The range of speeds for the car to safely round the curve without slipping is 9.0 - 21 m/s.
The range of speeds for a car to safely round a banked curve without slipping is given by the inequality: v²/rg <= tanθ + μs, where v is the speed of the car, r is the radius of the curve, g is the acceleration due to gravity, θ is the angle of banking, and μs is the coefficient of static friction. Substituting the given values, we get:
v²/50*9.81 <= tan(25) + 0.28Solving for v, we get:
v <= √((509.81)(tan(25) + 0.28)) ≈ 21 m/sand
v >= √((509.81)(tan(25) + 0.28)/4) ≈ 9 m/sTo learn more about static friction, here
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The range of speeds at which you can round the curve without slipping is approximately 4.29 m/s to 21 m/s
How to find range of speeds?The critical condition for not slipping is when the maximum frictional force (f_max) equals the centripetal force required to keep the car moving in a circle.
The centripetal force (F_c) is given by:
F_c = m × v² / r
where m = mass of the car, v = velocity of the car, and r = radius of the curve.
The maximum frictional force (f_max) is given by:
f_max = μ × N
where μ = coefficient of static friction and N = normal force.
The normal force (N) can be split into two components: N_vertical and N_horizontal.
N_vertical = m × g × cosθ
N_horizontal = m × g × sinθ
where g = acceleration due to gravity and θ = angle of the banked curve.
To find the range of speeds at which the curve can be rounded without slipping, equate the maximum frictional force (f_max) with the centripetal force (F_c) and solve for v.
μ × N = m × v² / r
μ × (N_vertical + N_horizontal) = m × v² / r
μ × (m × g × cosθ + m × g × sinθ) = m × v² / r
μ × g × (cosθ + sinθ) = v² / r
Substituting the given values:
μ × g × (cos25° + sin25°) = v² / 50
0.28 × g × (cos25° + sin25°) = v² / 50
Solving for v:
v² = 0.28 × g × (cos25° + sin25°) × 50
v = √(0.28 × g × (cos25° + sin25°) × 50)
Substituting the value of g (acceleration due to gravity) and evaluating the expression:
v ≈ √(0.28 × 9.8 × (0.9063 + 0.4236) × 50)
v ≈ √(0.28 × 9.8 × 1.3299 × 50)
v ≈ √(18.4122)
v ≈ 4.29 m/s
Therefore, the range of speeds at which you can round the curve without slipping is approximately 4.29 m/s to 21 m/s (rounded to one decimal place).
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The end point of a spring oscillates with a period of 2.0 s when a block with mass m is attached to it. When this mass is increased by 2.0 kg, the period is found to be 3.0 s. Find m.
Answer: The end point of a spring oscillates with a period of 2.0 s when a block with mass m is attached to it. When this mass is increased by 2.0 kg, the period is found to be 3.0 s. Then the mass m is 0.625kg.
Explanation: To find the answer, we need to know more about the simple harmonic motion.
What is simple harmonic motion?A particle is said to execute SHM, if it moves to and fro about the mean position under the action of restoring force.We have the equation of time period of a SHM as,[tex]T=2\pi \sqrt{\frac{m}{k} }[/tex]
Where, m is the mass of the body and k is the spring constant.How to solve the problem?Given that,[tex]T_1=2s\\m_1=m\\m_2=m+2kg\\T_2=3s[/tex]
We have to find the value of m,[tex]T_1=2\pi \sqrt{\frac{m}{k} } \\T_2=2\pi \sqrt{\frac{m+2}{k} } \\\frac{T_1}{T_2} =\sqrt{\frac{m}{m+2} }\\\frac{2}{3} =\sqrt{\frac{m}{m+2} }\\\\[/tex]
[tex]m=\frac{5}{8} =0.625kg[/tex]
Thus, we can conclude that, the mass m will be 0.625kg.
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The SI unit of current is the ampere, which is defined as the flow of charge in units of _____ over a period of time measured in _____.
The SI unit of current is the ampere, which is defined as the flow of charge in units of coulomb over a period of time measured in seconds.
