?
A) It is 45° above the celestial equator.
B) It is 45° below the celestial equator.
C) It is 45° to the left of the celestial equator.
D) It is 45° to the right of the celestial equator.
The star is approximately 45° above the celestial equator. (A)
"Declination" on the celestial coordinate system is equivalent to latitude on the terrestrial one.
Suppose that an object in free fall were somehow equipped with a speedometer. By how much would its speed readings increase with each second of fall? Express your answer to two significant figures and include the appropriate units.
A car accelerates from 14.0m/s to 21m/s in 6.0s. What was its acceleration?
How far did it travel in this time? Assume constant acceleration.
Answer:
Acceleration (a) = 1.167 m/s²
Distance travel = 105 m (Approx)
Explanation:
Given:
Initial speed (u) = 14 m/s
Final speed (v) = 21 m/s
Time taken (t) = 6 sec
Find:
Acceleration
Distance travel
Computation:
v = u + at
21 = 14 + a(6)
7 = 6a
Acceleration (a) = 1.167 m/s²
S = ut + (1/2)(a)(t²)
S = (14)(6) + (1/2)(1.167)(6²)
S = 84 + 21
S = 105 m (Approx)
Distance travel = 105 m (Approx)