The total energy of the pendulum is directly proportional to the square of the amplitude. Hence, if the amplitude is increased by a factor of 4, the total energy in the system will increase by a factor of 16.
Explanation:The subject of your question is related to the energy of a pendulum in simple harmonic motion. The total energy stored in an oscillating pendulum depends on the square of its amplitude. The total energy E of an oscillator is the sum of its kinetic energy K = mu² / 2 and the elastic potential energy of the force U(x)= k_x²/2 (formula for potential energy in a harmonic oscillator). These two forms of energy: kinetic energy and potential energy oscillate back and forth but their sum remains constant.
Since the total energy ETotal = (1/2)kA² is proportional to the square of the amplitude, if the amplitude of the pendulum's oscillations is increased by a factor of 4, this means you're multiplying the square of the quantity by 4. As a result, the energy in the pendulum increases by a factor of 4² which is 16.
So, as the amplitude of the pendulum increases by a factor of 4, the total energy increases by a factor of 16.
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When the amplitude of a swinging pendulum is increased by a factor of 4, the total energy stored in the moving pendulum increases by a factor of 16.
Explanation:The total energy of a swinging pendulum is given by the sum of its potential energy and kinetic energy, which is proportional to the square of the amplitude.
In this case, when the amplitude is increased by a factor of 4, the total energy increases by a factor of 16.
This is because the total energy is directly proportional to the square of the amplitude, so increasing the amplitude by a factor of 4 results in an increase of the total energy by the square of that factor.
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Four beakers of four different sizes are filled with water to the same depth. The temperature of the water is the same in all four beakers. If 100 grams of ice are added to each beaker, in which beaker will the temperature change the least?
Answer: ITS C ''X''
Explanation: Study island
Answer:
X
Explanation:
All the beakers are filled to the same depth. However, beaker X has the largest radius of all the beakers. Thus, beaker X contains a larger volume of water. Since beaker X has more water it will have the least change in temperature given the same amount of ice as the other three beakers.
What condition is necessary for the flow of heat? What analogous condition is necessary for the flow of charge?
A spring (k=15.19kN/m)is is compresses 25cm and held in place on a 36.87° incline. A block (M=10kg) is placed on the spring. When the spring is released the block slides up and off the end of the ramp. The block travels 1.12m along the ramp where the co efficient of kinetic friction is 0.300. Determine the maximum vertical displacement of the block after it becomes airborne relative to it's initial position on the spring
Answer:
The maximum vertical displacement is 2.07 meters.
Explanation:
We can solve this problem using energy. Since there is a frictional force acting on the block, we need to consider the work done by this force. So, the initial potential energy stored in the spring is transferred to the block and it starts to move upwards. Let's name the point at which the block leaves the ramp "1" and the highest point of its trajectory in the air "2". Then, we can say that:
[tex]E_0=E_1\\\\U_e_0=K_1+U_g_1+W_f_1[/tex]
Where [tex]U_e_0[/tex] is the elastic potential energy stored in the spring, [tex]K_1[/tex] is the kinetic energy of the block at point 1, [tex]U_g_1[/tex] is the gravitational potential energy of the block at point 1, and [tex]W_f_1[/tex] is the work done by friction at point 1.
Now, rearranging the equation we obtain:
[tex]\frac{1}{2}kx^{2}=\frac{1}{2}mv_1^{2}+mgh_1+\mu Ns_1[/tex]
Where [tex]k[/tex] is the spring constant, [tex]x[/tex] is the compression of the spring, [tex]m[/tex] is the mass of the block, [tex]v_1[/tex] is the speed at point 1, [tex]g[/tex] is the acceleration due to gravity, [tex]h_1[/tex] is the vertical height of the block at point 1, [tex]\mu[/tex] is the coefficient of kinetic friction, [tex]N[/tex] is the magnitude of the normal force and [tex]s_1[/tex] is the displacement of the block along the ramp to point 1.
Since the force is in an inclined plane, the normal force is equal to:
[tex]N=mg\cos\theta[/tex]
Where [tex]\theta[/tex] is the angle of the ramp.