What is Current?Electrical charge carriers, often electrons or atoms deficient in electrons, travel as current. The capital letter I is a typical way to represent the current. The ampere, denoted by the letter A, is the common unit. An ampere is a unit of measure of the rate of electron flow or current in an electrical conductor. One coulomb of electrical charge (6.24 x 1018 charge carriers) traveling by a given place in one second is represented by one ampere of current.
Conventional current, also known as Franklin current, is thought by physicists to flow from relatively positive points to comparatively negative locations. The most prevalent charge carriers, electrons, are negatively charged. From somewhat negative to relatively good points, they move.
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When starting a foot race, a 64 kilogram sprinter exerts an average force of 693 newtons backward on the ground for 0.59 seconds. how far does he travel in meters during this time?
The distance traveled by the sprinter in meters is determined as 1.88 m.
Acceleration of the sprinterThe acceleration of the sprinter is the rate of change of velocity of the sprinter with time.
The acceleration of the sprinter is calculated as follows;
Apply Newton's second law of motion as follows;
F = ma
a = F/m
where;
F is the applied force by the sprinterm is mass of the sprintera is acceleration of the sprintera = 693 N / 64 kg
a = 10.83 m/s²
Distance traveled by the sprinterThe distance traveled by the sprinter is calculated as follows;
s = ut + ¹/₂at²
where;
u is initial velocity = 0s = ¹/₂at²
where;
t is time of motiona is accelerations = (0.5)(10.83)(0.59²)
s = 1.88 m
Thus, the distance traveled by the sprinter in meters is determined as 1.88 m.
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What is constant in the horizontal direction for a projectile?
Answer:
initial velocity is the constant in horizontal projectile
A firm current ratio is 1. 0 and its quick ratio is 1. 0. If current liabilities are 12300, what are its inventories?
A firm current ratio is 1. 0 and its quick ratio is 1. 0. If current liabilities are 12300 then its inventories will be 12300
Inventory is the accounting of items, component parts and raw materials that a company either uses in production or sells
The quick and current ratios are liquidity ratios that help investors and analysts gauge a company's ability to meet its short-term obligations. The current ratio divides current assets by current liabilities. The quick ratio only considers highly-liquid assets or cash equivalents as part of current assets.
current ratio = current assets / current liabilities
current assets = current ratio * current liabilities
= 1 * 12300 = 12300
since , inventory is a current asset for accounting purpose , hence inventories will be 12300
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One of the primary advantages of CCDs over photographic plates is the former's high efficiency in detecting light.
True
What are the advantages of CCDs over photographic plates?In place of photographic plates or films, charge coupled devices, or CCDs, are sensitive photon detectors that can be employed in telescopes to create images. CCDs were created in the late 1960s and are now found in various devices, including digital cameras and photocopiers.
CCDs are more light-efficient, catch a greater proportion of incoming photons, can store and transfer digital data, and don't require development like film does. They respond linearly and capture up to 80% of the light that strikes them.
I understand the question you are looking for is this:
One of the primary advantages of CCDs over photographic plates is the former's high efficiency in detecting light. True or false.
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The electric field of an atom in an ionized helium atom, the most probable distance between the nucleus and the electron is r = 26.5 x 10-12m. what is the electric field due to the nucleus at the location of the electron?
The electric field due to the nucleus at the location of the electron is 4.101 × 10¹² N/C.
Given:
Distance between the electron and nucleus, r = 26.5 × 10⁻¹² m
Charge on an electron, Q = 1.6 × 10⁻¹⁹ C
Calculation:
We know that the Helium atom (He²⁺) has an atomic number Z = 2 and an atomic mass number A = 2 ( 2 protons + 2 neutrons). Thus the charge of a helium atom can be calculated as:
Q' = +2e = 2(+1.6 × 10⁻¹⁹ C) = 3.2 × 10⁻¹⁹ C
We know that the electric field on charge Q due to the nucleus is given as:
E = kQ' / r²
where E is the electric field
k is Coulomb's force constant
Q' is a charge ona Helium atom
r is the separation distance between the electron and nucleus
Applying values in the above equation we get:
E = (9×10⁹ Nm²/C²) (3.2 × 10⁻¹⁹ C) / (26.5 × 10⁻¹² m)²
= 4.101 × 10¹² N/C
Thus, the electric field on electrons due to the Helium nucleus is of magnitude 4.101 × 10¹² N/C.
