QUESTION 1
A uniform solid cylindrical disk of mass M = 1. 4 kg and radius R = 0. 085 m, rolls without slipping across a horizontal surface at velocity v = 15
m/s. What is the total kinetic energy, Ktotal, of the rolling disk? (Idisk = 12 MR2)
O a. 236. 3J
O b. 350. 3 J
O c. 144. 5 J
O d. 970. 1
Answers
The total kinetic energy, Ktotal, of the uniform solid cylindrical disk of mass M = 1. 4 kg and radius R = 0. 085 m is (D) 393.8 J.
To solve this problem, we need to use the formula for the kinetic energy of a rotating object, which includes both translational and rotational kinetic energy.
The translational kinetic energy of the disk is given by 1/2 mv², where m is the mass of the disk and v is its velocity. In this case, m = 1.4 kg and v = 15 m/s, so the translational kinetic energy is 1/2 (1.4 kg) (15 m/s)² = 157.5 J.
The rotational kinetic energy of the disk is given by 1/2 Iω², where I is the moment of inertia of the disk and ω is its angular velocity. For a solid cylindrical disk, the moment of inertia is 1/2 MR². We also know that the disk is rolling without slipping, so the velocity of its center of mass is equal to the product of its angular velocity and its radius, v = ωR. Solving for ω, we get ω = v/R.
Substituting these values into the formula for rotational kinetic energy, we get 1/2 (1/2 MR²) (v/R)^2 = 1/8 Mv². Plugging in the values for M and v, we get 1/8 (1.4 kg) (15 m/s)² = 236.3 J.
Adding the translational and rotational kinetic energies together, we get Ktotal = 157.5 J + 236.3 J = 393.8 J.
Therefore, the correct answer is (D) 393.8 J.
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Related Questions
Tariah is riding on her bike at 4m/s (North). If she accelerates at a rate of 1.5 m/s^2 for 2 s, what is her final velocity?
Answers
ANSWER:
7 m/s
STEP-BY-STEP EXPLANATION:
Given:
Initial velocity (u) = 4 m/s
Acceleration (a) = 1.5 m/s^2
Time (t) = 2 s
We can calculate the final velocity using the following formula:
\(v=u+a\cdot t\)We replace and calculate the value of the final velocity:
\(\begin{gathered} v=4+2\cdot1.5 \\ v=4+3 \\ v=7\text{ m/s} \end{gathered}\)The final velocity is equal to 7 m/s.
A 15 kg flywheel has all its mass around its outer rim. A string is wrapped around it and a m = 3.7 kg weight is hanging on the string. The flywheel has radius R = 0.25 m.
a) When the 3.7 kg weight is dropping with a speed of 1.7 m/s, what is the angular velocity of the flywheel?
w = ?? rad/s
b) When the 3.7 kg weight is moving with a speed of 1.7 m/s, what is the kinetic energy of the entire system?
K.E. = ?? J
c) If the system started from rest, how far has the weight fallen?
hfall = ?? m
d) What is the angular acceleration at this point?
a = ?? rad/s2
Answers
A 15 kg flywheel has all its mass around its outer rim. A string is wrapped around it and a m = 3.7 kg weight is hanging on the string. The flywheel has radius R = 0.25 m.
a) When the 3.7 kg weight is dropping with a speed of 1.7 m/s, the angular velocity of the flywheel 6.8 rad/s.
b) When the 3.7 kg weight is moving with a speed of 1.7 m/s, the kinetic energy of the entire system is 22.5 J.
c) If the system started from rest, the height weight fallen is 0.719 m
d) the angular acceleration at this point is 39.2 rad/s².
a) Angular velocity of the flywheel is given by :
w = v / r
Where, w = angular velocity of flywheel v = velocity of weight R = radius of flywheel
Therefore,w = v / r = 1.7 m/s / 0.25 m = 6.8 rad/s
Therefore, the angular velocity of the flywheel is 6.8 rad/s.
b) Kinetic energy of the entire system is given by :
K.E. = 1/2 * I * w²
Where, I = moment of inertia = mass of the flywheel * radius²
Thus,I = 15 kg * (0.25 m)²I = 0.9375 kg.m²
Therefore, K.E. = 1/2 * I * w²= 1/2 * 0.9375 kg.m² * (6.8 rad/s)²= 22.5 J
Therefore, the kinetic energy of the entire system is 22.5 J.
