A certain light truck can go around a flat curve having a radius of 150 m with a maximum speed of 32.5 m/s. With what maximum speed can it go around a curve having a radius of 66.0 m
Answer:
Approximately [tex]21.6\; {\rm m\cdot s^{-1}}[/tex], assuming that the coefficient of kinetic friction between the tires and the ground stays the same.
Explanation:
Let [tex]\mu_{k}[/tex] denote the coefficient of kinetic friction between the tires and the ground.
Let [tex]m[/tex] denote the mass of the truck. Let [tex]g[/tex] denote the gravitational field strength. The weight of this truck would be [tex]m\, g[/tex]. Since the curve is flat, the magnitude of the normal force [tex]F_\text{normal}[/tex] between the truck and the ground would also be [tex]m\, g\![/tex].
Let [tex]v = 32.5\; {\rm m\cdot s^{-1}}[/tex] denote the speed at which the truck goes around the curve with a radius of [tex]150\; {\rm m}[/tex]. The (horizontal) centripetal acceleration of the truck would be:
[tex]\displaystyle a = \frac{v^{2}}{r}[/tex].
The horizontal net force on the truck (of mass [tex]m[/tex]) would need to be exactly:
[tex]\displaystyle F_\text{net} = m\, a = \frac{m\, v^{2}}{r}[/tex].
The friction between the tires of the truck and the ground is the only horizontal force on the truck. Thus, this friction would need to supply the entirety of this horizontal net force:
[tex]\displaystyle F_\text{friction} = F_\text{net} = \frac{m\, v^{2}}{r}[/tex].
Notice that increasing [tex]v[/tex] would require an increase in the kinetic friction between the truck, [tex]F_\text{friction}[/tex]. However, since [tex]F_\text{friction}\![/tex] is at most [tex]\mu_{k}\, F_\text{normal}[/tex] (which is equal to [tex]\mu_{k}\, m\, g[/tex]):
[tex]\begin{aligned}\frac{m\, v^{2}}{r} &= F_\text{friction} \\ & \le \mu_{k}\, F_\text{normal} \\ &= \mu_{k}\, m\, g\end{aligned}[/tex].
Therefore, when the radius of the curve is [tex]r^{\prime}[/tex], the maximum velocity of this truck would be:
[tex]\begin{aligned}v^{\prime} &= \sqrt{\mu_{k}\, g\, r^{\prime}}\end{aligned}[/tex].
Likewise, it is possible to express [tex]\mu_{k}[/tex] in terms of [tex]r[/tex], [tex]g[/tex], and max speed [tex]v[/tex]:
[tex]\displaystyle \mu_{k} = \frac{v^{2}}{r\, g}[/tex].
Substitute this expression for [tex]\mu_{k}[/tex] back into the expression for [tex]v^{\prime}[/tex]:
[tex]\begin{aligned}v^{\prime} &= \sqrt{\mu_{k}\, g\, r^{\prime}} \\ &= \sqrt{\frac{v^{2}}{r\, g}\, g\, r^{\prime}} \\ &= \sqrt{v^{2}\, \frac{r^{\prime}}{r}}\end{aligned}[/tex].
Given that [tex]v = 32.5\; {\rm m\cdot s^{-1}}[/tex], [tex]r = 150\; {\rm m}[/tex], and [tex]r^{\prime} = 66.0\; {\rm m}[/tex]:
[tex]\begin{aligned}v^{\prime} &= \sqrt{v^{2}\, \frac{r^{\prime}}{r}} \\ &= \sqrt{(32.5\; {\rm m\cdot s^{-1}})^{2} \times \frac{66.0\; {\rm m}}{150\; {\rm m}}} \\ &\approx 21.6\; {\rm m\cdot s^{-1}}\end{aligned}[/tex].
It would be really helpful if someone answered this.
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
According to first law of reflection, we know that :
Angle made by the incident ray and normal [ i.e angle of incidence ] is always equal to Angle made by the reflected ray and normal [ i.e Angle of reflection ]
Therefore, we can say that the missing angle (angle of reflection) has the same value as the angle of incidence which is equal to 45°
Please read the statement through to understand the procedure ~
When two forces act in the same direction on an object, the net force is found by ....................the forces.
1. adding
2.subtracting
3.multipling
4.dividing
Answer:
By ADDING the forces
Explanation:
if both the mass and velocity of a moving object are doubled, how will the objects momentum change
Answer:
The momentum will quadruple
Explanation:
Original momentum
momen = mv
now increase both
momen = 2m * 2v = 4 mv <====== the momentum has quadrupled
A photon has an energy of 2.88 x 10^-18 j. convert this energy into ev.
