Answers
The angular velocity of the wheel at the bottom of the incline is 4.429 rad/sec
The angular velocity (ω) of an object is the rate at which the object's angle position is changing in relation to time.
For a wheel attached to an incline angle, the angular velocity can be computed by considering the conservation of energy theorem.
As such the total kinetic energy (K.E) and rotational kinetic energy (R.K.E) at a point is equal to the total potential energy (P.E) at the other point.
i.e.
P.E = K.E + R.K.E
[tex]\mathbf{mgh = \dfrac{1}{2}m(r \times \omega)^2 + \dfrac{1}{2}\times I \times \omega^2}[/tex]
[tex]\mathbf{gh = \dfrac{1}{2}(r \times \omega)^2 + \dfrac{1}{2}\times r^2 \times \omega^2}[/tex]
[tex]\mathbf{2 \times \dfrac{gh}{r^2} =\omega^2 + \omega^2}[/tex]
[tex]\mathbf{2 \omega^2=2 \times \dfrac{9.81 \times 8 m }{2.0 ^2} }[/tex]
[tex]\mathbf{\omega^2=\dfrac{39.24 }{2}}[/tex]
[tex]\mathbf{\omega=\sqrt{19.62 } \ rad/sec}[/tex]
[tex]\mathbf{\omega=4.429 \ rad/sec}[/tex]
Therefore, we can conclude that the angular velocity of the wheel at the bottom of the incline is 4.429 rad/sec
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The angular velocity of the wheel depends on the mass, radius and the
mode of rotation of the wheel (with or without slipping).
The angle velocity at the bottom of the incline, ω ≈ 4.43 rad/secReasons:
The given parameters are;
Radius of the wheel, r = 2.0 m
Height of the incline, h = 8.0 m
Required:
Angular velocity of the wheel at the bottom of the incline.
Solution:
The potential energy of the wheel at the top of the hill, P.E. = m·g·h
[tex]Sum \ of \ the \ kinetic \ energy \ of \ the \ wheel, \ K.E. = \mathbf{\displaystyle \frac{1}{2} \cdot m \cdot v^2 + \frac{1}{2} \cdot I \cdot \omega ^2}[/tex]
Where;
v = The translational velocity of the wheel = ω·r
I = The moment of inertia of the wheel = m·r²
Therefore'
[tex]Sum \ of \ K.E. = \displaystyle \frac{1}{2} \cdot m \cdot (\omega \cdot r)^2 + \frac{1}{2} \cdot m \cdot r^2 \cdot \omega ^2 = \mathbf{m \cdot r^2 \cdot \omega^2}[/tex]
At the bottom of the hill, the potential energy is converted to kinetic energy
Therefore;
P.E. = Sum of K.E.
m·g·h = m·r²·ω²
g·h = r²·ω²
[tex]\displaystyle \omega = \sqrt{ \frac{g \cdot h}{r^2} } = \mathbf{ \frac{\sqrt{g \cdot h} }{r}}[/tex]
Where;
g = Acceleration due to gravity ≈ 9.81 m/s²
Therefore;
[tex]\displaystyle \omega = \frac{\sqrt{9.81 \times 8} }{2} \approx \mathbf{ 4.43}[/tex]
The angular velocity of the of the wheel at the bottom of the incline, ω ≈ 4.43 rad/secLearn more about the law of conservation of energy here:
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Related Questions
A particle starts from the origin at t = 0 with a velocity of 6.0 m/s and moves in the xy plane with a constant acceleration of (-2.0 + 4.0) m/s2. At the instant the particle achieves its maximum positive x coordinate, how far is it from the origin
Answers
Answer:
9sqrt4
Explanation:
Assuming you mean 6.0i m/s and (-2.0i + 4.0j) m/s^2:
The maximum positive x coordinate is when the time is 3 seconds, because the horizontal velocity will be zero, and therefore will be a turning point, where after that point the x coordinate will only be more negative.
After 3 seconds the x coordinate is 6*3+1/2*-2*3^2=9, and the y coordinate will be 1/2*4*3^2=18.
The distance from the origin is sqrt(9^2+18^2) = 9*sqrt(1+4)
At the instant the particle achieves its maximum positive x coordinate, the displacement is 4.03 m.
Displacement of the particle
The displacement of the particle is calculated as follows;
v² = u² + 2as
where;
a is accelerationa = √(2² + 4²) = 4.47 m/s²
0 = u² + 2as
s = -u²/2a
s = -(6²)/(2 x 4.47)
s = -4.03 m
Thus, at the instant the particle achieves its maximum positive x coordinate, the displacement is 4.03 m.
