A wheel has a radius of r = 2.0 m and it rolls down a smooth incline. The height of the incline is h = 8.0 m . What is the angular velocity ω of the wheel at the bottom of the incline?
Express your answer in radians per second.
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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Raghu studies in grade 6th. He wants a cricket bat to be made by a carpenter. He tells the
that the length of the bat should be 7 hand spans. The tall carpenter tells Raghu that it
will be ready by tomorrow. When Raghu went to collect the bat the next day, he was very
disappointed. Why? Was the bat longer or shorter than what Raghu expected? Give reason.
carpenter
Based on the information given, it can be noted that the bat was either shorter or longer than what he expected.
From the information given, it was stated that Raghu wants a cricket bat to be made by a carpenter and he tells the carpenter that the length of the bat should be 7 hand spans.
Since he got disappointed when he collected the bat, the reason for this will be because the bat was either shorter or longer than what he requested.
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In the following free body diagram, what is the net force on the object?
A.10n
B.5 N to the right
C.20 N to the right
D.7 N to the right
Answer:
B
Explanation:
Simply take all forces pointing to the right of the box as positive and all of the forces pointing to the left of the box as negative and add all values.
ΣF = 7 + 18 + (-20) = 5N to the right
Which of the following statements is NOT true of a hypoosmotic solution?
A. It is also known as a hypotonic solution.
B. There are more dissolved solids within the cell than outside the
cell.
C. It may cause water to move into the cell, which will cause it to
swell.
D. It may cause the cell to shrink or crenate.
Answer:
Good luck on the test, you donuts.
Explanation:
What happens to the gravitational force between two objects if the distance between them triples?
A. The force increases by a factor of 9
B. The force decreases by a factor of 9
C. The force decreases by a factor of 3
D. The force increases by a factor of 3
Two steel guitar strings have the same length. String A has a diameter of 0.489 mm and is under 410 N of tension. String B has a diameter of 1.27 mm and is under a tension of 809 N. Calculate the ratio of the wave speeds, vA/vB, in these two strings.
Answer:
Explanation:
vA / vB = √(TA/(m/L)) / √(TB/(m/L))
The lengths are the same, so the L divides out to 1
The material is identical so the mass will be directly proportional to the cross sectional area of the string
vA / vB = √(TA/(πdA²/4)) / √(TB/(πdB²/4))
π/4 is common so divides out to 1
vA / vB = √(TA/dA²) / √(TB/dB²)
vA / vB = √(410/0.489²) / √(809/1.27²)
vA / vB = 41.407 / 23.396
vA / vB = 1.8488961...
vA / vB = 1.85
4. If a charged body is negatively charged, it has excess of _______
Answer:
Electrons
Explanation:
Electrons are negatively charged sub-atomic particles, therefore when a body's negatively charged, it means that there's more electrons than protons.
2. Where do hyperbolic comets originate?
A.the Oort cloud
B.the asteroid belt
B.the Kuiper belt
C.interstellar space
Answer:
Hyperbolic comets originate from the Kuiper Belt.
a car moving at 5 m/s accelerates at a rate of 10 m/s2 for 25 seconds. How far does it move during this time?
Answer:
t is time in s For example, a car accelerates in 5 s from 25 m/s to 3 5m/s. Its velocity changes by 35 - 25 = 10 m/s. Therefore its acceleration is 10 ÷ 5 = 2 m/s2
Explanation:
Water pumps use electrical energy to create mechanical energy needed to move water.
A 1875 W water pump is plugged into a 110 V electrical outlet.
Answer:
n/a
Explanation:
this question is not feasible
objects want to ______ ___________ doing what they're __________ ____________ because they are "lazy." This is called __________.
Answer:
Explanation:
Objects want to continue doing what they're already doing because they are "lazy." This is called inertia.
an object is traveling with a constant velocity of 5m/s. How far will it have gone after 7s
Answer:
35m/s
Explanation:
Answer:
35m/s
Explanation:
Simply multiply 5 and 7.
if a current of 2.0 A is flowing from point a to point b, the potential difference between Vb- Va (in V) is:
a. 6
b. 8
c. -6
d. -8
e. 22
Answer:
[tex]\huge\color{skyblue}\boxed{\colorbox{black}{Answer ☘}}[/tex]
[tex]total \: resistance \: ( R_{t} ) = (3 + 1)ohm \\ (since \: the \: resistors \: are \: connected \\ in \: series)[/tex]
[tex]current \: flowing \: through \: circuit(I) = 2A \\ \\ now... \: by \: ohms \: law \\ V = IR\\ V = (2)(4) \\ = > 8v[/tex]
therefore , option (b) is correct!!hope helpful~
Which is the independent variable in the graph of the U.S. population 1800-1900?