We can find the height [tex]h_1[/tex] using trigonometry:
[tex]h_1=s_1\sin\theta[/tex]
Then, our equation becomes:
[tex]\frac{1}{2}kx^{2}=\frac{1}{2}mv_1^{2}+mgs_1\sin\theta+\mu mgs_1\cos\theta\\\\\implies v_1=\sqrt{\frac{2(\frac{1}{2}kx^{2}-mgs_1\sin\theta-\mu mgs_1\cos\theta)}{m}}=\sqrt{\frac{kx^{2}}{m}-2gs_1(\sin\theta+\mu \cos\theta)}[/tex]
Plugging in the known values, we get:
[tex]v_1=\sqrt{\frac{(15190N/m)(0.25m)^{2}}{10kg}-2(9.8m/s^{2})(1.12m)(\sin36.87\°+(0.300) \cos36.87\°)}\\\\v_1=8.75m/s[/tex]
Now, we can obtain the height from point 1 to point 2 using the kinematics equations. We care about the vertical axis, so first we calculate the vertical component of the velocity at point 1:
[tex]v_1_y=v_1\sin\theta=(8.75m/s)\sin36.87\°=5.25m/s[/tex]
Now, we have:
[tex]y=\frac{v_1_y^{2}}{2g}\\\\y=\frac{(5.25m/s)^{2}}{2(9.8m/s^{2})}\\\\y=1.40m[/tex]
Finally, the maximum vertical displacement [tex]h_2[/tex] is equal to the height [tex]h_1[/tex] plus the vertical displacement [tex]y[/tex]:
[tex]h_2=h_1+y=s_1\sin\theta +y\\\\h_2=(1.12m)\sin36.87\°+1.40m\\\\h_2=2.07m[/tex]
It means that the maximum vertical displacement of the block after it becomes airborne is 2.07 meters.
The diagram shows a transformer. Based on the diagram the voltage at the second winding is ____ v
Answer:
60V
Explanation:
240V/12 loops = 20 volts per loop.
20 * 3 = 60 volts
Answer:
60V
Explanation:
A man travels to a foreign country and smuggles a pair of exotic snakes (one male and one female) back into his country of origin. Fearing that he will be arrested by the police, he releases the snakes into the wild. How will this action most likely affect his local ecosystem? A. There will be a reduction in the native snake population as they compete for resources with the exotic snakes. B. The addition of the exotic snakes will have no effect on the local ecosystem. C. The exotic snakes will become sterile and not be able to reproduce since they are not in their native environment. D. There will be an increase in the number of mice in the local ecosystem in order to provide more food for the snake populations.
Answer:
A. There will be a reduction in the native snake population as they compete for resources with the exotic snakes.
Explanation:
The new snakes will compete with the native snakes for food resources. The available food might not be able to support the growing demand when these new snakes start reproduce. The reduced available food Can lead to a population decrease of the native snakes.
The full range of energy in sunlight can best be described as
Answer:
Solar energy or infrared radiation energy
Two balls collide with each other. Ball 1 experiences a high acceleration as a result of the collision, while Ball 2 experiences a small acceleration. What can you conclude about Ball 2?
Answer:
We conclude that ball 2 has a larger mass.
Explanation:
This is because the internal forces at collision are an action reaction pair. The force on ball 1 due to ball 2 equals the force on ball 2 due to ball 1. Since these forces are equal in magnitude, let's denote it by F. So
For each ball, F = ma and a = F/m. Since F is the same for both balls, if follows that the acceleration of each ball is inversely proportional to its mass. That is, a ∝ 1/m.
Since ball 1 has a higher acceleration, it has a lower mass. Also ball 2 has a small acceleration, so it has a higher mass.
Answer:
See explanation
Explanation:
Solution:-
- Denote the following:
mass of ball 1 = m1
initial velocity of ball 1 = vi,1
Final velocity of ball 1 = vf,1
mass of ball 2 = m2
initial velocity of ball 2 = vi,2
Final velocity of ball 2 = vf,2
- Since there are no external forces acting on the system containing the two balls then we can say that the linear momentum of the system is conserved.