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What is force? And tell it's unit
Answers
Answer:
force is simply a push or a pull in a particular direction. The unit is N (newton)
Explanation:
hope this helped
Answer:
In physics force is an influence which changes the motion of an object which has mass
Its unit is N or kgms/2
Where is a divergent boundary most likely to be found?
Answers
Answer:
mid-ocean oceanic ridges
Explanation:
Answer:
mid-ocean oceanic ridges
Explanation:
Divergent boundaries are most likely to be found at mid-oceean oceanic ridges.
what forces would a person inside an elevator feel when it is going up?
Answers
So there are a few forces that act upon a person in an elevator. The first is Gravity. This is the downward force keeping us on the floor of the elevator. The second, is the upward force from where the cable takes the elevator upwards. The tension which is present means that for a short period of time, we are pushed into the floor more and our mass goes up.
Hope this helps :)
3 materials that are denser than water and 3 that arent denser than water
Answers
Answer:
denser than water:
1. clay
2. coins
3. rock
aren't denser than water
1. wood
2. sponge
3. apple
Need quite a bit of help
Answers
When the cart was at Table
Normal reaction (N)=mgNow acceleration due to gravity acting on the gravity.
When the air comes out of straw it tries to take the cart upwards.But the force is equal to that of acceleration due to gravity but in opposite direction.Hence.
[tex]\\ \sf\Rrightarrow F_{net}=0N[/tex]
So the cart doesn't moveThe 0.01 kg marble is dropped from rest at A through the smooth glass tube and accumulate in the basket at C as shown in Figure Q2(b). Determine: i) the velocity of the marble at B ii) the horizontal distance R of the basket from the end of the tube, and iii) the speed at which the marble falls into the basket.
Answers
Crazy Wally Ok Ok ok hhahahaha
Transverse waves move particles back and forth along the same direction in which the waves travel.
True false question.
True
False
Answers
Answer:
False, I am pretty sure.
Explanation:
Transverse waves are always characterized by particle motion being perpendicular to wave motion. ... As a sound wave moves from the lips of a speaker to the ear of a listener, particles of air vibrate back and forth in the same direction and the opposite direction of energy transport.
Why is visual constancy important?
A.
It gives people the ability to see things both close up and far away.
B.
It lets people of all ages see the edges of cliffs so they don’t fall over.
C.
It allows perceptions to remain the same even as images change.
D.
It offers the chance to use one retina at a time to interpret an image.
Reset
Answers
Answer:
C.
Explanation:
Visual constancy is a key mechanism that allows the perception to remain.the same even as images change
#CARRYONLEARNING
Visual constancy is important because it allows perceptions to remain the same even as images change.
What is Constancy phenomenon?Constancy phenomenon describes how people and animals tend to perceive familiar objects as having a constant shape, size, colour, or location regardless of adjustments to distance, illumination, or perspective. Instead of responding to the real stimulus, the impression has a tendency to adapt to the object as it is or is imagined to be.
The ability to recognise things in a variety of situations, which appear to be "taken into account" throughout a process of mental rebuilding of the known image, is a result of perceptual constancy. For instance, snow appears white in both the dim moonlight and the 800,000-fold brighter day. Reduced contextual cues that help with object identification and limited experience with the object both affect perceptual constancy.
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i need help with the problem below
Answers
Answer:
Explanation:
a) F = ma
a = F/m
a = 9(800) / 1 x 10⁹ = 7.2 x 10⁻⁶ m/s
b) t = v/a
t = 200 / 7.2 x 10⁻⁶
t = 2.8 x 10⁷ s about 10½ months
c) v² = u² + 2as
s = (v² - u²) / 2a
s = (200² - 0²) / (2( 7.2 x 10⁻⁶))
s = 2.8 x 10⁹ m nearly 7 times around the earth
And all this assumes NO FRICTION.
Consider the following force:
A horse is pulling forward on a wagon with a force of 200 N.
According to Newton's third law, what other force must be happening?
The horse is pushing backward on the wagon with a force of 200 N.
The ground is pushing backward on the horse with a force of 200 N.
The wagon is pulling backward on the horse with a force of 200 N.
Answers
Newton’s third law states that when two objects interact, they will exert an equal and opposite force on each other
So if the horse pulls the wagon, the wagon will also pull the horse
consider a throw ball to the air ,whre lagragian is given by ,L( m /2+Y^ '2 +Z^' 2 ]- msz, find the two concider momuntum when it is invariant under translation at x&x+E and y&yE(both x and y are cyclic cordinate)
Answers
Explanation:
ANDSHESAIDSHESAIDSHESAID☹️ SHE'S FROMHAWAIIYOUKNOWHOWTOSPEAKCUTEIN JAPANESE KAWAII
Who actually asked Abraham to sacrifice his son?
