Answer:
The car is 3.4 s in the air.
Explanation:
Hi there!
Please, see the attached figure for a graphical description of the problem.
The vertical position of the car can be obtained by the following equation:
y = y0 + v0 · t · sin α + 1/2 · g · t²
Where:
y = vertical position of car at time t.
y0 = initial vertical position.
v0 = initial velocity.
t = time.
α = launching angle.
g = acceleration of gravity.
The vertical component of the position vector when the car reaches the ground is -28 m (considering the edge of the cliff as the origin of the system of reference) and the initial vertical position is therefore 0 m. The launching angle is 22° below the horizontal (see figure). Then, we only have to find the initial velocity to solve the equation of vertical position for the time of flight.
To find the initial velocity, we have to use two equations: the equation of velocity of the car at the time it reaches the edge of the cliff and the equation of position of the car to find that time:
x = x0 + v0 · t + 1/2 · a · t²
v = v0 + a · t
Where:
x = position of the car at time t.
x0 = initial position.
v0 = initial velocity.
t = time.
a = acceleration.
v = velocity of the car at time t.
If we place the origin of the frame of reference at the point where the car starts rolling, then the initial position is zero. Since the car starts from rest, the initial velocity, v0, is zero. Then, we can find the time it takes the car to travel the 54 m down the incline:
x = x0 + v0 · t + 1/2 · a · t² (x0 = 0 and v0 = 0)
x = 1/2 · a · t²
54 m = 1/2 · 4.4 m/s² · t²
2 · 54 m / 4.4 m/s² = t²
t = 5.0 s
With this time, we can find the velocity of the car when it reaches the edge of the cliff:
v = v0 + a · t (v0 = 0)
v = a · t
v = 4.4 m/s² · 5.0 s
v = 22 m/s
Then, the initial velocity of the falling car is 22 m/s. Using the equation of vertical position:
y = y0 + v0 · t · sin α + 1/2 · g · t² (y0 = 0)
y = v0 · t · sin α + 1/2 · g · t²
-28 m = 22 m/s · t · sin 22° - 1/2 · 9.81 m/s² · t²
0 = 28 m + 22 m/s · t · sin 22° - 4.91 m/s² · t²
Solving the quadratic equation for t using the quadratic formula:
t =3.4 s (the other values is negative and, thus, discarded).
The car is 3.4 s in the air.
Final answer:
By solving the equation h = 1/2 g t^2 for the time it takes an object to fall 28 m, we find that the car is in the air for approximately 2.39 seconds before it hits the ocean.
Explanation:
To calculate how long the car is in the air, we need to analyze the car's vertical motion separately from its horizontal motion. The car falls 28 m, which we can use with the acceleration of gravity to find the time it takes to hit the water.
We use the equation h = ½ g t^2 where h is the height the car falls (28 m), and g is the acceleration due to gravity (9.81 m/s2). We're looking for t, the time in seconds.
28 m = ½ (9.81 m/s2) t^2
Rearranging for t: t = √(2 * 28 m / 9.81 m/s2)
t = √(5.70 s2)
t = 2.39 s
The car is in the air for approximately 2.39 seconds before hitting the water.
Which pairing of terms is incorrectly related? Which pairing of terms is incorrectly related? amplitude of a sound: intensity of the sound frequency of sound waves: number of wavelengths quality of a sound: frequency of the sound frequency of sound waves: loudness of the sound
Explanation:
Here some of the pairs of terms are given. We need to find the incorrect relation. The relation are as follows :
1. amplitude of a sound: intensity of the sound
2. frequency of sound waves: number of wavelengths
3. quality of a sound: frequency of the sound
4. frequency of sound waves: loudness of the sound
The intensity of sound is directly proportional to the square of its amplitude. So, relation 1 is correct.
If f is the frequency and [tex]\lambda[/tex] is the wavelength. Speed of sound wave is,
[tex]v=f\lambda[/tex]
So, relation 2 is correct.
The quality of sound wave depends on its amplitude. So, relation 3 is not correct.
The vibration depends on two factors i.e amplitude and the frequency. The loudness of sound depends on the amplitude of wave. So, relation 4 is incorrect.
The incorrectly related pair in the given set is "quality of a sound: frequency of the sound" because it is the unique combination of frequencies and intensities, and not only the frequency, that determines the quality (timbre) of a sound.
Explanation:In the provided set of term pairs, the pairing "quality of a sound: frequency of the sound" is incorrectly related. While the frequency of a sound wave indeed influences the pitch of a sound, it doesn't determine the quality (or timbre) of the sound directly. The timbre of a sound is determined by the unique set of frequencies and intensities produced by a musical instrument or a voice, not by the frequency of the sound alone.