1. United States
2. straight lines
3. years
4. population
Answer:
3. years
Explanation:
The independent variable is the x axis of graph
When a 1 is on the input of an inverter, what is the output?
Answer:
When the input to an inverter is high (1) the output is low (0); and when the input is low, the output is high.
explain how water erosion changes land forms
Answer:
Water erosion can slowly wash away dirt and rocks, wearing away landforms and sometimes forming rivers that can even carve out stone over time.
You are pulling a sled with a constant velocity using a rope held horizontally in
the snow. Using a spring scale attached to the rope, you measure the tension
to be 0.96 N. The sled's mass is 0.58 kg. Write the surface force the ground
exerts on the sled in component form, and determine its magnitude.
Answer:
Explanation:
if you are pulling in the positive direction and Upward is also positive.
F = -0.96i + 0.58(9.8)j
F = -0.96i + 5.7j
F = √(-0.96² + 5.7²) = 5.8 N
You are pulling a sled with constant velocity by using a rope then the surface force the ground exerts on the sled will be 5.8 N.
What is tension?The pulling force conveyed axially by a string, cable, chain, or another analogous object, or by either end of a rod, truss member, or another such three-dimensional object, is referred to as tension in physics. Another way to think of tension is as the action-reaction pair of forces acting at each end of the previous elements. Perhaps tension is the polar opposite of compression.
A restoring force may cause what is also referred to as tension when atoms or molecules are torn apart from one another at the atomic level and build up potential energy.
If you are moving upward and pushing in a positive way,
F = -0.96 i + 0.58(9.8) j
F = -0.96 i + 5.7 j
F = [tex]\sqrt{(-0.96^2 + 5.7^2)}[/tex]
F= 5.8 N
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is xenon a pure substance
[tex]\large\huge\green{\sf{Yes}}[/tex]
(c) It is suggested that one side of the copper sheet cools to a lower temperature than the
other side.
Explain why this does not happen.
[2]
Answer:
Explanation:
The word "sheet" implies that the copper is quite thin.
Copper is also a very good conductor of heat.
Therefore, with a very short heat flow distance to cover and a high rate of heat transmission, temperature differences on either side of the sheet are almost instantaneously eliminated by heat flow.
find the total volume of the material used to making the cylinder
Answer:
Hey mate
Explanation:
Whereas the basic formula for the area of a rectangular shape is length × width, the basic formula for volume is length × width × height.
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Using the formula below, calculate the kinetic energy of the 6 gram stone going 10 Mph
going 10 mph
KE = 1/2 Mass x Speed?
=
Answer:
Explanation:
A wonderful (NOT) mixed unit problem
convert mph to m/s
v = 10 mi/hr(5280 ft/mi)(12 in/ft)(2.54 cm/in) / (100 cm/m) / (3600 s/hr)
v = 4.4704 m/s
KE = ½(0.006)4.4704²
KE = 0.05995342848 J
KE = 0.06 J
What is the force exerted on a selectively permeable membrane because water has moved from an area of higher concentration to an area of lower concentration of water?
Diffusion
Facilitated transport
Osmotic pressure
Endocytosis
Question
what is the force exerted on a selectively permeable membrane beacuse water has moved from an area of higher concentration to an area of Lower concentration of water?
Answer
OSMOSIS
Explanation
Osmosis: This is the hydrostatic force acting to equalize the concentration of water on both sides of the membrane that is impermeable to substances dissolved in that water. Water will move along its concentration gradient.
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A person is drinking a glass of soda with ice.
which option describes the relative kinetic energy of molecules in and above the soda in the glass?
A. in : least energy
above : intermediate and greatest energy
B. in : greatest energy
above : least energy
C. in : least energy
above : greatest energy
D. in least and intermediate energy
above : greatest energy
The relative kinetic energy of molecules in the soda is least energy and above the soda in the glass is greatest energy.
The relative kinetic energy of gas molecules increases with increase in the mean distance between the gas molecules.
Also, relative kinetic energy of gas molecules increases with in the temperature of the gas molecules and decreases with a decrease in the temperature of the of the gas molecules;
ΔK.E ∝ T
The ice in the soda lowers the temperature of the gas molecules, thereby reducing their average speed which in turn reduces the average kinetic energy of the gas molecules in the soda.
Above the soda in the glass, the concentration of the gas molecules is less and their mean distance is greatest when compared to inside the soda. This results to an increase in the speed of the gas molecules which increases their average kinetic energy.
Thus, the relative kinetic energy of molecules in the soda is least energy and above the soda in the glass is greatest energy.