Answer:
E = V Q voltage * charge
Since the charge on an electron is e = 1.6E-19 coulombs
the energy of 1 eV is 1.6E-19 joules
E = 2.88E-18 joules / 1.6E-19 joules/electron volt
E = 18 eV
Show the molecular formula and electron structure of the simplest compound that forms with only carbon and hydrogen atoms.
The simplest compound of hydrocarbon is methane
The formula is CH_4It belongs to alkane group and has single bonds.The electron structure attached
A boy pushes a toy car along the floor at a steady speed. Are the forces on it balanced
or unbalanced?
Answer:
the forces are balanced :)
Explanation:
The brakes on a 17,600 N car exert a stopping force of 650. N. The car’s velocity changes from 25.0 m/s to 0 m/s.
a) What is the car’s mass?
b) What was its initial momentum?
c) What was the change in momentum for the car? d) How long does it take the braking force to bring the car to rest?
(a) The mass of the car is 1,795.92 kg
(b) The initial momentum of the car is 44,897.96 kgm/s.
(c) the change in momentum for the car is 44,897.96 kgm/s..
(d) The time it takes the braking force to bring the car to rest is 69.4 s.
Mass of the carThe mass of the car is calculated as follows;
W = mg
m = W/g
m = (17,600)/9.8
m = 1,795.92 kg
Initial momentum of the carPi = mvi
Pi = 1,795.92 x 25
Pi = 44,897.96 kgm/s
Change in momentum of the carΔP = Pf - Pi
ΔP = 0(1,795.92) - 44,897.96 kgm/s
ΔP = - 44,897.96 kgm/s
Time taken for the car to come to restF = ma
-650 = 1,795.92(a)
a = -650/1,795.92
a = -0.36 m/s²
v = u + at
0 = 25 - 0.36t
0.36t = 25
t = 69.4 s
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A uniform conducting rod of length 23 cm has a potential difference across its ends equal to 66 mV (millivolts). What is the magnitude of the electric field inside the conductor in units of N/C
The magnitude of the electric field inside the conductor will be 0.208 N/C.
What is an electric field?An electric field is an electric property that is connected with any location in space where a charge exists in any form. The electric force per unit charge is another term for an electric field.
Given data;
length of rod = 25 cm = 0.25 m
Potential Difference = 52 mV = 0.052 Volts
The electric field is found as the ratio of the potential difference and the length;
[tex]\rm E =\frac{0.052}{0.25} \\\\ E=0.208 \ N/C[/tex]
Hence,the magnitude of the electric field inside the conductor will be 0.208 N/C.
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What property of a wave remains unchanged when a wave enters a different medium? a. amplitude b. frequency c. wavelength d. velocity e. density
The characteristic of waves that remains unchanged when it enters a distinct medium is the frequency (Option B).
What is wave frequency?The expression 'wave frequency' indicates the period of time or occurrence of a particular type of wave.
This period or wave frequency is always an independent variable of the medium in which the wave travels.In conclusion, the characteristic of waves that remains unchanged when it enters a distinct medium is the frequency (Option B).
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Answer: B. frequency
Explanation: plato answer :)
A sound wave has a frequency of 265 hz and a wavelength measured at 1.3
m. the speed of the wave is 344.5 m/s.
how long will it take the wave to travel the length of a football field, which
is 91.4 m?
Answer:
V = f λ speed of wave in terms of frequency and wavelength
t = S / V time for wave to travel a distance S
t = 91.4 m / 344.5 m/s = .265 sec time to travel 91.4 m
True or false: Mass is a scalar quantity. * (10 Points)
Answer: True
Explanation:
A scalar quantity is those quantities that only have magnitude and no direction. Therefore the value doesn't change with direction.
1. In what direction does the Earth rotate?
2. How long does it take for the Earth to complete one rotation?
3. What causes day and night?
4. Why is it daytime on one side of the Earth and nighttime on the other side?
5. Is Earth’s rotation important? Explain your answer.
Answer:
In what direction does the Earth rotate?Earth rotates eastward, in prograde motion. As viewed from the north pole star Polaris, Earth turns counterclockwise.
How long does it take for the Earth to complete one rotation?The time it takes Earth to rotate so the sun appears in the same position in the sky, known as a solar day, is 24 hours. However, the time it takes Earth to complete one full rotation on its axis with respect to distant stars is actually 23 hours 56 minutes 4.091 seconds, known as a sidereal day.