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The photographer realizes that with the lens she is currently using, she can't fit the entire landscape she is trying to photograph into her picture. Should she switch to a lens with a longer or shorter focal length
She should use shorter focal length to fit the entire landscape which she is trying to photograph into her picture.
What is focal length?
The focal length is a measure of how strongly the system converges or diverges light.
A positive focal length indicates that a system converges light, while a negative focal length indicates that the system diverges light.
For a standard rectilinear lens,
FOV = 2 arctan (x/2f)
FOV ∝ 1 / f
where x is the diagonal of the film.
Focal length (f) and field of view (FOV) of a lens are inversely proportional.
From the equation we can say that,
A shorter focal length gives you a wide angle of view which allows more view to fit in the frame.
Hence,
She should use shorter focal length to fit the entire landscape which she is trying to photograph into her picture.
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Consider two celestial objects with masses m1 and m2 with a separation distance between their centers r. If the first mass m1 were to double and the second mass m2 were to triple, what would happen to the magnitude of the force of attraction
The new magnitude of the force of attraction will be 6 times the original force of attraction
How to determine the initial force Mass 1 = m₁Mass 2 = m₂ Gravitational constant = GDistance apart = rInitial force (F₁) = ?F = Gm₁m₂ / r²
F₁ = Gm₁m₂ / r²
How to determine the new force Mass 1 = 2m₁Mass 2 = 3m₂ Gravitational constant = GDistance apart (r) = rNew force (F₂) =?F = Gm₁m₂ / r²
F₂ = G × 2m₁ × 3m₂ / r²
F₂ = 6Gm₁m₂ / r²
But
F₁ = Gm₁m₂ / r²
Therefore
F₂ = 6Gm₁m₂ / r²
F₂ = 6F₁
Thus, the new magnitude of the force of attraction will be 6 times the original force of attraction
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Two boys with masses of 40 kg and 60 kg stand on a horizontal frictionless surface holding the ends of a light 10-m long rod. The boys pull themselves together along the rod. When they meet the 40-kg boy will have moved what distance?.
when they meet the 40-kg boy will have moved a distance of 6 m.
What is friction force:Friction is the force that resists motion when the surface of one object comes in contact with the surface of another.
The principle of center mass.It is the average position of all the parts of the system, weighted according to their masses.
here,
masses of the boys
M=40 kg,
m=60 kg
x1 = 10 m
The displacement of the 40 kg boy is calculated from the principle of center mass.
XM = ( mx1 + Mx2) / ( m + M )
X(40) = (60 x 10 + 40 x 0) / (40 kg + 60 kg)
X(40) = (600)/(100)
X(40) = 6 m
X(60) = (60 x 0 + 40 x 10 m) / (40 kg + 60 kg)
X(60) = (400)/(100)
X(60) = 4 m
Thus,
when they meet the 40-kg boy will have moved a distance of 6 m.
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Why is it that astronomers rely upon the 21-centimeter line associated with the spin flip in hydrogen and not the more familiar hydrogen Balmer lines to gather information from the far side of the galactic plane
Hydrogen, the element that is by far the most prevalent in the universe, exhibits radio emissions with a wavelength of 21 centimetres.
This makes it practical for using radio waves to explore space objects. An object in space emits radio waves that are more noticeable the more hydrogen it has.
What is a Galactic plane ?The majority of a disk-shaped galaxy's mass is located on the galactic plane. The galactic poles are shown by directions that are perpendicular to the galactic plane.