Answers
I think god did ??? I searched it up okay
God asked him to scarface his sons life
C. Answer the following questions.
1. Define Earthquake. Write any 3 precautions during earthquake
Answers
Answer:
1. An earthquake is a sudden violent shaking of the ground, typically causing great destruction, as a result of movements within the earth's crust or volcanic action. 2. (3 precautions during an earthquake are)... If you are indoors take cover under a desk, Stay away for glass doors, windows or outside doors and finally drop down or hold on to something until the shaking stops.
Hope that helped?
Explanation:
what are the applications of triangle law of forces
Answers
Answer:
The triangle law of forces can also be stated as. if a body is in equilibrium under the action of three forces acting at a point, then the three forces can be completely represented by the three sides of a triangle taken in order. A body might be subjected to further than one force at a similar time.
Explanation:
Hope it's help
stuck with this one.
Answers
Define the following units used for measuring distances in space.
a. Arcsecond
b. Astronomical unit
c. Parsec
d. Light year
Answers
Answer:
The astronomical unit is used primarily for measuring distances within the Solar System or around other stars.
what is the speed of a boy moving around a circular park of radius 6m if he goes around the park in 20s
Answers
Answer:
1.884 meters per second
Explanation:
s = d/t
d = C = 2πr = 2π(6) = 37.68 m
t = 20 s
s = (37.68 m)/(20 s)
s = 1.884 m/s
The speed of the boy is 1.88 m/s while he is moving around a circular park of radius 6m and taking time 20 seconds.
What is speed?Speed can be defined as a measurement of how quickly the distance an object traveled changes with time. Speed is a scalar quantity as it has magnitude but no direction as a unit of measurement.
An object that moves quickly and with high speed, traveling a lot of ground in a lesser time.
Given, the radius of the circular park, r = 6m,
The time taken to cover one round of the park, t = 20 s
The total distance traveled by the boy is equal to the circumference of the circular park, so
Circumference of park, C = d = 2πr = 2× 3.14 × 6 =37.68 m
The speed of the boy, S = d/t
S = 37.68 /20
S = 1.88 m/s
Therefore, the speed of the boy is equal to 1.88 m/s.
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A converging-diverging nozzle has a throat area of 10 cm2 and an exit area of 28.96 cm2 . A normal shock stands in the exit when the back pressure is sea-level standard. If the upstream tank temperature is 400 K, estimate (a) the tank pressure and (b) the mass fl ow
Answers
The tank pressure is 5.08 kPa and the mass flow rate is 2.6 kg/s.
The given parameters:
Throat area of the nozzle, [tex]A^*[/tex] = 10 cm² = 0.001 m²The exit area of the nozzle, A = 28.96 cm² = 0.002896 m²Air pressure at sea level = 101.325 kPaThe ratio of the areas of the converging-diverging nozzle is calculated as follows;
[tex]= \frac{A}{A^*} \\\\= \frac{0.002896}{0.001} \\\\= 2.896[/tex]
From supersonic isentropic table, at [tex]\frac{A}{A^*} = 2.896[/tex], we can determine the following;
[tex]M_e = 2.6 \ kg/s\\\\\frac{P_o}{P_e} = 19.954[/tex]
The tank pressure is calculated as follows;
[tex]\frac{P_o}{P_e} = 19.954 \\\\P_e = \frac{P_o}{19.954} \\\\P_e = \frac{101.325 \ kPa}{19.954} \\\\P_e = 5.08 \ kPa[/tex]
Thus, the tank pressure is 5.08 kPa and the mass flow rate is 2.6 kg/s.
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Someone please help with this question. From my knowledge the answer I believe to be correct is 4Em but I’m still not so sure. Please explain!
Answer choices:
1/2 Em
Em
2Em
4Em
Answers
Answer:
Explanation:
For an ideal spring over a frictionless horizontal surface, stored energy is only a function of the spring constant k and the distance of compression. The mass of the block doing the compressing is irrelevant
Energy stored in the first example is
Em = ½kd²
Energy stored in the second example is
E₂m = ½k(2d)² = 4(½kd²) = 4Em
So the second situation has four times as much stored spring potential energy as the first situation
4 Em is correct
Good job!