What causes day and night?Earth's axis is an imaginary pole going right through the center of Earth from "top" to "bottom." Earth spins around this pole, making one complete turn each day. That is why we have day and night, and why every part of Earth's surface gets some of each. Earth has seasons because its axis doesn't stand up straight.
Why is it daytime on one side of the Earth and nighttime on the other side?Earth and sun are part of the solar system, with the sun at its centre. An Earth day is 24 hours because the Earth spins on its axis once every 24 hours. At any one time half of the Earth's sphere is in sunlight (day) while the other half is in darkness (night).
Is Earth’s rotation important? Explain your answer.The Earth's axis runs from the North Pole to the South Pole. It takes the Earth 24 hours, or one day, to make one complete rotation around this invisible line. As the Earth rotates, each area of its surface gets a turn to face and be warmed by the sun. This is important to all life on Earth
What does a capacitor do in a circuit?
Identify evidence that supports the theories of continental drift and plate tectonics. put responses in the correct input to answer the question. select a response, navigate to the desired input and insert the response. responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. responses can also be moved by dragging with a mouse. glossopteris plant fossils found in several southern hemisphere continents. the same types of rocks are found on either side of the atlantic ocean. there are no ocean floor rocks older than 180 million years. the pattern of rock ages shows new rock forming at mid-ocean ridges and spreading away from the ridge in both directions. the shapes of south america and africa appear to fit together. the majority of earthquakes and volcanoes occur along easily recognized bands called tectonic plate boundaries. lystrosaurus reptile fossils are found on several southern hemisphere continents. the same type of sediment deposits are found in several southern continents. magnetism in rocks of different ages don't point to the same north pole locations. science
The evidence that supports continental drift and plate tectonics includes different fossils, the same rocks and the shapes of continents that fit together.
What is continental drift?Continental drift is a theory that states continents once were part of one big landmass known as Pangea.
Nowadays, the theory of continental drift proposed by Alfred Wegener has been replaced by plate tectonics.
In conclusion, the evidence that supports continental drift and plate tectonics includes fossils, the same rocks and the shapes of continents that fit together.
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______ is how something feels.
Color
Volume
Length
Temperature
Texture
Answer:
Texture is how something feels.
The sun will spend most of its lifetime in which stage?.
What is an example of an analogue signal?
Examples of analog signals are Human voice, Thermometer, Analog phones etc.
What is signal?Signal is defined as an electromagnetic wave that carries information through a medium. In this, the data is converted into electromagnetic signal which may be analog or digital and then sent from sender to receiver.
Signal which are continuous as time varies are analog signals.
Thus, examples of analog signals are Human voice, Thermometer, Analog phones etc.
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Answer:
Examples of analog signals are Human voice, Thermometer, Analog phones etc. Examples of digital signals are Computers, Digital Phones, Digital pens, etc.
Which layer of the sun can easily be viewed by visible light?.
On an ice skating rink, a girl of mass 50 kg stands stationary, face to face with a boy of mass 80 kg. the children push off of one another, and the boy moves away with a velocity of 3 m/s. what is the final velocity of the girl? –1.9 m/s 1.9 m/s –4.8 m/s 4.8 m/s
The final velocity of the girl after the collision is determined as -4.8 m/s.
Final velocity of the girl
The final velocity of the girl is determined from the principle of conservation of linear momentum.
m1u1 + m2u2 = m1v1 + m2v2
50(0) + 80(0) = 50(v1) + 80(3)
0 = 50v1 + 240
50v1 = -240
v1 = -240/50
v1 = -4.8 m/s
Thus, the final velocity of the girl after the collision is determined as -4.8 m/s.
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6. What quantity does the gradient of the distance - time graph represent? Justify your answer.
Answer:
speed
Explanation:
In a distance-time graph, the gradient of the line is equal to the speed of the object. The greater the gradient (and the steeper the line) the faster the object is moving.
Air masses that form over continents in source regions that are cold are called__________.
Group of answer choices:
continental tropical (cT)
maritime tropical (mT)
maritime polar (mP)
continental polar (cP)
Answer:
Continental polar.
Explanation:
it should be a continental polar air mass because, it is cold.
What is the best definition
of the atomic number?
A. the number of protons found in the nucleus
B. the number of protons found outside the
nucleus
C. the number of neutrons found in the nucleus
a is the correct answer
Explanation:
no.of proton defines atomic number in an atom
Answer: a
Explanation:
An atomic number is the number of protons found in the nucleus. The number of protons is equal to the number of electrons. The atomic mass the atomic number add the amount of neutrons.