On the other hand, aspects like the "amplitude of a sound: intensity of the sound" and "frequency of sound waves: number of wavelengths" are correctly related. Larger-amplitude waves indicate greater pressure maxima and minima, thus higher intensity sounds. Similarly, the frequency is related to the number of wavelengths that pass in a given amount of time.
The pair "frequency of sound waves: loudness of the sound" can be both correct and incorrect depending on interpretation. Loudness is perceived volume and is influenced by both intensity and frequency. At the same frequency, greater intensity equates to more loudness. However, if the frequency changes without adjusting intensity, it can affect our perceived volume due to the varying sensitivity of human ears at different frequencies. Thus, frequency alone does not specify 'loudness'
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Water is pumped through a pipe of diameter 15.0 cm, from the Colorado River up to Grand Canyon Village, located on the rim of the canyon. The river is at an elevation of 564 m, and the village is at an elevation of 2096 m. What is the minimum pressure at which the water must be pumped if it is to arrive at the village?
Answer:
p= 1.50289×10⁷ N/m²
Explanation:
Given
HA = (564 m)................(River Elevation)
HB = (2096 m).............(Village Elevation)
Area = A =(π/4){Diameter}² = (π/4){0.15 m}² = 0.017671 m²
ρ = (1 gram/cm³) = (1000 kg/m³)........(Water Density)
p(pressure)=?
Solution
p=PA - PB
p= ρ*g*HB - ρ*g*HA
p= (ρ*g)*(HB - HA)
p= (1000×9.81 )×{2096 - 564}
p= 1.50289×10⁷ N/m²
What is stellar parallax?a.It describes the fact that stars are actually moving relative to one another, even though to our eyes the stars appear fixed in the constellations. b.It is the change in the set of constellations that we see at different times of year in the evening sky. c.It is the slight back-and-forth shifting of star positions that occurs as we view the stars from different positions in Earth's orbit of the Sun. d.It is the daily rise and set of the stars.
Answer:
Option C
C. It is the slight back-and-forth shifting of star positions that occurs as we view the stars from different positions in Earth's orbit of the Sun.
Explanation:
The angle due to the change in position of a nearby object against the background stars it is known as parallax.
The parallax angle can be used to find out the distance by means of triangulation. Making a triangle between the nearby star, the Sun and the Earth(as is shown in the image below), knowing that the distance between the Earth and the Sun (150000000 Km) is defined as 1 astronomical unit.
[tex]d(pc) = \frac{1}{p('')}[/tex] (1)
Equation (1) represents the distance in a unit known as parsec (pc).
Key terms:
Parsec: Parallax of arc second
Stellar parallax is the small apparent shift in the position of a star resulting from the change in the Earth's position as it orbits the sun. This effect is similar to the apparent motion of nearby objects against a distant background when you're moving.
Explanation:Stellar parallax is the slight back-and-forth shifting of star positions that occurs as we view the stars from different positions in Earth's orbit of the Sun. To put it in simple terms, as Earth revolves around the Sun, we see nearby stars from slightly different angles at different times of year. This apparent shift in position of the star is what we refer to as the stellar parallax effect.
Think of this as similar to the parallax effect you get when you're travelling in a car. Objects closer to you seem to move faster than the objects farther away. In the case of stellar parallax, the stars closer to us appear to move against the background of distant stars.
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You observed three different star clusters and found that the main-sequence turnoff stars in cluster 1 had spectral type A, the main-sequence turnoff stars in cluster 2 had spectral type B, and the main-sequence turnoff stars in cluster 3 had spectral type G. Which star cluster is the oldest
The oldest star cluster is cluster 2, which has B type main-sequence turnoff stars. These stars are cooler and less massive, implying that they have been burning their hydrogen fuel longer than the A and G types in the other clusters.
Explanation:The age of a star cluster can be determined by the spectral type of its main-sequence turnoff stars. In the main sequence, stars with higher masses tend to burn out faster because they deplete their hydrogen fuel more quickly. When these stars fuse all their hydrogen, they leave the main sequence, becoming red giants. This point is the 'turn-off' point.
Spectral type is related to a star's mass and temperature. Type A stars are hotter and more massive than type G, who are in turn hotter and more massive than type B. As a result, cluster 1 with the A type turn-off stars is the youngest, followed by the G type in cluster 3 and finally, the B type in cluster 2 is the oldest.
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The oldest star cluster can be determined by looking at the main-sequence turnoff point in an H-R diagram. In this case, the cluster with main-sequence turnoff stars of spectral type G is the oldest.