The Galaxy is divided in half by the planetary plane (top and bottom). The celestial equator is at an angle of 63 degrees with the galactic plane, whereas the ecliptic is at an angle of 60 degrees.The poles of all three coordinate systems each point in a different sky direction.Learn more about Galactic plane here:
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A straight current-carrying wire carries a current I. If the magnetic field at a distance d from the wire has magnitude B, what is the magnitude of the magnetic field at a distance 2d from the wire
0.07 is the magnitude of the magnetic field at a distance of 2d from the wire
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What is the tangential speed of a lug nut on a wheel of a car if the lug nut is located 0.114 m from the axis of rotation; and the wheel is rotating at 6.53 rev/sec
The tangential speed of a lug nut on a wheel of a car will be 4.68 m/s
Given:
Distance of lug nut = 0.114 m
wheel is rotating at speed = 6.53 rev/sec
To Find:
tangential speed of a lug nut
Solution: Tangential velocity is the linear speed of any object moving along a circular path. A point on the outside edge of a turntable moves a greater distance in one complete rotation than a point near to the center
Vr = r.ω
(0114 m)(41.03 rad/s) = Vr
Vr = 4.68 m/s
Hence, tangential speed of lug nut on wheel of car is 4.68 m/s
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15. When you cannot stop safely at a yellow traffic light before entering an intersection, ______________. A. stop in the intersection as soon as the light turns red B. accelerate so you'd cross the intersection before the light turns red C. enter the intersection carefully and continue across
Answer: When you cannot stop safely at a yellow traffic light before entering an intersection, enter the intersection carefully and continue across.
Explanation: To find the correct answer, we need to know more about the traffic signal rules.
What is the traffic signal rules?Red light- Indicator for the motorists to stop.Green-Signal for safety and word GO.Yellow- This signal let you know that the red signal is about to be displayed.when it's turned on, you can start slowing down to come to a stop in anticipation of red light.when we cannot stop safely at a yellow traffic light before entering an intersection, enter the intersection carefully and continue across.Thus, we can conclude that, the option C is correct.
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A block of mass 0.248 kg is placed on top of a light, vertical spring of force constant 5 025 N/m and pushed downward so that the spring is compressed by 0.090 m. After the block is released from rest, it travels upward and then leaves the spring. To what maximum height above the point of release does it rise
The maximum height above the point of release it rises is 8.82 m
What is spring force:
The force exerted by a spring on objects attached to its ends is proportional to the spring's change in length away from its equilibrium length.
F(spring) = k*x
here,
mass, m=0.240 kg
vertical spring constant, k = 5050 N/m
compression, x=0.090 m
When the spring is compressed, the spring potential energy is:
E = (k*x^2) / 2
substituting the values,
E = 5050* 0.090^2 / s
E = 20.91 J
This energy would be converted to kinetic, so the mass gains speed, which is then converted to gravitational potential energy once the mass reaches its highest point
E(p) = m*g*h
where, h is the maximum height
E(p) = E
m*g*h = 20.91
h = 20.91 / ( 9.8 * 0.248 )
h = 8.82 m
hence
The maximum height above the point of release is 8.82 m
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A hydraulic system contains 3 pistons. The input piston has an area of 0.625 in2, one of the output pistons ( piston A ) has an unknown area and the other piston ( Output Piston ) has a diameter of 3.75 inches. If system pressure is 1,440 psi, and Piston A is supporting 20,000 lb, what is the area of Piston A
The area of Piston A is 13.88 in^2
What is a hydraulic system?
The hydraulic system functions by using pressurized fluid. The power of liquid fuel in hydraulics is significant and as a result, they are commonly used in heavy equipment.
Hydraulic system simply means a mechanical function that operates through the force of liquid pressure.
Here
A hydraulic system contains 3 pistons.
Pressure, P = 1440 psi
for piston A:
Area, A= 0.625 in^2
Force, F = 20,000 lb
We know that,
Force = Pressure x Area
F = P x A
Area ( piston A) = F / P
A = 20,000 / 1440
A = 13.88 in^2
Hence,
The area of Piston A is 13.88 in^2
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What minimum volume must the slab have for a 75.0 kgkg woman to be able to stand on it without getting her feet wet
V = 0.9375 m3 is minimum volume .