- The conservation of linear momentum says that the momentum before or after the collision remains conserved:
Pi = Pf
Where, p = m*v
- The conservation of momentum for the given system:
m1*vi,1 + m2*vi,2 = m1*vi,1 + m2*vi,2
- Since no information is given about the initial conditions. We will consider the internal force (F) that acts when two balls come in contact. Then apply Newton's second law of motion on both balls individually:
F = m*a
Where, m: Mass of object
a: Acceleration of the object
- For ball 1:
F1 = m1*a1
- For ball 2:
F2 = m2*a2
Given that a1 > a2, and the the internal force that acts on both balls during collision obeys Newton's 3rd Law i.e for every action there is an equal but opposite reaction: So , F1 = F2
F = m1*a1
F = m2*a2
m1*a1 = m2*a2
- Since, a1 > a2 for above equation to hold true then m1 < m2. That is the mass of ball 1 is quite less compared to ball 2.
Batteries have potential energy in their
energy stores. What one word completes the sentence?
Answer:
Chemical
Explanation:
Answer:
The right answer is "chemical"
Explanation:
Batteries store energy in the chemical bonds in the metals inside them.
When checking the charging system on a late-model vehicle: Technician A connects a scan tool to monitor the system voltage output. Technician B connects a scan tool to retrieve any DTCs that may be in the system. Who is correct:a.Technician Ab.Technician Bc.both 1 and 2d.neither 1 and 2
Answer:
C) Both 1 and 2
Explanation:
The scan tool may include a bi-directional control that allows the technician to control the output of the alternator for testing purposes.
The Diagnostic Trouble Codes (DTCs), are used by automobile manufacturers to diagnose problems related to the vehicle.
The scan tool can also be used to monitor the output voltage of the vehicle to verify if the correct amount of voltage is supplied by the alternator.
Both Technicians A and B are correct because the steps they both take are necessary for the diagnosis of the vehicle.
what voltage would be required to run a 600-watt motor with a current of 400 amperes
Answer:
Voltage can be calculated in various ways but I am a easier solution to it:
Explanation:
V=I×R instead of this formula I use:
P=I×V
600=400×V
600=400V
Divide both sides by 400
V=3÷2
V=1.5 J/C
1volt=1coulomb or joule
Answer:1.5V
Explanation: power =IV
Where I= current
V= voltage
Therefore Voltage=power/current
V= 600/400= 1.5
A child in an inner tube is bobbing up and down in the ocean and notices that after a wave crest passes, four more crests pass in a time of 42.4 s and the distance between the crests is 47 m.
If possible, determine the following properties for the wave. (If not possible, enter IMPOSSIBLE.)
(a) period s
(b) frequency Hz
(c) wavelength m
(d) speed m/s
(e) amplitude m
Answer:
period = 10.6 sec, frequency = 0.094 Hz, wavelength = 47 m and speed = 4.418 m/s.
Explanation:
Given:
Four more crests pass in a time of 42.4 s and the distance between the crests is 47 m.
We have to determine five terms.
Lets start with one-one basis.
a.
Period = Time taken by a wave to pass though.
⇒ [tex]P = \frac{Total\ time}{No.\ of\ waves}[/tex]
⇒ [tex]P = \frac{42.4}{4}[/tex]
⇒ [tex]P=10.6[/tex] s
b.
Frequency = Reciprocal of time period in Hertz.
⇒ [tex]f=\frac{1}{T}[/tex]
⇒ [tex]f=\frac{1}{10.6}[/tex]
⇒ [tex]f=0.094[/tex] Hertz
c.
Wavelength = Distance between two consecutive trough and crest.
⇒ [tex]\lambda = 47[/tex] m
d.
Speed (v) = Product of frequency and wavelength.
⇒ [tex]v=f\times \lambda[/tex]
⇒ [tex]v=0.094\times 47[/tex]
⇒ [tex]v = 4.418[/tex] ms^-1
e.
Amplitude = The maximum displacement or half the distance from crest to trough.
⇒ Here it can't be determined.
⇒ Impossible.
So,
The period = 10.6 sec, frequency =0.094 Hz, wavelength = 47 m and speed = 4.418 m/s.
Answer:
Period: 10.6 sec
Frequency = 0.094 Hz
Wavelength = 47 m
Speed = 4.418 m/s
Amplitude : Impossible
Explanation:
How can you measure the wavelength of a longitudinal wave
Answer:
In longitudinal wave, wavelength is obtained by measuring the distance from a compression to the next compression or from a rarefaction to the next rarefaction.
Explanation:
What is a longitudinal wave?