Explanation:The main-sequence turnoff point in an H-R diagram is a key indicator of the age of a star cluster. The turnoff point represents the stage at which stars begin to leave the main sequence and evolve into red giants. In general, the lower the turnoff point, the older the cluster. Therefore, based on the given information, cluster 3 with main-sequence turnoff stars of spectral type G is the oldest.
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When light energy hits the retina, the retinal changes from a _____ to a _____ configuration.
Answer:
Cis, Trans.
Explanation:
Rhodopsin also known as visual purple, pigment which contains sensory protein that helps to convert light into an electrical signal. Rhodopsin present in wide range of organisms from bacteria to vertebrates.
Rhodopsin is composed of opsin, and 11-cis-retinaldehyde which is derived from vitamin A. When the eye contact with light the 11-cis component converted to all trans-retinal, which results in the changes in configuration fundamental in the rhodopsin molecule.
A newborn weighing 9 lb 14 oz (4479 g) is delivered by cesarean due to cephalopelvic disproportion. The Apgar scores are 7 at 1 minute and 9 at 5 minutes. Which nursing action should be taken after the initial physical assessment?
Answer:
Determine the blood glucose level
Explanation:
Determining the blood glucose level of the infant will uncover if the child is affected with hypoglycemia. The increase in the Apgar scores from 7 to 9 in five minutes shows that the newly born child is adapting very well to the outside life.
Explains the significance of Apgar scores in assessing a newborn's health after birth.
The Apgar score is a quick evaluation of a newborn's health status with scores ranging from 0 to 10 based on heart rate, respiration, muscle tone, reflex response, and color. A score of 7 at 1 minute and 9 at 5 minutes are generally positive signs, indicating improvements in the baby's condition after birth. Based on these scores, continuous monitoring and supportive care should be provided to ensure the baby's well-being.
A satellite orbits the earth a distance of 1.50 × 107 m above the planet's surface and takes 8.65 hours for each revolution about the earth. The earth's radius is 6.38 × 106 m. The acceleration of this satellite is closest to___________.
Answer:
The acceleration of the satellite is [tex]0.87 m/s^{2}[/tex]
Explanation:
The acceleration in a circular motion is defined as:
[tex]a = \frac{v^{2}}{r}[/tex] (1)
Where a is the centripetal acceleration, v the velocity and r is the radius.
The equation of the orbital velocity is defined as
[tex]v = \frac{2 \pi r}{T}[/tex] (2)
Where r is the radius and T is the period
For this particular case, the radius will be the sum of the high of the satellite ([tex]1.50x10^{7} m[/tex]) and the Earth radius ([tex]6.38x10^{6} m[/tex]) :
[tex]r = 1.50x10^{7} m+6.38x10^{6}m [/tex]
[tex]r = 21.38x10^{6}m [/tex]
Then, equation 2 can be used:
[tex]T = 8.65 hrs \cdot \frac{3600 s}{1hrs}[/tex] ⇒ [tex]31140 s[/tex]
[tex]v = \frac{2 \pi (21.38x10^{6}m)}{31140s}[/tex]
[tex]v = 4313 m/s[/tex]
Finally equation 1 can be used:
[tex]a = \frac{(4313m/s)^{2}}{21.38x10^{6}m}[/tex]
[tex]a = 0.87 m/s^{2}[/tex]
Hence, the acceleration of the satellite is [tex]0.87 m/s^{2}[/tex]
The acceleration of the satellite is 0.87 m/s²
The given parameters;
distance of the satellite, r₁ = 1.5 x 10⁷ m
radius of the earth, r₂ = 6.38 x 10⁶ m
time of motion, t = 8.65 hours
The radius of the satellite is calculated as;
R = r₁ + r₂
R = (1.5 x 10⁷) m + (6.38 x 10⁶) m
R = 2.138 x 10⁷ m
The time of motion of the satellite in seconds;
T = 8.65 hours x 3600 s
T = 31,140 s
The velocity of the satellite is calculated as;
[tex]V = \frac{2\pi R}{T} \\\\V = \frac{2\pi \times (2.138\times 10^7)}{31, 140} \\\\V = 4314.45 \ m/s[/tex]
The acceleration of the satellite is calculated as;
[tex]a_c = \frac{V^2}{R} \\\\a_c = \frac{4314.45^2}{2.138\times 10^{7}} \\\\a_c = 0.87 \ m/s^2[/tex]
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Transmission of Borrelia burgdorferi is most likely to occur after a tick feeds a minimum of _______ hours
Answer:
36 hours
Explanation:
Transmission of Borrelia burgdorferi is most likely to occur after a tick feeds a minimum of 36 hours.