What is density ?We use the word "density" to indicate how much space (or "volume") an object or substance occupies in relation to the amount of matter contained therein (its mass). Density can also be defined as the quantity of mass per unit of volume. A dense object is one that is both hefty and small.Given,
1000 kg/m3 = density of water
920 kg/m3 = density of ice
BF = Woman Weight + Slab Weight
Pvg = 75 + Pvg
V = 75 kg / (1000 - 920)
V = 75 / 80
V = 0.9375 m3
Therefore, V = 0.9375 m3 is minimum volume .
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we observe stars orbiting at distances of 25000 light years from the centers of galaxy x and galaxy y for this orbital distance stars in galaxy x have higher orbital speeds tan stars in galaxy y what can we conclude
Galaxy X contains more total mass within 25,000 light-years of its center than Galaxy Y.
Light-yearsA light-year, a significant unit of length used to express astronomical distances, is roughly 9.46 trillion kilometers, or 5.88 trillion miles. A light-year is the distance that light travels in a vacuum in one Julian year, according to the International Astronomical Union. The name "light-year" is occasionally misunderstood as a unit of time since it contains the time measurement word "year". When expressing distances to stars and other distances on a galactic scale, the light-year is most frequently employed, especially in non-specialized situations and popular science publications. The parsec, which comes from astrometry and is the distance at which one astronomical unit subtends an angle of one second of arc, is the unit that is most frequently used in professional astronomy.
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How many outer-orbital electrons are found in an atom of:a) Na?b) P?c) Br?d) I?e) Te?f) Sr?
Answer:
Na=1P=5Br=7I=7Te=6Sr=2The requried number of outer-orbital electrons in an atom of Na is 1, P is 5, Br is 7, I is 7, Te is 6, and Sr is 2.
What is orbital?An orbital is a region of space around the nucleus of an atom where there is a high probability of finding an electron. The electrons in an atom are arranged in specific energy levels or shells, and each shell contains one or more subshells, which in turn contain one or more orbitals.
Here,
To determine the number of outer-orbital electrons in an atom, we need to look at the position of the element in the periodic table. The number of outer-orbital electrons is equal to the group number of the element for groups 1, 2, and 13 to 18. For groups 3 to 12, we need to subtract the group number from 10.
a) Na is in group 1, so it has 1 outer-orbital electron.
b) P is in group 15, so it has 5 outer-orbital electrons.
c) Br is in group 17, so it has 7 outer-orbital electrons.
d) I is in group 17, so it has 7 outer-orbital electrons.
e) Te is in group 16, so it has 6 outer-orbital electrons.
f) Sr is in group 2, so it has 2 outer-orbital electrons.
Therefore, the number of outer-orbital electrons in an atom of Na is 1, P is 5, Br is 7, I is 7, Te is 6, and Sr is 2.
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Consider the following forces. (1) frictional (2) gravitational (3) tension (4) strong nuclear (5) normal (6) electroweak which of the forces listed are considered fundamental forces?
The forces listed are considered fundamental forces (2) gravitational (4) strong nuclear (6) electroweak.
Fundamental force, also called fundamental interaction, in physics, is any of the four primary forces—gravitational, electromagnetic, sturdy, and weak—that govern how gadgets or particles interact and how certain particles decay. All of the regarded forces of nature may be traced to those essential forces.
Now, physicists say they have discovered viable symptoms of a fifth essential force of nature. The findings come from studies performed at a laboratory near Chicago. The four fundamental forces govern how all of the objects and particles inside the Universe engage with each other.
The strong nuclear pressure pulled definitely and negatively charged quarks collectively to form undoubtedly charged protons and neutrally charged neutrons. The strong nuclear force also binds protons and neutrons within the nucleus of atoms. The weak nuclear force enabled complicated atoms to form through nuclear fusion.
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If the strength of a magnetic field at B is three units the strength of the magnetic field at A is ____?
If the strength of a magnetic field at B is three units the strength of the magnetic field at A, means that point B has three times more turns as compared to point A.
How strength of the magnetic field should be increased?We can increase the strength of the magnetic field by increasing the number of turns which increases the strength of the current flow.
So we can conclude that point B has three times more turns as compared to point A.