A truck travels a curve of radius 17 m and the mass of the truck is 5,900kg. The force of the truck is F = 2.685 x ?
The acceleration of the truck is 45.5 m/s² and the velocity of the truck is 27.8 m/s.
Acceleration of the truck
The acceleration of the truck is calculated as follows;
F = ma
a = F/m
a = (2.685 x 10⁵)/(5900)
a = 45.5 m/s²
Velocity of the trucka = v²/r
v² = ar
v² = 45.5 x 17
v² = 773.64
v = 27.8 m/s
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The magnetic field 0.225 m from a
wire is 4.29 x 10-7 t. how much
current is flowing through the wire?
need asap please will give brainiest
Answer:
i = 0.483 A
Explanation:
B = [tex]\frac{U.i}{2pi*r}[/tex]
So, here the r is 0.225 m
The Magnetic field is 4.29 x [tex]10^{-7}[/tex] t
U. = 4π x [tex]10^{-7}[/tex] x i
4.29 x [tex]10^{-7}[/tex] = (4π x [tex]10^{-7}[/tex] x i) / (2π * 0.225)
Cutting [tex]10^{-7}[/tex]
4.29 = [tex]\frac{4π * i}{2π * 0.225}[/tex]
4π and 2π canceled, left with 2
4.29 = [tex]\frac{2i}{0.225}[/tex]
4.29*0.225 = 2i
0.96525 = 2i
i = [tex]\frac{0.96525}{2}[/tex]
i = 0.482625 A
Rounding to 3 digits after decimal, we get
∴ i = 0.483 A
All the following are momentum oscillators except a. Relative Strength Index (RSI) b. Moving Average Convergence/Divergence (MACD) c. Stochastics d. Advance/Decline Line
All the following are momentum oscillators except Advance/Decline Line.
What are momentum oscillators?
Momentum oscillators measure the amount that a security's price has changed over a given period of time.
Examples of momentum oscillatorsRelative Strength Index (RSI) Moving Average Convergence/Divergence (MACD) StochasticsThus, all the following are momentum oscillators except Advance/Decline Line.
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What is the radius of a cone with a volume of 96π cubic inches and a height of 18 inches? 1. rewrite the formula using the base area: 2. substitute the values into formula: 3. simplify the right side: 4. undo the multiplication of 6π: 5. undo the square: what is the radius of the cone? inches v = one-third pi r squared h. 96 pi = one-third pi r squared (18). 96 pi = 6 pi r squared. 16 = r squared. startroot 16 endroot = startroot r squared endroot.
Based on the calculations, the radius of this cone is equal to 4 inches.
How to calculate the radius of a cone?Mathematically, the volume of a cone is calculated by using this formula:
V = 1/3 × r²h
Where:
h is the height.r is the radius.Making r the subject of formula, we have:
r = √(3V/πh)
Substituting the given parameters into the formula, we have;
r = √(3 × 96π/π × 18)
r = √(288/18)
r = √16
Radius, r = 4 inches.
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Explain what happens to plasma osmolarity when you give a severely dehydrated person large amounts of pure water.
Plasma osmolarity increases when you give a severely dehydrated person large amounts of pure water.
What is plasma osmolarity?The electrolyte–water balance of the body is measured by plasma osmolality. This amount can be determined in a variety of ways, including measurement and computation.
Osmolality and osmolarity are two separate measurements that are used interchangeably in everyday situations.
When you are dehydrated, osmolality rises, and when you have too much fluid in your blood, it drops.
The way your body regulates osmolality is unique. When your body's osmolality rises, your body produces antidiuretic hormone.
Hence,plasma osmolarity increases when you give a severely dehydrated person large amounts of pure water.
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Which direction will the box move?
Net force
F1-F2-F35-10-205-30-25NAs it's negative the box will move left
The acceleration due to gravity on earth is 6 times that on the moon. An object weighs 10 kg on Earth. What is the mass on the moon?
Answer:
The object obeys the equation
F = M a on both the earth and the moon (mass does not depend on location)
The problem is a little misleading because if an object has a mass of
10 kg then its weight is 10 kg * 9.8 m/s^2 = 98 Newtons
That means that weight is not expressed in Kg but rather in Newtons
Newton's Law is true on the moon as it is on the earth and F = M a
An object that weighed 10 N on earth would weigh 10 / 6 = 1.67 N on the moon
One must take care in describing a force in units of Newtons not in Kg