The infected ticks are most likely to transmit infection after approximately 2 or more days after feeding. If it remains unchecked, the B. Burgdorferi may trigger systemic infection by passing through the bloodstream and being rooted in different body tissues.
A conveyor belt at a quarry lifts 1,800 kg of sand per minute up a vertical distance of 9.5 meters. The sand is initially at rest, then moves at a speed of 0.28 m/s along the conveyor belt. What is the instantaneous power generated by this machine?
2.8 kW
1.0 kW
3.9 kW
890 W
Answer:
The power of the quarry belt is, P = 2.8 kW
Explanation:
Given data,
The mass of the sand, m = 1800 kg
The displacement of the quarry belt, s = 9.5 m
The initial velocity of the sand, u = 0
The final velocity of the sand, v = 0.28 m/s
The acceleration of the belt, a = (v-u)/ t
= 0.28/10
= 0.028 m/s²
The net force acting on the quarry belt is,
F = mg + ma
= m (g +a)
= 1800 (9.8 + 0.028)
= 17690 N
The work done by the quarry belt,
W = F S
= 17690 x 9.5
= 168058 N
The power of the quarry belt,
P = W / t
= 168058 / 60
= 2800 W
= 2.8 kW
Hence, the power of the quarry belt is, P = 2.8 kW
If you double your speed, your kinetic energy will increase by: A. Double B. Triple C. Quadruple D. Quintuple
Answer:
C. Quadruple
Explanation:
[tex]m[/tex] = mass
[tex]v_{i}[/tex] = initial speed = [tex]v[/tex]
[tex]K_{i}[/tex] = initial kinetic energy
Initial kinetic energy is given as
[tex]K_{i} = (0.5) m v_{i}^{2}\\K_{i} = (0.5) m v^{2}[/tex]
[tex]v_{f}[/tex] = Final speed = [tex]2 v[/tex]
Final kinetic energy is given as
[tex]K_{f} = (0.5) m v_{f}^{2}\\K_{f} = (0.5) m (2v)^{2}\\K_{f} = 4 (0.5) m v^{2}\\K_{f} = 4 K_{i}[/tex]
Hence the kinetic energy is quadruple
You stand on top a building 44 m tall with a water balloon. You drop the water balloon from rest. How fast is the balloon moving when it is halfway down the building? (assume no friction)
Explanation:
We have equation of motion v² = u² + 2as
Initial velocity, u = 0 m/s
Acceleration, a = 9.81 m/s²
Displacement, s = 0.5 x 44 = 22 m
Substituting
v² = u² + 2as
v² = 0² + 2 x 9.81 x 22
v² = 431.64
v = 20.78 m/s
Velocity at 22 m = 20.78 m/s
The balloon is moving when it is halfway down the building at 20.78 m/s.
When an alkali metal is involved in a chemical reaction with a nonmetal, what charge will its atoms most likely form? 1- 2- 2+ 1+
Answer:
+1 ion
Explanation:
Alkali metals are metals that are found in Group I of the periodic table. Their electronic configuration is such that their valence shell in grounds state is always holding only one electron which they always lose when reacting with non-metals. A loss in an electron makes the atom electrically imbalanced and hence becoming a +1 ion.
Based on the research of Albert Einstein, what change would most likely result in stopping the emission of electrons from this metal? a) an increase in the intensity of the light b) a decrease in the intensity of the light c) the use of light that has a higher frequency d) the use of light that has a lower frequency.
Answer:
option (d)
Explanation:
In the experiment of photo electric emission, it starts only when the incident energy has some minimum frequency so that the electrons just emits from the cathode surface. Such frequency is called threshold frequency.
So, if we use light of frequency lower than the threshold frequency, no photo electric emission takes place.
Thus, option (d) is correct.
Answer:
the use of light that has a lower frequency
Explanation:
At 35.0°C and 3.00 atm pressure, a gas has a volume of 1.40 L. What pressure does the gas have at 0.00°C and a volume of 0.950 L? Which equation should you use? A balloon containing 0.500 mol Ar at 0.00°C and 65.0 kPa pressure is expanded by adding more argon. How many moles of argon are added to bring the sample to a final volume of 60.0 L at 30.0°C and 45.0 kPa? What is the original volume of the gas? L
Answer :
The final pressure of gas will be, 3.92 atm
The original volume of gas is, 17.46 L
The number of moles of argon gas added is, 0.57 mol.