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The rarest type of stars are A. stars that are about 1 solar mass. B. stars that are more than 50 solar masses. C. stars that are about 10 solar masses. D. stars that are about 0.5 solar mass.
The rarest type of stars is those that are more than 50 solar masses.
How are stars categorized?
Stars are categorized on the basis of mass, spectral behavior, and temperature.
There are 7 spectral types of stars:
O-type (Blue) stars have more than 50 times the solar mass of the sun and are the rarest main sequence stars present in the universe. Their abundance is merely 0.000001% of known stars.Thus, the rarest type of stars are the O-type stars that have more than 50 times the solar mass of the sun.
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Rewrite the following sentence in the negative form >Each library contains 3000 brand new books
Which type of motorcycle features rear-positioned footrests, high power-to-weight ratio, and a forward leaning ride
Sport-type motorcycles typically feature a higher than average power-to-weight ratio.
Sport-style motorcycles often have a power-to-weight ratio that is above average. Fuel refers to opening the fuel supply valve, if available. Set the choke and squeeze the clutch lever together is referred known as "choke and clutch." Even though some motorcycles lack a choke, the choke should be ON for a cold engine.What is scrambler motorcycle?
Scrambler motorbikes, also referred to as dirt bikes, have special features designed for off-road activities and sports. Off-road, to be clear, is any route that isn't paved or that follows a set pattern. Scrambler bicycles feature relatively straightforward designs, long suspensions, and high ground clearance.Learn more about Scrambler motorbikes
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Which restricted basin has the coolest temperatures?
Hudson Bay is the restricted basin that has the coolest temperatures
Hudson Bay is a restricted basin which remains frozen or is dominated by ice over the summer solstice and through- out much of the high-sun season. This basin experiences a harsh continental climate.
The average annual temperature in almost the entire bay is around 0 °C (32 °F) or below. In the extreme northeast, winter temperatures average as low as −29 °C or −20.2 °F. The region of this basin has very low year-round average temperatures.
This basin starts freezing up by early November, and the northern part of the basin is typically entirely iced over by the end of the month.
correct answer is Hudson bay
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A gymnast initially has a moment of inertia of 6 kgm^2 and rotation rate of 12rad/s. His rotation rate slows to 8rad/s because he extends his arms and legs. What is his new moment of inertia
The new moment of inertia of the gymnast is 9kgm^2.
To find the answer, we need to know about the conservation of angular momentum.
What's conservation of angular momentum?It says the angular momentum of a rotating body remains conserved until an external torque is applied on it. Angular momentum= moment of inertia × angular velocity = I×wWhat's the final moment of inertia of the gymnast, if his initial moment of inertia, initial angular velocity and final angular velocity are 6 kgm^2, 12rad/s and 8rad/s respectively?Let I₁= 6 kgm^2, w₁= 12rad/s, w₂= 8rad/s and I₂= final angular velocityFrom conservation of angular momentum,I₁×w₁= I₂×w₂
I₂= I₁×w₁/w₂
= (6×12)/8
= 9kgm^2
Thus, we can conclude that the new moment of inertia of the gymnast is 9kgm^2.
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There are many muscles in our body. our body uses muscles to move parts of our body. a part that needs to move a lot will have a higher number of muscles. which of the following parts is most likely to have the most muscles? a. ear lobe b. stomach c. teeth d. brain
Option b) Stomach is most likely to have the most muscles.
There are five main muscles in stomach pyramidalis, rectus abdominus, external obliques, internal obliques, and transversus abdominis.
Muscles circulate frame parts by contracting after which relaxing. muscular tissues can pull bones, however, they cannot push them to return to their unique role. so they paintings in pairs of flexors and extensors. The flexor contracts to bend a limb at a joint.
The muscle groups that circulate our frame elements are called skeletal muscles, and they're a form of striated muscle. We will actively manipulate those with our brains. another sort of striated muscle is those that maintain our hearts pumping, which we are not able to actively control.
Muscles pull at the joints, allowing us to move. a couple of muscular tissues are used for any sort of motion of a bone. Although we are sitting flawlessly nevertheless, muscle tissues at some point in the frame are constantly shifting.