c) Potential energy of the weight at the top of the wheel is given by:
U = mgh
Where, m = mass of the weight = 3.7 kg g = acceleration due to gravity = 9.8 m/s² h = height fallen
Thus,U = 3.7 kg * 9.8 m/s² * h
Therefore, h = U / (mg) = (1.7 * 3.7 * 9.8) / (15 * 9.8)= 0.719 m
Therefore, the height fallen by the weight is 0.719 m
d) At this point, angular acceleration is given by:
a = alpha * r
Where, alpha = angular acceleration of flywheel
Therefore, alpha = a / r = g / r= 9.8 m/s² / 0.25 m= 39.2 rad/s²
Therefore, the angular acceleration at this point is 39.2 rad/s².
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When digitizing an analog signal, why must the sampling frequency be more than twice the highest frequency of interest?
Answers
The sampling frequency must be more than twice the highest frequency of interest to avoid aliasing, which can cause distortion in the digital signal.
When an analog signal is digitized, it is sampled at regular intervals to create a series of discrete values. The sampling frequency determines how often the analog signal is sampled, and it must be high enough to accurately capture the signal without aliasing. Aliasing occurs when the sampling frequency is too low, and high-frequency components of the analog signal are incorrectly represented as lower-frequency components in the digital signal.
This can result in distortion and loss of information in the digitized signal. To prevent aliasing, the sampling frequency must be at least twice the highest frequency of interest in the analog signal, according to the Nyquist-Shannon sampling theorem. By sampling the analog signal at a higher frequency, more information can be accurately captured and preserved in the digitized signal.
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when an unknown weight w was suspended from a spring with an unknown force constant k it reached its equilibrium position and the spring was stretched by 21.9 cm because of the weight w . then the weight w was pulled further down to a position 30 cm (8.1 cm below its equilibrium position) and released, which caused an oscillation in the spring. calculate the cyclic frequency of the resulting motion. the acceleration due to gravity is 9.8 m/s 2 . answer in units of hz.
Answers
The cyclic frequency of the resulting motion is 1.438 Hz. when the acceleration due to gravity is 9.8 m/s 2. Because the mass possesses kinetic energy at the static equilibrium displacement, which is translated into potential energy stored in the spring at the extremes of its journey, oscillations happen.
Given:
Force constant of the spring = k
Displacement from equilibrium point = 21.9 cm
Displacement from equilibrium point during oscillation = 8.1 cm
Acceleration due to gravity = 9.8 m/s²Formula used:
The frequency of oscillation is given by the formula f = 1/2π √(k/m)
where k is the force constant of the spring and m is the mass of the object.
In this case, we do not have the mass of the weight, but we can assume that the weight is the only object oscillating, and therefore its mass will be considered as m. If the weight is denoted by w, then its mass will be w/g, where g is the acceleration due to gravity.
Therefore,
m = w/g
Displacement during oscillation = 8.1 cm
= 0.081 m
The maximum extension of the spring from the equilibrium point during the oscillation will be the sum of the equilibrium position and the displacement from the equilibrium point during oscillation, i.e.
y = 21.9 cm + 8.1 cm
= 30 cm
= 0.3 m
Frequency of oscillation f
1/2π √(k/m)
Substituting m = w/g, we get
f = 1/2π √(k/(w/g))
f = 1/2π √(kg/w)
Now we will calculate k.
k = mg/y
where m is the mass of the weight, g is the acceleration due to gravity, and y is the maximum extension of the spring from the equilibrium point during the oscillation.
Substituting values, we get
k = (w/g)(9.8 m/s²)/(0.3 m)
k = 32.67w/g
Substituting this value in the equation for frequency, we get
f = 1/2π √(32.67w/gw)
f = 1/2π √(32.67/g)
f = 1.438 Hz
Therefore, the cyclic frequency of the resulting motion is 1.438 Hz.
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On earth, how can you tell up from down
1.by looking at a paper map
2.by using your cell phone gps
3.in reference to the earth
4.by standing on a scale
Answers
Answer:
I think is 3 I am not sure
A skydiver reaches terminal velocity. Then he opens his parachute.
What happens to the skydiver as the parachute opens?