Explanation :
Part 1 :
Combined gas law is the combination of Boyle's law, Charles's law and Gay-Lussac's law.
The combined gas equation is,
[tex]\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}[/tex]
where,
[tex]P_1[/tex] = initial pressure of gas = 3.00 atm
[tex]P_2[/tex] = final pressure of gas = ?
[tex]V_1[/tex] = initial volume of gas = 1.40 L
[tex]V_2[/tex] = final volume of gas = 0.950 L
[tex]T_1[/tex] = initial temperature of gas = [tex]35.0^oC=273+35.0=308K[/tex]
[tex]T_2[/tex] = final temperature of gas = [tex]0.00^oC=273+0.00=273K[/tex]
Now put all the given values in the above equation, we get:
[tex]\frac{3.00atm\times 1.40L}{308K}=\frac{P_2\times 0.950L}{273K}[/tex]
[tex]P_2=3.92atm[/tex]
Therefore, the final pressure of gas will be, 3.92 atm
Part 2 :
First we have to calculate the original volume of gas.
Using ideal gas equation:
[tex]PV=nRT[/tex]
where,
P = pressure of gas = 65.0 kPa
V = volume of gas = 3.06 L
T = temperature of gas = [tex]0.00^oC=273+0.00=273K[/tex]
n = number of moles of gas = 0.500 mol
R = gas constant = 8.314 kPa.L/mol.K
Now put all the given values in the ideal gas equation, we get:
[tex](65.0kPa)\times V=(0.500mol)\times (8.314kPa.L/mol.K)\times (273K)[/tex]
[tex]V=17.46L[/tex]
Now we have to calculate the final moles of sample of gas.
Using ideal gas equation:
[tex]PV=nRT[/tex]
where,
P = pressure of gas = 45.0 kPa
V = volume of gas = 60.0 L
T = temperature of gas = [tex]30.0^oC=273+30.0=303K[/tex]
n = number of moles of gas = ?
R = gas constant = 8.314 kPa.L/mol.K
Now put all the given values in the ideal gas equation, we get:
[tex](45.0kPa)\times (60.0L)=n\times (8.314kPa.L/mol.K)\times (303K)[/tex]
[tex]n=1.07mol[/tex]
Now we have to calculate the number of moles of argon gas added.
Moles of argon gas added = Final moles of gas - Initial moles of gas
Moles of argon gas added = 1.07 mol - 0.500 mol
Moles of argon gas added = 0.57 mol
Thus, the number of moles of argon gas added is, 0.57 mol.
In what state must matter exist for fusion reactions to take place
Answer:
Plasma
Explanation:
For a fusion reaction to take place, there must be conditions in which the particles have extreme thermal kinetic energies, in this way the collisions that cause the nuclear fusion are generated. Therefore, it is necessary to reach very high temperatures, in which the state of matter will necessarily be plasma.
Why is it unwise to stir a pot of soup with a metal spoon?
Answer:
To prevent the soup from cooling soon and prevent our hands from high temperature of the spoon by the contact of soup.
Explanation:
It is unwise to stir a pot of soup with a metal spoon because the metal has a much lower specific heat capacity than that of water i.e. it requires lesser heat energy to raise its temperature.Soup being a blend of edible fats and vegetables forms a layer of fat and starch on the surface preventing much of the heat from escaping to the environment and thus delaying the process of loosing the heat to the ambiance.When a spoon is put into soup it becomes an accessible good conductor path for the heat to escape easily as a result it also increases the temperature of spoon significantly due to its low specific heat capacity.Which statement is true about divorce in the United States? `
A. The divorce rate is lower for second marriages than first marriages.
B. Divorce usually leads to a higher income and higher standard of living.
C. Similarities between spouses guarantee that they will not divorce.
D. About half of first marriages end in divorce.
Answer:D
Explanation:
D. About half of first marriages end in divorce. - Gradpoint
How can you reduce the exposure to ionizing radiation? A. Don't live near a nuclear facility. B. Stand at least two inches away from the radiation source. C. Spend as little time as possible in a radiation field. D. Avoid standing next to a metal doorway.