7. Which of the following explains how radiometric dating is used to estimate absolute
age.
a. By comparing how deep in the curst the radioactive material in a sample of rock
is, scientists can calculate the length of time since the rock formed.
b. By comparing the amount of organic material in a sample of rock, to the known
rate of decay of the parent rock, scientists can calculate the length of time since
the rock formed.
C. By comparing the amount of radioactive material in a sample of rock, to the
surrounding rocks, scientists can calculate the length of time since the rock
formed.
d. By comparing the amount of a radioactive material in a sample of rock, to the
know rate of decay of the parent rock, scientists can calculate the length of time
since the rock formed.
Answers
Answer:
d.
Explanation:
Radiometric dating is a method of dating geological/ archaeological specimens by determining the relative proportions of particular radioactive isotopes present in a sample. Carbon dating is a form of radiometric dating, but, in choice b, you're not comparing the carbon to the rock. One would compare ¹⁴C levels within the organic compound, just as one would compare radioactive isotope levels in a rock.
Question: Self-test 3.12 Calculate the change in G for ice at -10°C, with density 917 kg mº, when the pressure is increased from 1.0 bar to 2.0 bar.
Answers
The change in the Gibb's free energy per mole (G) is 1.96 J.
The given parameters:
Density of the ice, ρ = 917 kg/m³Initial pressure, P₁ = 1.0 barFinal pressure, P₂ = 2.0 barTemperature, T = - 10 CMass of water = 18 gThe change in the Gibb's free energy per mole (G) is calculated as follows;
[tex]\Delta G = V(P_2-P_1) \\\\[/tex]
where;
V is the volume of the ice
[tex]Density = \frac{Mass}{Volume} \\\\Volume = \frac{Mass}{Density} \\\\Volume = \frac{18 \times 10^{-3} \ kg}{917 \ m^3} \\\\Volume = 1.96 \times 10^{-5} \ m^3\\\\Volume = 1.96 \times 10^{-5} \ m^3 \times \frac{1000 \ L}{m^3} \\\\Volume = 0.0196 \ L[/tex]
Change in pressure;
[tex]P_2 - P_1 = 2.0 \ bar \ - \ 1.0 \ bar = 1.0 \ bar = 0.987 \ atm[/tex]
The change in the Gibb's free energy per mole (G);
[tex]\Delta G= V(P_2-P_1)\\\\\Delta G = 0.0196\ L \times 0.987\ atm \\\\\Delta G = 0.0193 \ L.atm\\\\1 \ L.atm = 101.325 \ J\\\\\Delta G = 0.0193 \ L.atm \times \frac{101.325 \ J}{1 \ L.atm} \\\\\Delta G = 1.96 \ J[/tex]
Thus, the change in the Gibb's free energy per mole (G) is 1.96 J.
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Two satellites are in orbit around a planet. Satellite 1 has a mass of mm and an orbital radius of 2r2r. Satellite has a mass of 2m2m and an orbital radius of rr. If the magnitude of the gravitational force the planet exerts on Satellite 1 is FF, the magnitude of the gravitational force the planet exerts on Satellite 2 is
a) F
b) 1/2F
c) 2F
d) 1/4F
Answers
The magnitude of the gravitational force the planet exerts on Satellite 2 is 1/2F.
We recall that from Newton's law of universal gravitation, the gravitational force is given by;
F =G m1m2/r^2
m1 and m2 are the respective masses
r is the distance of separation.
Let the mass of the planet be M and the mass of the satellite be m. The distance of separation is r.
For satellite 1;
F = GmM/(2r)^2
F = GmM/4r^2
For satellite 2;
F2= G2mM/r^2
Hence, the magnitude of the gravitational force the planet exerts on Satellite 2 is 1/2F.
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the book has a mass of 2.5 kg. What net force must act on the book to mak it accelerate to the left at a rate of 7.0m/s2?
Answers
Answer:
17.5 N
Explanation:
Given :Mass (m) = 2.5 kgAcceleration (a) = 7.0 m/s²To calculate :Force exerted (F)Calculation :• F = ma→ F = (2.5 × 7.0) N
→ F = 25/10 × 7 N
→ F = 5/2 × 7 N
→ F = (5 × 7)/2 N
→ F = 35/2 N
→ F = 17.5 N towards left
Hence, 17.5 N of net force must act on the book to make it accelerate to the left.
In what way does Isaac represent us?
Answers
Answer:
I believe The Knowledge that we apply everyday or based on these methods and discoveries may represent us
Explanation:
Why is it important that we learn about our solar system, the sun, and planets in our solar system other than Earth?