A longitudinal wave is a wave in which the particles of the medium are displaced in a direction parallel to the direction of energy transport
What is a wave length?
wavelength of a wave is basically the length of one complete wave cycle. The wavelength can always be determined by measuring the distance between any two corresponding points on adjacent waves.
Final answer:
To measure the wavelength of a longitudinal wave, identify two consecutive compressions or rarefactions and measure the distance between them. In a classroom setup, produce a standing wave in a medium like a rubber tubing and measure the distance between nodes, then use the speed-frequency-wavelength equation to find the wavelength.
Explanation:
To measure the wavelength of a longitudinal wave, such as a sound wave, we must first understand that the wavelength is the distance between two consecutive compressions or two consecutive rarefactions. In practice, measuring the wavelength of a longitudinal wave can be achieved through various experiments depending on the medium of wave propagation. For waves in a slinky or spring, you can measure the distance between compressions after creating a wave. For sound waves, you may use a tuning fork and a tube with a movable piston to find the point of resonance, which corresponds to a specific wavelength.
In the classroom, a common method to measure the wavelength is to use a wave generator and a medium such as a rubber tubing or a spring. You generate a standing wave and measure the distance between two consecutive nodes (points of no displacement) which corresponds to half a wavelength. By multiplying this distance by two, you get the full wavelength.
To relate wavelength to period and frequency, the fundamental equation v = f × λ (where v is the speed of the wave, f is frequency, and λ is wavelength) can be used. By finding the period (T, the time it takes for a single wavelength to pass a point), and knowing that the frequency is the inverse of the period (f = 1/T), you can determine the wave speed.
What does the left y-axis show?
a- sea surface temperature anomaly, in degrees celsius
b- sea surface temperature anomaly, in degrees fahrenheit
c- time, in four-year intervals
d- incidence of cholera, as a percentage of the normal rate
e- sea surface temperature, in degrees celsius
Answer:
The correct option is;
a- sea surface temperature anomaly, in degrees Celsius
Explanation:
From the diagram related to the question we have two graphs super imposed of Sea surface temperature anomaly, in degrees Celsius and cholera incidence anomaly (%) both plotted against time in years.
On the left the y-axis represents the sea surface temperature anomaly while on the right, the y-axis represents the cholera incidence anomaly (%).
The display of the graph shows the sea surface temperature anomaly in blue.
The left y-axis of a graph generally represents the dependent variable or the outcome of the specific subject being explored. The correct answer to the question would depend on what the graph is representing. Without additional context, it's difficult to determine which option would be correct.
Explanation:The left y-axis on a graph traditionally represents the dependent variables; the outcome of the subject being studied. The answer depends on what the graph is about. If it is about sea surface temperature anomaly, then either option a (in degrees celsius) or option b (in degrees fahrenheit) would be shown on the left y-axis, depending on the measure used in the investigation. If it is about the regular progression of time with respect to the incidence of cholera or temperature, then option c would be displayed on the y-axis. If it is about the incidence of cholera as a percentage of normal rate, then option d would be shown. If it's about sea surface temperature generally, then option e might be displayed on the y-axis. Without context, it's difficult to say which option is correct.
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"A horizontal loop of wire has a magnetic field passing upward through the plane of the loop. If this magnetic field increases with time, is the direction of the induced current clockwise or counterclockwise (viewed from above) as predicted by Lenz's law?
Answer:
See explanation
Explanation:
If the magnetic field increases up through the loop a current will flow such that the magnetic field from this current will oppose the change in magnetic flux. (As per Lenz's Law)
The magnetic field is increasing up so the field from the current must be directed down.
From the application of right hand rule by pointing the thumb downwards and curl our fingers the current flows clockwise then the magnetic field from this current will be directed downward inside the loop of wire.
According to Lenz's law, the induced current in a horizontal loop of wire with an increasing magnetic field passing upward through it will flow clockwise when viewed from above, as it acts to oppose the change in the magnetic field.
When a horizontal loop of wire has an increasing magnetic field passing upward through it, Lenz's law helps us determine the direction of the induced current in the loop. According to Lenz's law, the induced current will flow in such a way that it creates a magnetic field that opposes the change in magnetic flux. Since the magnetic field through the loop is increasing upwards, the induced current must produce a magnetic field that points downwards.