Answer:
c
Explanation:
Your car is stalled in the middle of a large patch of ice (assumed to be frictionless). You have a friend that has thrown a rope to you and you attach it to the car.Your friend then applies a continuous horizontal force of 550 N to you and the car. If you and the car have a total mass of 1430 kg, how long will it take for you to reach
Answer:
The time depends on the distance that they have to travel
[tex]x(t) = \frac{0.3846t^{2} }{2}[/tex]
Explanation:
The only horizontal force exerts over the car and you, it is the force that your friend is applied
Newton's Second Law of Motion defines the relationship between acceleration, force, and mass, thus
[tex]\sum{F} = ma[/tex]
550 = 1430a
a = 0.3846 m/s2
The car and you have a motion under constant acceleration, then theirs position to a time-based is:
[tex]x(t) = x_{0} + v_{0}t +\frac{at^{2} }{2}[/tex]
By the initial conditions
[tex]x(t) = \frac{at^{2} }{2}[/tex]
[tex]x(t) = \frac{0.3846t^{2} }{2}[/tex]
The time depends on the distance that they have to travel
What is the formula for the expected number of successes in a binomial experiment with n trials and probability of success p?
Answer:
np
Explanation:
If
n= number of trials
p= probability of success
then the expected number of successes in a binomial experiment is given by
E(X) = n×p.
standard deviation
σ= √(npq)
where q is probability of failure.
The expected number of successes in a binomial experiment is calculated as μ = np, where 'n' is the number of trials and 'p' is the probability of success on each trial. The trials are independent and occur under identical conditions. The binomial distribution can approximate the normal when np and nq are both greater than five.
Explanation:The formula for the expected number of successes in a binomial experiment with n trials and probability of success p is given by μ = np, where 'n' denotes the number of independent trials and 'p' represents the probability of success on one trial. For a binomial distribution, there are only two possible outcomes per trial, labeled success and failure. These trials are independent and possess identical conditions. Moreover, the outcomes of a binomial experiment fit a binomial probability distribution. The random variable X signifies the number of successes, with outcomes x = 0, 1, 2, 3, ..., n.
Further, it's crucial to note that the probability of failure, 'q', is represented by q=1-p. So, both np (number of trials times probability of success) and nq (number of trials times probability of failure) should be greater than five (np > 5 and nq > 5) for the binomial distribution of a sample to approximate the normal distribution.
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Difference between global warming and climate change
Answer:
Global warming refers only to the Earth’s rising surface temperature, while climate change includes warming and the “side effects”
what are the charge and the charge density on the surface of a conducting sphere of radius 0.15 m whose potantial is 200v?
Answer:
The charge and the charge density on the surface of a conducting sphere is [tex]3.34\times 10^{-9}\ C[/tex] and [tex]1.18\times 10^{-8}\ C/m^2[/tex] respectively.
Explanation:
It is given that,
Radius of the conducting sphere, r = 0.15 m
Potential, V = 200 V
Potential on the surface of sphere is given by :
[tex]V=\dfrac{kq}{r}[/tex]
q is the charge on the sphere
[tex]q=\dfrac{Vr}{k}[/tex]
[tex]q=\dfrac{200\times 0.15}{9\times 10^9}[/tex]
[tex]q=3.34\times 10^{-9}\ C[/tex]
Charge per unit area is called charge density on the surface. it is given by :
[tex]\sigma=\dfrac{q}{A}[/tex]
[tex]\sigma=\dfrac{q}{4\pi r^2}[/tex]
[tex]\sigma=\dfrac{3.34\times 10^{-9}}{4\pi (0.15)^2}[/tex]
[tex]\sigma=1.18\times 10^{-8}\ C/m^2[/tex]
So, the charge and the charge density on the surface of a conducting sphere is [tex]3.34\times 10^{-9}\ C[/tex] and [tex]1.18\times 10^{-8}\ C/m^2[/tex] respectively. Hence, this is the required solution.
Final answer:
The charge on the conducting sphere with a radius of 0.15 m and a potential of 200V is approximately 3.34 × 10⁻⁶ C, and the surface charge density is approximately 1.18 × 10⁻⁵ C/m².
Explanation:
To find the charge (q) and the surface charge density (σ) on the surface of a conducting sphere with a given potential (V), we can use the relationship between potential, charge, and radius of a sphere, along with the equation that relates charge to surface charge density.
The potential (V) of a conducting sphere is given by V = (k × q)/R, where k is Coulomb's constant (k = 8.99 × 10⁹ N.m²/C²), q is the charge on the sphere, and R is the radius of the sphere.
In this case, V = 200V and R = 0.15m. Using the formula, we can find the charge q on the sphere:
V = (k × q)/R
200V = ((8.99 × 109 N.m²/C²) × q)/0.15m
q = (200V × 0.15m)/(8.99 × 10⁹ N.m²/C²)
q ≈ 3.34 × 10⁻⁶ C
Once we have q, we can use the equation q = σ(4πR2) to find the surface charge density σ:
σ = q / (4πR²)
σ ≈ 3.34 × 10⁻⁶ C / (4π × (0.15m)²)
σ ≈ 1.18 × 10⁻⁵ C/m²
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1. if you push a ball and it rolls down a ramp, is it gravitational to kinetic energy?
