a 1300-kg car moving on a horizontal surface has speed v = 65 km/h when it strikes a horizontal coiled spring and is brought to rest in a distance of 2.1 m. What is the spring stiffness constant of the spring? Express your answer using two significant figures.
Answers
Answer:
Approximately \(9.7\times 10^{6}\; {\rm N\cdot m^{-1}}\).
Explanation:
Apply unit conversion and ensure that the initial speed of the vehicle is in the standard unit of meters per second:
\(\begin{aligned}v &= 65\; {\rm km\cdot h^{-1}}\, \frac{1\; {\rm h}}{3600\; {\rm s}}\cdot \frac{1000\; {\rm m}}{1\; {\rm km}} \\ &\approx 18.1\; {\rm m\cdot s^{-1}} \end{aligned}\).
Before hitting the spring, the kinetic energy (\(\text{KE}\)) of this vehicle would be:
\(\begin{aligned} (\text{KE}) = \frac{1}{2}\, m\, v^{2} \end{aligned}\),
Where:
\(m = 1300\; {\rm kg}\) is the mass of the vehicle, and\(v = 18.1\; {\rm m\cdot s^{-1}}\) is the speed of the vehicle.Let \(k\) denote the spring constant. When the spring is compressed by \(x\) from equilibrium, the elastic potential energy (\(\text{EPE}\)) in the spring would be:
\(\displaystyle (\text{EPE}) = \frac{1}{2}\, k\, x^{2}\).
Assuming that the kinetic energy of the vehicle was entirely turned into the elastic potential energy in the spring:
\((\text{loss in KE}) = (\text{gain in EPE})\).
\(\begin{aligned}\frac{1}{2}\, m\, v^{2} &= \frac{1}{2}\, k\, x^{2}\end{aligned}\).
Rearrange this equation to find the spring constant \(k\):
\(\begin{aligned}k &= \frac{m\, v^{2}}{x^{2}} \\ &\approx \frac{(1300)\, (18.1)^{2}}{(2.1)^{2}}\; {\rm N\cdot m^{-1}} \\ &\approx 9.7\times 10^{6}\; {\rm N\cdot m^{-1}} \end{aligned}\).
Related Questions
Which statement best describes why an organism would carry out aerobic respiration?
It needs to store sugars and is unable to process glucose.
It needs to create glucose to be used for energy later.
It needs to process carbon dioxide and does not have oxygen available.
It needs to generate energy and has oxygen available.
Answers
Aerobic respiration is used by an organism because it needs to generate energy and has availability of oxygen. Option D is correct.
Aerobic respiration is a cellular process that occurs in the presence of oxygen and involves the breakdown of glucose to produce ATP (adenosine triphosphate), which is the main energy currency of cells. Organisms carry out aerobic respiration to generate energy needed for various cellular functions such as growth, metabolism, movement, and reproduction.
Oxygen acts as the final electron acceptor in the electron transport chain of aerobic respiration, allowing for the efficient production of ATP through oxidative phosphorylation. If an organism has access to oxygen, it would preferentially use aerobic respiration to produce ATP because it is more efficient in generating energy compared to other forms of cellular respiration.
Hence, D. is the correct option.
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--The given question is incomplete, the complete question is
"Which statement best describes why an organism would carry out aerobic respiration? A) It needs to store sugars and is unable to process glucose. B) It needs to create glucose to be used for energy later. C) It needs to process carbon dioxide and does not have oxygen available. D) It needs to generate energy and has oxygen available."--
Prepare a summary to explain how much the final birds varied from the original birds after 1 million years of natural selection. How does natural selection explain the changes? Use the following terms or phrases in your explanation: natural selection, survival, genetic variation, and extinction.
Answers
Answer:
what????????
Explanation:
what is the magnitude of the potential difference needed to give an alpha particle (composed of 2 protons and 2 neutrons) 324.0 kev of kinetic energy? (in kv)
Answers
The magnitude of the potential difference needed to give an alpha particle 324.0 keV of kinetic energy is 2.50 x 10^6 kV.
The magnitude of the potential difference needed to give an alpha particle 324.0 keV of kinetic energy is calculated using the formula KE=1/2mv^2. Here, m is the mass of the alpha particle (6.644 x 10^-27 kg) and v is its velocity.
Thus, we have 324.0 keV = (1/2) (6.644 x 10^-27 kg)[v^2].
Solving for v, we get v = 1.38 x 10^7 m/s.