Answers
Answer:
Explanation:
Remark
He's pulled upwards by the parachute. The formula is given below. Details are found searching for terminal velocity.
\(V_t=\sqrt\frac{2mg}{\rho A C_d}\)
Whatever that calculation turns out to be, a person has to be going a whole lot slower before he can safely hit the ground. The parachute is designed so that the person will be slowed very quickly to a safe velocity so when he hits the ground the impulse will not be as great as it could be. The force that the parachute delivers acts upward and opposes the force of gravity which is a downward force.
Pressure sensor sensitivity is 11mV/ bar ,and 592/cm pot. level sensor for 1.5m range used for measuring tanklevel (Vs-9V, R1= 150 22),Design circuit to turn ON green LED if (the level is more than 64cm and pressure less than 4bar),led LED if water level is less than 20cm, turn on release valve if pressure is more than 11 bar. [20pts]
Answers
To design a circuit to turn on a green LED if the level is more than 64 cm and pressure is less than 4 bar, a red LED if the water level is less than 20 cm, and turn on the release valve if the pressure is more than 11 bar, we can follow the steps below:
Step 1: Firstly, let's draw the circuit diagram for the given problem.
Step 2: After drawing the circuit diagram, calculate the equivalent resistance (R1) using the formula:
1 / R1 = 1 / 150 + 1 / 22
R1 = 19.34 Ω ~ 19 Ω (approx.)
Step 3: Next, calculate the sensitivity of the 592 / cm potentiometer level sensor.
592 cm = 59.2 mV
Therefore, the sensitivity = 59.2 mV / 150 Ω = 0.394 mV / Ω
Step 4: Now, we need to calculate the output voltage of the level sensor for the given range of 1.5 m = 150 cm.
Minimum voltage = 20 cm × 0.394 mV / Ω = 7.88 mV
Maximum voltage = 64 cm × 0.394 mV / Ω = 25.22 mV
Step 5: Calculate the pressure sensor's output voltage for 4 bar using the sensitivity formula.
Sensitivity = 11 mV / bar
Output voltage for 4 bar = 4 bar × 11 mV / bar = 44 mV
Step 6: Based on the output voltage values from the level sensor and pressure sensor, we can design the required comparator circuits.
Comparator 1: Turn on green LED if level > 64 cm and pressure < 4 bar.
For this, we can use an LM358 comparator circuit.
Here, the output voltage of the level sensor is compared with a reference voltage of 25.22 mV (maximum voltage for 64 cm level). Similarly, the output voltage of the pressure sensor is compared with a reference voltage of 44 mV (maximum voltage for 4 bar pressure). If the level is greater than 64 cm and the pressure is less than 4 bar, the output of the comparator will be high, which will turn on the green LED.
Comparator 2: Turn on red LED if level < 20 cm.
For this, we can use another LM358 comparator circuit.
Here, the output voltage of the level sensor is compared with a reference voltage of 7.88 mV (minimum voltage for 20 cm level). If the level is less than 20 cm, the output of the comparator will be high, which will turn on the red LED.
Comparator 3: Turn on release valve if pressure > 11 bar.
For this, we can use an NPN transistor circuit.
Here, the output voltage of the pressure sensor is compared with a reference voltage of 121 mV (minimum voltage for 11 bar pressure). If the pressure is greater than 11 bar, the transistor will be turned on, which will trigger the release valve to open.
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place in order the stages of nuclear burning that evolving high-mass stars experience.
Answers
High-mass stars in evolution go through the following stages of nuclear combustion: e-hydrogen, a-helium, f-carbon, b-neon, c-oxygen, & d-silicon.
What is nuclear explain?Nuclear energy is the term used to describe the power present in the nucleus, or core, of an atom. The atoms everything in the universe are minute building blocks, and energy holds the nucleus of each atom together. An atom's compact nucleus contains a huge quantity of energy.
Why nuclear is a threat?Nuclear weapons' utter devastation cannot be contained to military objectives or combatants. Ionizing radiation, as nuclear weapons emit, causes genetic damage and cancer in addition to killing or injuring persons who are exposed to it and contaminating the environment.
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What is the volume of the water in the graduated cylinder gizmo Student Volume Lab Sheet (cm3 and mL)
Answers
Answer:
The volume of water in the graduated cylinder will be equal to the calculated volume of the sphere.