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8/10
A person stands on a square pedestal whose side lengths are
1.20 m. The person and pedestal together weigh 1.84 x 103 N.
What is the pressure the person and and pedestal exert on the
floor in Pa?
Answer:
Explanation:
P = 1.84 x 10³ N / 1.20² m² = 1,277.77777... N/m²
P = 1.28 x 10³ Pa
What effect does the time taken to lift the mass have on power output?
What is the half-life of the imaginary element Lokium? Show your work
Answer:What is the half life of the element Lokium?
The half-live of the element Lokium is 4.
Explanation:
sorry if im wrong, have good day
Answer:
The half-life of the element Lokium is 4
What is half-life?
Whether or not a given isotope is radioactive is a characteristic of that particular isotope. Some isotopes are stable indefinitely, while others are radioactive and decay through a characteristic form of emission. As time passes, less and less of the radioactive isotope will be present, and the level of radioactivity decreases. An interesting and useful aspect of radioactive decay is the half-life. The half-life of a radioactive isotope is the amount of time it takes for one half of the radioactive isotope to decay. The half-life of a specific radioactive isotope is constant; it is unaffected by conditions and is independent of the initial amount of that isotope.
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The following is an example of what type of reaction?
Answer:
Single Displacement Reaction
Explanation:
Here, only one element is getting replaced during the reaction, that is, silver gets replaced by copper, hence, single displacement reaction.
Hope it helps :)
Suppose you want to make the demonstration more dramatic by attracting as much hair as possible with the balloon. Which of the following is the best choice to accomplish your goal? A. Decrease the electric force by holding the balloon closer to the hair. B. Increase the electric force by rubbing the balloon for a longer period of time. C. Decrease the electric force by using a larger balloon. D. Increase the electric force by holding the balloon farther away from the hair.
Answer:
B. Increase the electric force by rubbing the balloon for a longer period of time.
Explanation:
HELP ME the mean free path λ and the mean collision time τ of the molecules of a diatomic gas of molecular mass 6.00 × 10⁻²⁵ kg and radius r = 1.0 x 10⁻¹⁰ m are measured. From these microscopic data can we obtain macroscopic properties such as temperature T and pressure P? If so, consider λ = 4.32 x 10⁻⁸ m and τ = 3.00 x 10⁻¹⁰ s and calculate T and P.
The temperature of the diatomic gas is 300.5 K and the pressure is 5.33 atm.
The given parameters;
Mass of the gas molecules, m = 6 x 10⁻²⁵ kgRadius of the gas, r = 1 x 10⁻¹⁰ mMean free path, [tex]\lambda_{rms}[/tex] = 4.32 x 10⁻⁸ mMean collision time, [tex]\tau = 3 \times 10^{-10} \ s[/tex]The mean velocity of the gas molecules is calculated as follows;
[tex]\tau = \frac{\lambda _{rms}}{V_{rms}} \\\\V_{rms} = \frac{\lambda _{rms}}{\tau} \\\\V_{rms} = \frac{4.32 \times 10^{-8} }{3 \times 10^{-10}} \\\\V_{rms} = 144 \ m/s[/tex]
The temperature of the gas molecules is calculated as follows;
[tex]V_{rms} = \sqrt{\frac{3kT}{M} } \\\\V_{rms}^2 = \frac{3kT}{M} \\\\T = \frac{V_{rms} ^2 M}{3k}[/tex]
where;
k is Boltzmann constant[tex]T = \frac{V_{rms} ^2 M}{3k} \\\\T = \frac{(144)^2 \times (6.0 \times 10^{-25})}{3 \times 1.38 \times 10^{-23}} \\\\T = 300.5 \ K[/tex]
The number of gas molecules per unit volume is calculated as follows;
[tex]\lambda = \frac{1}{4\pi \sqrt{2} \ r^2 n} \\\\n = \frac{1}{\lambda 4\pi \sqrt{2} \ r^2} \\\\n = \frac{1}{(4.32 \times 10^{-8}) \times 4 \pi \times \sqrt{2} \ \times (1\times 10^{-10})^2} \\\\n = 1.303 \times 10^{26} \ molcules/m^3[/tex]
The pressure of the gas molecule is calculated as follows;
[tex]n = \frac{P}{kT} \\\\P = nkT\\\\P = (1.303 \times 10^{26} ) \times (1.38 \times 10^{-23}) \times (300.5)\\\\P = 540,341.07 \ Pa\\\\P = 5.33 \ atm[/tex]
Thus, the temperature of the diatomic gas is 300.5 K and the pressure is 5.33 atm.
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stuck with this one.