2. if a ball that is rolling down a ramp hits a wedge that moves and pushes a car, it is kinetic to gravitational energy?
Answer:
1) It will be potential to kinetic energy. 2) kinetic energy is partly transformed into heat and partly spent in generating elastic waves within the two colliding bodies.
Explanation:
We have to first understand the principle of energy conservation and that it is that energy is transformed from one form to another, from potential energy to kinetics or vice versa. When a body is immobile at a height relative to a reference point it is said that at that height the body has potential energy, as the reference point is taken as a point where all potential energy is zero and has been transformed into kinetic energy
1)
In the moment when the ball is in the highest point of elevation with respecto to the reference point the potential energy will be:
[tex]E_{p} =m*g*h\\where:\\E_{p}= potential energy [J]\\m= mass [kg]\\h=elevation [m], respect to the reference point or level[/tex]
When the ball is in the lowest point the energy is kinetic and it will be defined by:
[tex]E_{k} =E_{p}\\E_{k} =\frac{1}{2}*m*v^{2} \\where:\\E_{k} =kinetic energy [J]\\v= velocity of the body [m/s][/tex]
2)
When the ball is rolling and moving with a velocity and hits a wedge it will be kinetic energy transformed into kinetic energy but with less amount of the initial energy because the lost kinetic energy is partly transformed into heat and partly spent in generating elastic waves within the two colliding bodies.
We have seen in lab that when adhesive tape is pulled from a dispenser, the detached tape has a positive charge. If the tape pulled from the dispenser was electrically neutral before it was pulled, and if it has 0.14 microcoulombs of charge per centimeter after being pulled, approximately what length of tape must be pulled if a total of 1.8 10^13 electrons are transferred during the pulling ?
Answer:
20.6 cm
Explanation:
charge per cm = 0.14 μC
number of electrons (e) = [tex]1.8 x 10^{13}[/tex]
to get the length of tape pulled we can apply the formula below
length of tape = [tex]\frac{magnitude of charge of the electrons}{charge per cm}[/tex]
therefore we need to find the magnitude of the charge of the electrons
1 electron = [tex]1.602 x 10^{-19}[/tex] C[tex]1.8 x 10^{13} electrons = 1.8 x 10^{13} x 1.602 x 10^{-19} = 2.88μC}[/tex]
now that we have the magnitude of the charge, we can find the length of the tape
length of the tape = [tex]\frac{2.88}{0.14}[/tex] = 20.6 cmA length of 20.6 cm of tape must be pulled if a total of 1.8 × 10^13 electrons are transferred during the pulling, given that the tape acquires 0.14 microcoulombs of charge per centimeter.
Explanation:To find out what length of tape must be pulled if a total of 1.8 × 10^13 electrons are transferred during the pulling, we first need to determine the total charge in coulombs transferred to the tape. Since each electron has a charge of approximately -1.602 × 10^-19 coulombs, we can multiply this value by the number of electrons to get the total charge:
Total charge = Number of electrons × Charge per electron = 1.8 × 10^13 × -1.602 × 10^-19 C = -2.8836 × 10^-6 C.
Since the charge is negative and we are looking for the positive charge transferred to the tape, we take the absolute value of this charge. Now, given that each centimeter of tape acquires 0.14 microcoulombs (or 0.14 × 10^-6 C), we can divide the total charge by the charge per centimeter to find the length of the tape:
Length of tape = Total charge / Charge per cm = 2.8836 × 10^-6 C / (0.14 × 10^-6 C/cm) = 20.6 cm
Therefore, a length of 20.6 cm of tape must be pulled to have 1.8 × 10^13 electrons transferred to it, assuming the tape was electrically neutral before being pulled.
Sam's job at the amusement park is to slow down and bring to a stop the boats in the log ride. If a boat and its riders have a mass of 900 kg and the boat drifts in at 1.6 m/s how much work does Sam do to stop it?
Answer:
Sam will do 1152 J of work to stop the boat
Explanation:
Work: This is defined as the product of force and distance, the S.I unit of work is Joules. At any point in science, during calculation Energy and worked can be interchange because they have the same unit.
E = W = 1/2mv²................ Equation 1
Where E = energy, W = work, m = mass, v = velocity.
Given: m = 900 kg, v = 1.6 m/s
Substituting these values into equation 1
W = 1/2(900)(1.6)²
W = 450×2.56
W = 1152 J.