Applying the right-hand rule, if you orient your right hand with the thumb pointing downwards (opposing the increasing magnetic field), your fingers would curl in a clockwise direction when viewed from above. Therefore, the induced current in the loop will flow in a clockwise direction, as viewed from above, when the magnetic field is increasing through the plane of the loop.
two vehicles have a head on collision. one vehicle has a mass of 3000 kg and moves at 25 m/s while the second vehicle has a mass of 2500 kg and moves at -15 m/s. if the vehicles stick together after the collision what is the speed of the combined vehicles
Answer:
The speed of the combined vehicles is 6.82m/s
Explanation:
Using the law of conservation of momentum which stayed that the sum of momentum of bodies before collision is equal to their sum of momentum after collision. After collision, both object moves with the same velocity.
Momentum = mass×velocity
Before collision:
Momentum of vehicle or mass 3000kg moving with velocity 25m/s
= 3000×25
= 75000kgm/s
Pa = 75000kgm/s
Momentum of vehicle with mass 2500kg moving with velocity of -15m/s
= 2500×-15
= -37500kgm/s
After collision:
Momentum = (3000+2500)V
Where v is their common velocity
Momentum after collision = 5500V
Based on the law:
75000+(-37500) = 5500V
75000-37500 = 5500V
37500 = 5500V
V = 37500/5500
V = 6.82m/s
The following 1h nmr absorptions were obtained on a spectrometer operating at 200 mhz and are given in hz downfield from tms. Convert the absorptions to δ units.
Answer:
Explanation:
We will use the formula below:
Chemical shift in ppm = peak position in Hz (relative to TMS) /
spectrometer frequency in MHz.
a) 956Hz/200Hz= 4.78 ppm
b) (2.40E3)/200Hz= 12 ppm
c) (1.97E3)/200Hz = 9.85 ppm
Final answer:
In NMR spectroscopy, absorptions are converted to δ units using the formula δ = (absorption in Hz) / spectrometer frequency in MHz. This conversion helps standardize chemical shift values across different spectrometer frequencies.
Explanation:
Absorptions in NMR spectroscopy are typically reported in parts per million (ppm) downfield from TMS. To convert these absorptions to δ units, you can use the formula: δ = (absorption in Hz) / spectrometer frequency in MHz. For example, if an absorption is 280 Hz on a 70 MHz spectrometer, the chemical shift in ppm would be 4 ppm.
Which one of the following is NOT among the characteristics of light gauge steel frames? A. Thermally inferior in itself. B. Susceptible to decay and termites. C. Dimensional stability unaffected by humidity. D. Noncombustible, enabling its use in higher construction types and larger buildings.
Answer:
C. Dimensional stability unaffected by humidity
Explanation:
very wide range of lightweight structural sections are produced by cold forming thin gauge strip material to specific section profiles. These are often termed light gauge or cold formed steel sections. In most cases, galvanized steel strip material is used.
Light gauge steel structures have many of the advantages of light wood framed structures: They are light, and allow quick building without heavy tools or equipment. Every component can easily be carried by hand - a house is like a carpentry job on a larger scale.
Light framed structures allow the passage of sound more readily than the more solid masonry construction.
Light gauge steel will lose strength in the advent of fire. Adequate fire protection must be used.
Light gauge steel structures are non-combustible, which is a code requirement for some types of structures.
Why was the term inert gas once used to refer to noble gases and why is it no longer in common use?
Answer:
Because unlike inert gas Noble gas sometimes indergo reaction
Explanation:
Inert gas as the name suggest means it can not undergoing reaction at most conditions.But as a science progresses it was found that some group 8 elements under special conditions of temperature and pressure can under go reaction this discovery led to why inert gas is not commonly used
Answer:
Explanation:
Noble gases are gases that belongs to group 18(8A) in the periodic table, they have 8 electrons in their outermost shell. Examples includes helium, neon, argon, krypton and Radon.
These gases were formerly referred to as inert gases meaning they are chemically inactive, this is because they have a complete octet structure which makes them stable, but as time goes on scientist realised that referring to these gases as inert might not be outrightly correct because :
1.Some members of the noble gases form compounds meaning that they are not inert under all conditions, for example Xenon tetrafluoride
2.Radon is a dangerous radioactive element, it unstable to such an extent that its radioactivity makes any chemical reaction with it almost impossible.
3.Gases like Nitrogen are inert under various conditions.