Answers
Answer:
To understand all the different kind of elements and how they work. Nature is a beautiful thing and it is important we understand how they survive and how we can help. The solar system is a mandatory nature. Learning about other planets also helps us feel safe and more knowledgable.
A garden hose shoots water horizontally from the top of a tall building toward the wall of a second building 20 meters away. If the speed with which the water leaves the hose is 5 m/sec, how long does it take the water to reach the second building, and what distance does the water fall in this time?
Answers
Answer:
Explanation:
If air resistance is ignored, the water travels for a time of
t = d/v = 20 m / 5 m/s = 4 s
falling from vertical rest, the water strikes the wall a distance below the hose
d = ½gt² = ½(10)4² = 80 m
Yeah, I think ignoring air resistance is wishful thinking considering the time and distances involved.
a rectangular block has the density of 350g/cm3 the dimensions are 3.5 6.cm 2.5
cm calculate the mass of the bock
Answers
Answer:
18375g
Explanation:
[tex]\boxed{density = \frac{mass}{volume} }[/tex]
[tex]∴ mass = density \times volume[/tex]
Let's find the volume of the rectangular block.
Volume
= length ×breadth ×height
= 3.5 ×6 ×2.5
= 52.5cm³
Mass of the block
= 350(52.5)
= 18375g
25.Figure 22.22 shows a plot
of potential versus position
along the x-axis. Make a plot
of the x-component of the
electric field for this situation.
Answers
The relationship between the potential and the electric field allows to find the results for the value of the electric field as a function of the distance is:
In the attachment we see the graph of the electric field as a function of distance.
Electric potential is defined by the change in potential energy of a test charge between two points, between the value of the test charge.
dV = - E . ds
E = [tex]- \frac{dV}{ds} \ \hat s[/tex]
Where the bold letters indicate vectors, V is the potential difference, E the electric field and s the path.
Let's apply this expression for each section of the given graph:
1) section from x₀ = 0 to x_f = 2 m, the potential is V₀ = 2 V is constant.
The derivative of a constant is zero.
E = 0
2) Section between x₀ = 2 and x_f = 4 m, the potential varies linearly from V₀ = 2 v to V_f = -2 V.
We look for the equation of the line.
V-V₀ = m (x- x₀)
We carry out the derivative.
E = - m i ^
The slope (m) is:
[tex]m= \frac{V_f - V_o}{x_f- x_o}[/tex]
Let's calculate.
[tex]m= \frac{-2 -2}{4-2} = \ -2 \ V/m[/tex]
Let's substitute.
E = [tex]2 \hat i \ V/m[/tex]
3) From x₀ = 4 to x_f = 4.5 m, the potential varies from V₀ = -2 to V_f = 0.
We look for the equation of the line and we derive.
E = - m i ^
Let's substitute.
[tex]m = \frac{0-(-2)}{4.5-4} = \ 4 V/m[/tex]
E = - 4 [tex]\hat i[/tex] V / m
4) From x₀ = 4.5 m to x_f = 6m. The potential is constant and the derivative of a constant is zero.
E = 0
5) From x₀ = 6m to x_f = 8 m, the potential changes linearly from v₀ = 0 to V_f = 1 V
We look for the equation of the line and we derive.
E = - m i ^
[tex]m = \frac{1-0}{8-6} = \ 0.5 \ V/m[/tex]
E = - 0.5 [tex]\hat i[/tex] V/m
6) From x₀ = 8m to x_f = 9m, the potential changes linearly from V₀ = 1 V to V_f = -1.
We look for the equation of the line and we derive.
E = - m i ^
[tex]m = \frac{-1-1}{9-8} = \ -2 \ V/m[/tex]
Let's substitute.
E = 2 [tex]\hat i[/tex] V/m
7) From x₀ = 9m to x_f = 10 m, the potential changes linearly from V₀ = -1 V to V_f = -2 V
We look for the equation of the line and we derive.
E = - m i ^
[tex]m = \frac{-2+1}{10-9} = \ -1 \ V/m[/tex]
Let's substitute.
E = 1 [tex]\hat i[/tex] V/m
In the attachment we can see these Electric fields as a function of distance.
In conclusion, the relationship between the potential and the electric field we can find the results for the value of the electric field as a function of the distance is:
In the attachment we see the graph of the electric field as a function of distance.
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What is the unit of pressure
is it P=F/A?
Answers
Answer:
Units of pressure include: Pa, bar, at, atm, torr, lbf/in^2
Explanation:
P = F/A is a formula for pressure not a unit.
Pa = Pascal
Bar = Bar
at = Technical Atmosphere
Torr = Torr
lbf/in^2 = pounds per square inch