The potential difference, V, can then be calculated using the formula
V = (mv^2)/(2e)
where e is the charge of the alpha particle (charge of two protons, or 4.803 x 10^-10 C).
Thus, V = (6.644 x 10^-27 kg)(1.38 x 10^7 m/s)^2/(2(4.803 x 10^-10 C)) = 2.50 x 10^6 kV.
Therefore, the magnitude of the potential difference needed to give an alpha particle 324.0 keV of kinetic energy is 2.50 x 10^6 kV.
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2. During a summer storm, a bolt of lightning is seen. A short time later, thunder is heard. If the lightning struck 3.50 km away, what was the time period between the lightning and thunder? The speed of sound in air is 331.0 m/s at 0.00 °C but the temperature is actually a warm 30.0 °C. Show your work!
Answers
The time period between the lightning and thunder is approximately 12.84 seconds.
Speed = Distance x Time
The time period between the lightning and thunder can be calculated using the formula:
time = distance / speed
First, we need to convert the distance from kilometers to meters, as the speed of sound is given in meters per second:
distance = 3.50 km = 3,500 meters
Next, we need to adjust the speed of sound for the temperature of the air. The speed of sound in air increases with temperature, so we can use the following equation to calculate the speed of sound at 30.0 °C:
speed = 331.0 m/s * sqrt(1 + (30.0 °C / 273.15 K))
where 273.15 K is the standard temperature of 0.00 °C in Kelvin.
Plugging in the values, we get:
speed = 331.0 m/s * sqrt(1 + (30.0 °C / 273.15 K))
= 331.0 m/s * sqrt(1 + 0.109)
= 351.9 m/s (rounded to one decimal place)
Now we can calculate the time period between the lightning and thunder:
time = distance / speed
= 3,500 meters / 351.9 m/s
= 9.954 seconds (rounded to three decimal places)
However, this calculation only gives us the time it takes for the sound to travel from the lightning to our location. We also need to account for the time it took for us to hear the thunder after it was produced. The speed of sound is approximately 343 m/s at normal atmospheric pressure and temperature, so we can use this value to calculate the additional time:
time = distance / speed + time delay
= 3,500 meters / 343 m/s + 0.00 seconds
= 10.204 seconds (rounded to three decimal places)
Therefore, the time period between the lightning and thunder is approximately 10.204 seconds, or about 12.84 seconds (rounded to two decimal places) if we include the delay due to the speed of sound.
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The downward force due to water on a diver under water is about one thousand newtons. Why this force is not pushing him down?.
Answers
The 1000 newtons isn't pushing down the diver because it is balanced out by the 1000 newtons of force from the downward direction onto the down surface of the diver.
This will happen if the buoyant force on the diver is equal to the weight of that diver
The principle of buoyancy holds that the buoyant or lifting force of an object submerged during a fluid is equal to the weight of the fluid it has displaced. The concept is additionally known as Archimedes's principle, after the Greek mathematician, physicist, and inventor Archimedes (c. 287-212 b.c.), who discovered it.
Applications of Archimedes's principle are often seen across a wide vertical spectrum: from objects deep beneath the oceans to those floating on its surface, and from the surface to the upper limits of the stratosphere and beyond.
Buoyancy is usually a double-edged proposition.
If the buoyant force on an object is greater than the weight of that object,
In other words, if the thing weighs less than the amount of water it has displaced—it will float.
But if the buoyant force is a smaller amount than the object's weight, the thing will sink.
It stays at same place if both forces cancel out each other.
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It takes 700 joules to lift an object straight up, but 1400 joules to push it up a ramp, what is the
efficiency of the ramp?
Answers
Answer:
561
Explanation: it would most definitely go down as a number because it isn't the same
a galvanometer of 50 ohms and 1m a can be converted into voltmeter of range 0 - 5v connecting the resistance of
Answers
One of the descriptions below is from the perspective of anatomical study, the rest are from a physiological perspective. Select the description below that comes from
an anatomical perspective
Answers
Answer:
The innermost lining of the lungs is composed primarily of thin tissue cakes simple squamous epithelium.
Explanation:
A light ray travels through water and reflects off a glass surface back into the water. How do the phases of the incident light and the reflected light compare?.
Answers
The light travels through water and gets reflected off on the glass surface into the water. There had been a 180° phase change between the incident and the reflected wave. This is called Total internal reflection (TIR).
In total internal reflection, in physics, a ray of light in a medium such as water or glass is completely reflected back into the medium from the surrounding surfaces. This phenomenon occurs when the angle of incidence is greater than a certain critical angle called the critical angle.