When laser light shines on a screen after passing through two closely spaced slits, it becomes
Answer:
diffracted into semicircular waves. constructive interference occurs where the waves are crest to crest or trough to trough, destructive interference occurs where they are crest to trough. The light that falls on the screen produces bands of light and dark fringes on the screen as a result of these constructive and destructive interferences. This is called the young's slit experiment.
Laser light passing through two closely spaced slits and shining on a screen will produce an interference pattern of bright and dark fringes due to the wave properties of light, specifically diffraction and interference, which is illustrated through Young's double-slit experiment.
Explanation:When a laser light passes through two closely spaced slits and shines on a screen, it creates an interference pattern known as interference fringes. This phenomenon occurs due to the wave property of light known as diffraction and interference. Light waves passing through the two slits interfere with each other, creating a series of bright and dark lines or fringes on the screen.
The bright lines, called constructive interference, happen when the light waves enhance each other, and the dark lines, called destructive interference, occur when the light waves cancel each other out. The spacing and number of these fringes depend on the wavelength of the laser light and the distance between the slits. This is illustrated through Young's double-slit experiment.
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A dumbbell-shaped object is composed by two equal masses, m, connected by a rod of negligible mass and length r. If I_1 is the moment of inertia of this object with respect to an axis passing through the center of the rod and perpendicular to it and l_2 is the moment of inertia with respect to an axis passing through one of the masses, it follows that l_1 = l_2. l_l > l_2. l_2 > l_1
Answer:[tex]I_2>I_1[/tex]
Explanation:
Given
Shape of the object is dumbbell shaped
Moment of Inertia w.r.t an axis passing through center and perpendicular to it
[tex]I_1=m(\frac{r}{2})^2+m(\frac{r}{2})^2[/tex]
[tex]I_1=\frac{mr^2}{2}[/tex]
For the axis which passes through one of the masses
[tex]I_2=mr^2[/tex]
so [tex]I_2>I_1[/tex]
Solids,liquids,and gases are three forms of matter that?
The total momentum of two marbles before a collision is .06 kg·m/s. No outside forces act on the marbles. What is the total momentum of the marbles after the collision?
Answer:
0.06kgm/s
Explanation:
According to law of conservation of momentum, the sum of momentum of bodies before collision is equal to the momentum of the bodies after collision.
If the total momentum of two marbles before collision is 0.06kgm/s and no outside marbles acts on them, then the momentum of the bodies after collision will also be 0.06kgm/s. This type of collision is elastic i.e both momentum and energy are conserved since no external force acts on them.
A student lifts a 1.5 kg book from a chair seat 41 cm off the ground to a table that is 71 cm off the ground.
What is the book's change in gravitational potential energy?
Answer:
4.4j
Explanation:
The change in gravitational potential energy of the book is 3.57 J.
Explanation:The change in gravitational potential energy of the book can be calculated using the equation:
ΔPE = mgh
where ΔPE is the change in potential energy, m is the mass of the book, g is the acceleration due to gravity (9.8 m/s²), and h is the change in height.
In this case, the mass of the book is 1.5 kg, the initial height is 41 cm (or 0.41 m), and the final height is 71 cm (or 0.71 m).
Substituting these values into the equation:
ΔPE = (1.5 kg)(9.8 m/s²)(0.71 m - 0.41 m) = 3.57 J
Therefore, the book's change in gravitational potential energy is 3.57 J.
Which of the following describes wavelength?
A.
the number of waves that pass a point in a given amount of time
B.
the distance between crests of adjacent waves
C.
the distance a wave travels in a given amount of time
D.
the height of a wave
Answer:
B.
Explanation:
The distance between two crests of adjacent waves is called wavelength.
Final answer:
Wavelength is (option B) the distance between consecutive crests of adjacent waves and is parallel to the direction of wave propagation, typically represented by the Greek letter lambda (λ).
Explanation:
The correct description of wavelength in the context of waves is the distance between crests of adjacent waves. Wavelength is the distance between two consecutive points of similar position along the wave such as from one crest to the next crest, or one trough to the next trough. It's important to note that wavelength is parallel to the direction in which the wave is traveling, so it measures the length of one complete cycle of the wave.
Options such as the number of waves passing a point in a given time (frequency) and the wave's height (amplitude) are different wave properties. Thus, the correct answer is option B: the distance between crests of adjacent waves.