Explanation:
The volume of solid objects can be measured by completely immersing these solids in an overflow faucet filled to brim with a liquid in which the solid does not dissolve. This is known as the displacement method. When water is used, it is known as water displacement method.
In the Volume Lab Sheet, a sphere whose volume has been pre-calculated is immersed in the overflow faucet containing water. The displaced water is collected in a beaker and the volume is obtained using a 50 mL measuring cylinder.
The volume of a sphere is calculated using the following formula:
Vsphere = 4πr³/ 3
The symbol π represents the number pi, which is about 3.14. The letter r stands for the radius of the sphere, which is the distance from the center of a sphere to its surface. The radius is exactly half of the diameter, which is the distance across the sphere through its center.
The volume of the water in the measuring cylinder is found to be equal to the calculated volume of the sphere. This is because an object immersed completely in a liquid displaces a volume of liquid equal to its own volume.
Katie is making a strawberry milkshake in her blender. A 0.05kg strawberry is rapidly spun around the inside of the container with a speed of 11.0 m/s, held by a centripetal force of 12.0 N. What is the radius of the blender at the strawberry’s location? Round answers to two decimal places.
Answers
Answer:
The radius of the blender is approximately 0.5041\(\bar 6\) meters
Explanation:
The given parameters are;
The mass of the strawberry, m = 0.05 kg
The speed with which the strawberry is spun, v = 11.0 m/s
The centripetal force holding the strawberry = 12.0 N
The formula for the centripetal force, \(F_c\), is given as follows;
\(F_c = \dfrac{m \cdot v^2}{r}\)
Where;
r = The radius of the centripetal rotation, which is the radius of the blender
\(\therefore r = \dfrac{m \cdot v^2}{F_c}\)
Substituting the values gives;
\(\therefore r = \dfrac{0.05 \times 11^2}{12} = \dfrac{121}{240} \approx 0.5041 \bar 6\)
The radius of the blender, r ≈ 0.5041\(\bar 6\) meters.
I need help! PLZZZZZZ
Solar flares produce lethal levels of radiation. What type of warning will astronauts receive before these high-energy particles are hurled at them?
Answers
Answer:
Even inside their ships, astronauts are exposed to a slow drizzle of cosmic rays coming right through the hull. The particles penetrate flesh, damaging tissue at the microscopic level. One possible side-effect is broken DNA, which can, over the course of time, cause cancer, cataracts and other maladies.
omogeneity means that the universe is the same __________. Choose one: A. at all size scales; at all times B. in all directions; in all locations C. at all times; at all size scales D. in all locations; in all directions
Answers
Option(D) is the correct answer.
In astronomy, homogeneity means that the universe is the same in all locations.
What is isotropy and homogeneity?The Copernican principle essentially examines if the universe is homogenous and isotropic when it comes to cosmology and its structure. These two concepts have a distinct meaning in cosmology and are not interchangeable. Because the universe is homogenous and isotropic, there are no unique directions or locations in it.
Again, despite their similarities, these two descriptions explain vastly distinct aspects of the universe as a whole. For instance, if the universe is isotropic, then seeing in different directions won't change how the universe is structured. The Universe seems the same to all witnesses when seen at the biggest scales, and it appears the same to a specific observer when viewed from all directions. When the Universe is examined on the biggest sizes, homogeneity means that the average density of matter is roughly the same everywhere and that the Universe is relatively smooth.
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Sobre un gas contenido en un cilindro provisto de un pistón se realiza un trabajo de 7000 Joules, mediante un proceso isotérmico. Determinar: a) La variación de la energía interna del gas. b) El calor absorbido o cedido por el gas. c) Extrae una conclusión del ejercicio.
Answers
Answer:
En un proceso isotérmico, es decir, la temperatura no cambia, el trabajo puede escribirse como:
W = n*R*T*Ln(P1/P2)
Donde P1 es la presión inicial y P2 la presión final.
Donde las cantidades:
n = número de moles
R = constante de los gases ideales
T = temperatura no cambian.
Y sabemos que la ecuación de la energía interna es:
U = C*n*R*T
Donde C es otra constante que depende del gas.
De aca, podemos concluir que ninguna de estas variables cambia en nuestro proceso, por lo que la variación de la energía interna es cero.