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An air conditioner runs 15 minutes each hour on a hot summer day. It is on a 240 volt circuit and uses 21 amps. Rate is $.10/kWh
How much does it cost to run for one day? Round to the nearest cent. $Answer
Answer:
Approximately [tex]\$ 3.02[/tex].
Explanation:
Note that the electric rate in this question is in the unit dollar-per-[tex]{\rm kWh}[/tex], where [tex]1\; {\rm kWh}[/tex] is the energy to run an appliance of power [tex]1\; {\rm kW}[/tex] for an hour.
Number of minutes for which the air conditioner is running in that day: [tex]15 \times 24 = 360\; \text{minute}[/tex]. Apply unit conversion and ensure that this time is measured in hours (same as the unit of the electric rate.)
[tex]\begin{aligned} \text{time} &= 360\; \text{minute} \times \frac{1\; \text{hour}}{60\; \text{minute}} = 6\; \text{hour} \end{aligned}[/tex].
The power of this air conditioner is:
[tex]\begin{aligned} \text{power} &= \text{voltage} \times \text{current} \\ &= 240\; {\rm V} \times 21\; {\rm A} \\ &= 5040\; {\rm W} \\ &= 5.04\; {\rm kW} \end{aligned}[/tex].
Thus, the energy that this air conditioner would consume would be:
[tex]\begin{aligned}\text{energy} &= \text{power} \times \text{time} \\ &= 5.04\; {\rm kW} \times 6\; \text{hour} \\ &= 30.24\; {\rm kWh} \end{aligned}[/tex].
At a rate of [tex]0.1[/tex] dollar-per-[tex]{\rm kWh}[/tex], the cost of that much energy would be approximately [tex]3.02[/tex] dollars (rounded to the nearest cent.)
A bicycle with 20 -inch diameter wheels is traveling at 16 mi/h. Find the angular speed of the wheels in rad/min.
The angular speeds of the wheels is 1,647.28 rad/min
What is Angular Velocity?angular velocity is the speed at which the angle between two bodies changes as an item rotates or revolves around an axis.
The diameter of a bicycle, d = 20inches
Radius, r = 10 inches
The bicycle is travelling at 16 mi/h.
We need to find the angular speed of the wheels in rad/min.
We know that,
1 mi/h = 0.0166667 mi/min
It means,
16 mi/h = 0.26 mi/min
Also,
10 inch = 0.0001578356 miles
The angular speeds of the wheels is given by :
v = rω
ω = v/r
ω = 0.26/0.0001578356
ω = 1,647.28 rad/min
So, the angular speeds of the wheels is 1,647.28 rad/min
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A satellite with a mass of 110 kg and a kinetic energy of 3.0 ´ 109 J must be moving at a speed of
Answer: A satellite with a mass of 110 kg and a kinetic energy of 3.08×10^9 J must be moving at a speed of 7483 m/s.
Explanation: To find the answer we need to know about the kinetic energy of a body.
How to solve the problem the equation of kinetic energy?We have the expression for kinetic energy of a body as,[tex]KE=\frac{1}{2}mv^2[/tex]
Given that,[tex]m=110kg\\KE=3.08*10^9J\\[/tex]
We have to find the speed of the satellite,[tex]v=\sqrt{\frac{2KE}{m} } =\sqrt{\frac{2*3.08*10^9}{110} } =7.483*10^3 m/s[/tex]
Thus, we can conclude that, the velocity of the satellite will be 7438m/s.
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In order to move at a speed of 7483 m/s, a satellite with a mass of 110 kg and a kinetic energy of 3.08× 10^-9 J must be travelling.
Understanding a body's kinetic energy is necessary in order to determine the solution.
How can the kinetic energy equation be solved?The phrase "kinetic energy of a body" might be used as,[tex]KE=\frac{1}{2}mV^2[/tex]
Given that,[tex]m=110kg\\KE=3.08*10^9J[/tex]
We must determine the satellite's speed.[tex]V=\sqrt{\frac{2KE}{m} }=7.48km/s[/tex]
Thus, we can infer that the satellite will move at a speed of 7438 m/s.
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