A policeman investigating an accident measures the skid marks left by a car on the horizontal road. He determines that the distance between the point that the driver slammed on the brakes (thereby locking the wheels) and the point where the car came to a stop was 28.0 m. From a reference manual he determines that the coefficient of kinetic friction between the tires and the road under the prevailing conditions was 0.300. How fast was the car going when the driver applied the brakes
Answer:
The car was 12.8m/s fast when the driver applied the brakes.
Explanation:
The equations of motion of the car in the horizontal and vertical axes are:
[tex]x: f_k=ma\\\\y: N-mg=0[/tex]
Since the kinetic friction is defined as [tex]f_k=\mu_kN[/tex] and [tex]N=mg[/tex] we have:
[tex]\mu_kmg=ma\\\\a=\mu_kg[/tex]
Next, from the kinematics equation of speed in terms of distance, we have:
[tex]v^2=v_0^2-2ax\\\\v^2=v_0^2-2\mu_kgx[/tex]
Since the car came to a stop, the final velocity [tex]v[/tex] is zero, and we get:
[tex]0=v_0^2-2\mu_kgx\\\\v_0=\sqrt{2\mu_kgx}[/tex]
Finally, plugging in the known values, we obtain:
[tex]v_0=\sqrt{2(0.300)(9.81m/s^2)(28.0m)}\\\\v_0=12.8m/s[/tex]
It means that the car was 12.8m/s fast when the driver applied the brakes.
The car was moving at the speed of 12.8 m/s, when the driver applied the brakes.
From kinamatic equation,
[tex]\bold {v^2 = v_0^2-2ax}\\[/tex]
Since, car stops the final veocity will be zero. and
Acceleration [tex]\bold {a = \mu_kg}[/tex]
So,
[tex]v_0 = \sqrt {2\mu k_gx}[/tex]
Where,
Vo - initial speed =?
[tex]\mu[/tex] - friction constant = 0.3
g - gravitational acceleration = 9.8 m/s²
x - distance = 25 m
Put the values,
[tex]v_0 = \sqrt {2\times 0.3 \times 9.81 \times 0.25 m}\\\\v_0 = 12.8\ m/s[/tex]
Therefore, the car was moving at the speed of 12.8 m/s, when the driver applied the brakes.
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A light bulb produces light with frequency = 4.65 x 1014 Hz. What is the wavelength of light the bulb produces?
6.45 x 10-7 meters
1.55 x 106 meters
6.45 x 1021 meters
1.395 x 1023 meters
Answer:
6.45 x 10-7 meters
Explanation:
Taking speed of light as 300000000 m/s
We know that speed of light is product of wavelength and frequency and expressed as
s=fw
Where s represent speed, f is frequency and w is wavelength
Substituting 4.65*10^14 Hz for frequency then the wavelngth will be given by
300000000=4.65*10^14 *w
w=300000000÷4.65*10^14
w=6.451612903225*10^-7 m
Rounded off, the wavelength is 6.45 x 10-7 meters
Ablock is released from rest al height d= 40 cm and slides down a frictionless ramp and onto a first plateau, which has length d and where the coefficient of kinetic friction is 0.50. If the block is still moving, it then slides down a second frictionless ramp through height d/2 and __________.
Here is the complete part of the question
A block is released from rest at height d= 40 cm and slides down a frictionless ramp and onto a first plateau, which has length d and where the coefficient of kinetic friction is 0.50. If the block is still moving, it then slides down a second frictionless ramp through height d/2 and onto a lower plateau, which has length d/2 and where the coefficient of kinetic friction is again 0.50. If the block is still moving, it then slides up a frictionless ramp until it (momentarily) stops. Where does the block stop?