U2 - U1 = 0
b) Para el calor cedido o absorbido, la formula básica es:
ΔQ = C*(T2 - T1)
Donde ΔQ es el calor absorbido o cedido por el gas, C es una constante que depende del gas, T2 es la temperatura final del gas y T1 es la temperatura inicial del gas.
Como la temperatura no cambia en el proceso, entonces:
T2 = T1
ΔQ = C*(T2 - T1) = C*0 = 0
No hay calor absorbido ni cedido.
c) Podemos concluir que en un proceso isotérmico la energía interna no cambia, y no hay un intercambio de calor.
Please answer the following question
Answers
Answer:
1. Light Bulb
2. A switch
3. A battery
4. Ammeter
5. Resistor
6. Voltmeter
A narrow tube on a road bike should be inflated to about 100 psi. What is this pressure in atmospheres? 1 atm = 14. 70 psi Select one: O a. 0. 5atm b. 7 atm O O c. 200000atm d. 1000atm e. 0. 1atm
Answers
Calculate the momentum for the 5 kg bowling ball moving at 6 m/s.
Answers
Answer:
Given
mass (m) =5kg
velocity (v) =6m/s
momentum (p) =?
Form
p=mv
5kgx6m/s
p=30kg.m/s
momentum =30kg.m/s
Convert 30.0 degrees Celsius into Fahrenheit
Answers
in most cases, letters of reconmendation are required for addmission to?
Answers
Answer:
Get your recommenders to mention diverse achievements. ...
Help your recommenders with relevant info. ...
The letter should always include examples of things you did. ...
The letter should show how you improved over time. ...
The tone of the letter should not be too dry.
in series connection if one lamp is off the rest will be off
true or false. pls answer fast
Answers
Answer:
yes I think
Explanation:
because lamp is connected to eac other
True or False: A balanced force acts on different objects, and action-
eaction forces act on the same object. *
A. True
B. False
Answers
Answer:
true
Explanation:
according to the Newton's third law
How many atoms of hydrogen are there in one molecule of water, if the chemical formula is H2O? 0 1 2 3
Answers
Answer:
2
Explanation:
H2O has -
2 hydrogen atoms
1 oxygen
Answer: 2
Explanation:
A sharpening wheel is traveling at 5 rad/s, it slows down to rest in 30 seconds while sharpening an axe. What is its angular acceleration?
Answers
Answer:
Angular acceleration \(= 0.167\) rad/s^2
Explanation:
Given
Initial Angular velocity (w1) \(= 5\) rad/s
Final Angular velocity (w2) \(= 0\) rad/s
Time taken to change velocity from w1 to w2 \(= 30\) seconds
Angular acceleration is equal to the change in angular velocity to the time taken for making thing change
Hence, Angular acceleration
\(\frac{w_2 -w_1}{t} \\\frac{5-0}{30}\\0.167\)rad/s^2
if earth were a ping pong what size ball would jupiter be
Answers
Answer:
a large beach ball
Explanation:
Calculate the volume of this regular solid.
A cone 4.5 centimeters high with a radius of 3 centimeters. Label B is pointing to the circular base of the cone.
What is the volume of the cone?
Use the button on your calculator to complete this problem.
Round at the end to the nearest hundredth.
Answers
Answer:
42.41
Explanation:
What is the angle sum of a 19 sided regular polygon
Answers
A regular polygon's interior angles add up to 3060° of a 19 sided polygons.
What is polygon's?Polygons are defined as a flat shape surrounded by sides, or line segments.
It can be defined as a plane figure whose description is given by a closed polygonal chain made up of a finite number of straight line segments.
It can also be defined as any closed curve made up of a number of connected line segments that do not cross one another.
Sum of interior angle = (p - 2) x 180°
Where p = 19
Sum of interior angle = (19 - 2) x 180°
= 17 x 180°
= 3060°
Thus, a regular polygon's interior angles add up to 3060° of a 19 sided polygons.
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Coal and gas are fossil fuels which are non renewable what percentage of world electricity production in 2008 came from burning fossil fuels(there is a little chart also I feel I'm overthinking it)
Answers
In 2008, approximately 68% of the world's electricity production came from burning fossil fuels such as coal and gas.