Therefore Sam will do 1152 J of work to stop the boat
A pressure cooker is a pot whose lid can be tightly sealed to prevent gas from entering or escaping. Even without knowing how big the pressure cooker is
Answer:
3801.13 N
Explanation:
Pressure exerted on a surface is equivalent to applied force divided by the cross sectional area. Then, the applied force will be equal to the product of the pressure exerted and the cross sectional area.
Where given:
Atmospheric pressure (P1) = 1.013*10^5 Pa
T1 = 20+273.15 = 293.15 K
P2 = ?
T2 = 120+273.15 = 393.15 K
Using the gas equation: P1/T1 = P2/T2
Therefore, P2 = P1*T2/T1 = 1.013*10^5 *393.15/293.15 = 13.6*10^4 Pa
The net pressure = P2 - P1 = 13.6*10^4 - 1.013*10^5 = 34.6 kPa
The net force [tex]F_{120} = net pressure * area[/tex]
Area = 0.11 m^2
Thus:
The net force [tex]F_{120} = 34555.7*0.11[/tex] = 3801.13 N
Explains the concept of pressure cookers and the force latches must withstand due to high pressure inside. Uses physics principles to calculate the force required.
Pressure cookers work by increasing the boiling temperature through high pressure inside the sealed vessel. In this scenario, to calculate the force the latches must withstand, you can utilize the formula for pressure, force, and area.
A car travels 60 km in the first 2 hours and 68 km in the next 2 hours. What’s the cars average speed?
Answer:
The car's average speed is 32 kilometers per hour
Explanation:
1. Let's review the information given to us to answer the question correctly:
First two hours = 60 kilometers
Next two hours = 68 kilometers
2. What is the car's average speed?
Total distance traveled by the car = 60 + 68
Total distance traveled by the car = 128
Total time of travel = 2 + 2 hours
Total time of travel = 4 hours
Average speed = Total distance/Total time
Replacing with the real values, we have:
Average speed = 128/4
Average speed = 32 kilometers per hour
You’re responsible for server room security. You’re concerned about physical theft of computers. Of the following, which would best be able to detect theft or attempted theft?
A) Motion-sensor activated cameras
B) Smart card access to the server rooms
C) Strong deadbolt locks for server rooms
D) Logging everyone who enters the server room
Answer:
A) Motion-sensor activated cameras
Explanation:
Motion sensor activated cameras are the ones which actuate a trigger when any sort of motion is detected by them. They can play alarming sound, send e-mails and zoom the frame of motion as a response to the detected motion.
Motion sensor cameras can be of two types:
1. Fixed view camera
2. Rotating view camera
Fixed view cameras are in fixed position and they always point in the same direction for the view while the rotating cameras are the ones which can change their direction of view.
For a small and high security space we can use the fixed type camera so that we do not miss any suspicious movements. For wide areas and distant vision we use rotating cameras.
What happens to the amount of kinetic energy if the mass is tripled at constant speed?
Answer:
If the mass is tripled, the kinetic energy is also tripled
Explanation:
Kinetic Energy: This is the energy possessed by a body due to motion.
The S.I unit of kinetic energy is Joules.
Mathematically it can be represented as,
Ek = 1/2mv²................ Equation 1
Where Ek = kinetic energy, m = mass, v = velocity of the body.
From the equation above,
(i) Kinetic Energy is directly proportional to mass
(ii) Kinetic energy is directly proportional to velocity squared.
When the mass is tripled,
Ek₁ = 3/2mv².................... Equation 2
Comparing equation 1 and 2,
Ek₁ = 3×Ek
Therefore if the mass is tripled, the kinetic energy is also tripled
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If you hold a bar magnet in each hand and bring your hands together, will the force be attractive or repulsive if the magnets are held:
a) with the two north poles together?
b) with a north pole and south pole together?
a) The force is repulsive
b) The force is attractive
Explanation:
Every magnet has a magnetic field around it. It is possible to distinguish two different poles in the magnet, according to the direction of the magnetic field: in particular, the lines of the field go out from the North pole and go into the South Pole. When a magnet is broken, two new magnets are formed, each of them having its own north and south pole.
The force between two magnets can be either attractive or repulsive, depending on which poles are facing each other. We have the following situation:
The magnetic force between two like poles (north-north and south-south) is repulsiveThe magnetic force between two opposite poles (north-south) is attractiveTherefore, we have the following situations in this problem:
a)
Here we are holding the two north poles together: since they are like poles, they repel each other, so the force in this case is repulsive
b)
Here we are holding a north pole and a south pole together: since they are opposite poles, they attract each other, so the force in this case is attractive
Learn more about magnetic fields:
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