Answer:
0.3 m
Explanation:
Given that :
the height h = 40 cm = 0.40 m
Coefficient of kinetic friction is [tex]\mu[/tex] =0.50
Using the Law of conservation of energy = [tex]\frac{1}{2} m \mu_1^2 = mgd[/tex]
As the blocks slides down a frictionless ramp and onto a first rough plateau region.So kinetic energy is decreased to :
[tex]\frac{1}{2}mu^2_2 = mgd - \mu_2_k mgd \\ \\ u^2_2 = 2gd - 2 \mu_kgd[/tex]
If the block is still moving, it then slides down a second frictionless ramp through an height h = d/2
Then , we can say that the gained kinetic energy is :
[tex]\frac{1}{2} mu_2^2 = mg (\frac{d}{2})+\frac{1}{2}mu_2^2 \\ \\ \frac{1}{2} mu_2^2 = mg (\frac{d}{2})+ mgd - \mu_k mgd \\ \\ \frac{1}{2} mu_2^2 = 2g(\frac{d}{2})+2gd - 2 \mu_k gd[/tex]
Futhermore , it moves on the horizontal surface where the coefficient of friction causes some of the kinetic energy to disappear
So, the final value of kinetic energy at the end just before climbing is :
[tex]\frac{1}{2}mv^2 = \frac{1}{2}m \mu_2 ^2 - \mu_k mg (\frac{d}{2}) \\ \\ \frac{1}{2}mv^2 = mg \frac{d}{2} + mgd - \mu_k mgd - \mu_k mg (\frac{d}{2}) \\ \\ v^2 = gd + 2gd - 2 \mu_kgd -\mu_kgd[/tex]
[tex]= 3gd - 3 \mu_k gd \\ \\ = 3[g- \mu_kg ]d[/tex]
Let represent H to be the height above the lower plateau when it momentarily stops; From the law of conservation of energy :
[tex]\frac{1}{2}mv^2 = mgH \\ \\ \frac{3}{2}[g-\mu_kg]d = gH \\ \\ H = \frac{3}{2}[1-\mu_k]d \\ \\ = \frac{3}{2}[1-(0.50)](0.40 \ m) \\ \\ =0.3 m[/tex]
1. In the picture below, energy is being converted to heat water. What type of energy transformations take place in this model?
Kinetic energy is formed when water is heated.
Explanation:
Suppose in an electric kettle there is water , when water is boiled the electrical energy changes into thermal energy when heating is done.The thermal energy then gets transferred to the water . When the boiling takes place in the water the energy gets transformed into sound. Lastly at the end the gravitational potential energy finally changes to the kinetic energy.There are three types of energy transformations taking place
(i) conversion of kinetic energy to rotational energy
(ii) conversion of rotation energy to electrical energy
(iii) conversion of electrical energy to heat energy
As seen in the image attached, there is running water that is falling on the blades of a small turbine and makes it rotate. The turbine is connected to the heating system with wires.
Now, the energy transformations that take place in heating water are described as follows:
The flowing tap water is falling on the blades of the turbine which produces torque and makes the blade rotate. Hence, the kinetic energy of the tap water is converted into rotational energy.Now the turbine is connected to the heating system with wire, which means it must produce electricity. Here, The rotation energy is converted into electrical energy. Lastly, the electrical energy produced by the turbine is being converted into heat energy by the heating system to warm water.Learn more:
https://brainly.com/question/19305456?referrer=searchResults
Technician A says that in any type of fluid coupling not equipped with a mechanical lock-up some slippage exists resulting in a difference between input and output speeds. Technician B says that in torque converter coupling phase impeller and turbine rpms match. Who is correct
Final answer:
Technician A is correct, as there is slippage between input and output speeds in fluid couplings without a mechanical lock-up. Technician B is incorrect, as the impeller and turbine rpms do not match in a torque converter coupling.
Explanation:
Technician A is correct. In any type of fluid coupling without a mechanical lock-up, there is always some slippage between the input and output speeds. This means that the output speed will be less than the input speed, resulting in a difference between them.
Technician B is incorrect. In a torque converter coupling, the impeller and turbine do not have matching rpm (revolutions per minute). The impeller rpm is higher than the turbine rpm, which allows the torque converter to efficiently transfer power from the engine to the transmission.
How much mass does the sun lose through nuclear fusion per second?
Answer:
1.10^6 kg of mass per second
Explanation:
All energy lost by the sun comes from nuclear fusion.
Sun loses energy at 2.5*10^{19}J per hour, that is 9*10^{22}J/s
To find the mass lost by the sun in liberation of energy you use the famous Einstein's equation:
[tex]E=mc^2\\\\m=\frac{E}{c^2}=\frac{9*10^{22}}{(3*10^{8}m/s)^2}=1*10^6kg[/tex]
hence, the sun liberates 1.10^6 kg of mass per second