This highlights the heavy reliance of the world on non-renewable energy sources. Fossil fuels are finite resources, which means they are non-renewable, and their production leads to environmental pollution and climate change. The burning of fossil fuels releases carbon dioxide and other greenhouse gases that contribute to global warming. As a result, there is an urgent need to reduce our dependence on fossil fuels and switch to cleaner, renewable energy sources. The transition to renewable energy sources such as solar, wind, hydro, and geothermal energy will not only reduce carbon emissions but also improve energy security and promote sustainable development.
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A wire is designed to ensure that its strain does not exceed 4. 0 × 10–4when a force of 8. 0kN is applied. The Young modulus of the metal of the wire is 2. 1 × 1011Pa. It may be assumed that the wire obeys Hooke’s law. For a force of 8. 0kN, calculate, for the wire:a)the maximum stress, (15%)b)the minimum cross-sectional area. (15%
Answers
The maximum stress in the wire is 2.0 × 10⁷ N/m², and the minimum cross-sectional area of the wire is 1.0 × 10⁻¹ m² or 100 mm².
The maximum stress will be given by the formula:
stress = force/area
From Hooke's law, we know that stress is proportional to strain:
stress = Young's modulus × strain
Therefore, we can write:
Young's modulus × strain = force/area
Rearranging for stress, we get:
stress = (force/area) / strain
We are given that the strain must not exceed 4.0 × 10⁻⁴, and the force is 8.0 kN. We also know that the Young's modulus is 2.1 × 10¹¹ Pa. So we can substitute the values into the equation:
stress = (8.0 × 10³ N) / (area × 4.0 × 10⁻⁴)
= 2.0 × 10⁷ N/m²
We can rearrange the formula for stress to give:
area = force / (stress × strain)
Substituting the values we know, we get:
area = (8.0 × 10³ N) / (2.0 × 10⁷ N/m² × 4.0 × 10⁻⁴)
= 1.0 × 10⁻¹ m²
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What are the four theories of the origin of the moon?
Answers
2. Capture theory - the moon originated elsewhere in the Milky Way.
3. Co-accretion theory - The moon and the Earth formed together when orbiting a black whole.
4. Giant impact hypothesis - A planetary object impacted Earth, causing a portion of the plant to come off and become the moon.
2.capture theory
3. Co-accretion theory
4. Giant impact hypothesis
monochromatic x rays are incident on a crystal for which the spacing of the atomic planes is 0.440 nm . the first-order maximum in the bragg reflection occurs when the incident and reflected x rays make an angle of 39.4 ∘ with the crystal planes.
Answers
The incident X-rays have a wavelength of approximately 0.545 nm.
The incident monochromatic X-rays are reflected by the atomic planes in the crystal in a phenomenon known as Bragg reflection. In this case, the spacing between the atomic planes in the crystal is given as 0.440 nm.
The first-order maximum in Bragg reflection occurs when the incident and reflected X-rays make an angle of 39.4 degrees with the crystal planes.
To understand why this occurs, let's consider the Bragg's law. According to Bragg's law, the condition for constructive interference between X-rays reflected from adjacent atomic planes in a crystal is given by the equation:
When monochromatic X-rays are incident on a crystal with atomic plane spacing of 0.440 nm, the first-order maximum in the Bragg reflection occurs when the incident and reflected X-rays make an angle of 39.4° with the crystal planes.
To understand this phenomenon, we can apply the Bragg's Law equation, which states:
\(nλ = 2d sinθ\)
Where:
- n is the order of the maximum (in this case, n=1 for the first-order maximum)
- λ is the wavelength of the X-rays
- d is the spacing between the atomic planes in the crystal
- θ is the angle of incidence/reflection with respect to the crystal planes
We can rearrange the equation to solve for λ:
λ = 2d sinθ /
Plugging in the values given in the question, we have:
\(λ = 2 * 0.440 nm * sin(39.4°) / 1\)
Calculating this, we find that the wavelength of the incident X-rays is approximately 0.545 nm.
In conclusion, the incident X-rays have a wavelength of approximately 0.545 nm.
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How many stars are contained in the milking way galaxy A) 0 b)1 c) billions d)infinite
Answers
Answer:
c) billions
Explanation:
there are more than 0 stars, because our sun is a star
and there are more than one because the milky way has a lot of suns
there aren't infinite because the milky way is finite it has some volume and even you made the smallest star possible you wouldn't have infinite stars
so the only option is billions