TIR only occurs when both of the following two conditions are met
Light is in a denser medium and is approaching a less dense medium. The angle of incidence should be greater than the so-called critical angle.Thus, the phases which include the TIR are the incident and the reflected phase and the incident light hits the surface while the reflected light reflects back.
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what is the unit of destiny what are the basic unit involve in it
Answers
The basic unit involved are kg which is weight of the body and m^3 which is the area of the body
A container gas expands to fill a 3l container has a mass of 129g what is its density
Answers
A container gas expands to fill a 3l container and has a mass of 129g its density is equal to 0.043 \(kgm^{-3}\)
Let's understand the answer in detail
Density is equal to the mass of a substance divided by its volume. The SI unit of density is Kg/m3. Other units of density are g/cm3, g/mL, kg/L
The formula we are using is going to be
D=m/v, where
D= density
m=mass
V=volume
The data that is given to us states that
mass = 129g
volume= 3 L
density = ?
Now we will put the values in the formula,
d= m/v
d = 0.129 Kg / 3L
d = 0.043 Kg / L
Therefore the density of the gas is 0.043 Kg / L.
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What happens to the water after it goes
down the drain?
Answers
Answer:
, it flows through your community's sanitary sewer system to a wastewater treatment facility.
When a p.D of 150 qpplied to the plates of a parallel plate. The plate carry a surface charge density of 30nc/cm^2 what is the spacing bettwen the plates
Answers
Answer:
d = 4.425 x 10⁻⁶ m = 4.425 μm
Explanation:
The charge on plates can be given as:
\(q = \sigma A=CV\\where,\\\\C = Capacitance\ of\ parallel\ plate\ capacitor = \frac{\epsilon_oA}{d}\\\\therefore,\\\\\sigma A=(\frac{\epsilon_oA}{d})V\\\\d = (\frac{\epsilon_o}{\sigma})V\)
where,
d = spacing between plates = ?
ε₀ = Permitivity of free space = 8.85 x 10⁻¹² C²/Nm²
σ = surface charge density = (30 nC/cm²)(10⁻⁹ C/1 nC)(1 cm²/10⁻⁴ m²)
σ = 3 x 10⁻⁴ C/m²
V = Potential Difference = 150 V
Therefore,
\(d = \frac{(8.85\ x\ 10^{-12}\ C^2/Nm^2)}{3\ x\ 10^{-4}\ C/m^2}(150\ V)\\\)
d = 4.425 x 10⁻⁶ m = 4.425 μm
16. True/False: Protons are exchanged between objects by induction
Answers
Five workers from the same factory developed angiosarcoma, a rare cancer of the veins and arteries. Which part of the scientific method is this? Group of answer choices conclusion experiment observation none of these hypothesis
Answers
Answer:
a
Explanation:
i took the test
Five workers from the same factory developed angiosarcoma, a rare cancer of the veins and arteries. This is observation of the scientific method.
What is scientific method?Since at least the 17th century, the scientific method—an empirical approach to learning—has guided the advancement of science. Since one's interpretation of the observation may be distorted by cognitive presumptions, it requires careful observation and the application of severe skepticism regarding what is observed.
It entails developing hypotheses through induction based on these observations, testing the validity of those hypotheses through experimental and measurement-based statistical testing of the inferences made from them, and then fine-tuning (or discarding) those hypotheses in light of the experimental results.
These are the guiding principles of the scientific process, as opposed to a predetermined set of steps that apply to all scientific endeavors.
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if the electron affinity for an element is a negative number, does it mean that the anion of the element is more stable than the neutral atom?
Answers
No, the anion of the element is more stable than the neutral atom but an electron in an atom or ion is lower in energy than a free electron.
We know that,
Kinetic energy is defined as the energy of the object that occurs due to the motion of the object. The total work needed by the body to starts accelerating it by the help of given mass which is supplied from the rest position and its mentioned velocity.
The energy body gets due to the process of acceleration by this the body will able to main the kinetic energy of the body without changing the speed of the body.
The energy which has been stored in the body or any object by the help of the particular position or the proper arrangement of the parts is known as potential energy.
There will be no effect of the outside environment on the potential energy that present inside the body.
The kinetic energy decrease or increase with change into the velocity.
Therefore, No, the anion of the element is more stable than the neutral atom but an electron in an atom or ion is lower in energy than a free electron.
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The figure shows the standard way of measuring the angle. The angle θ is measured to the vector from the x axis, and counterclockwise is positive.
Express Fx and Fy in terms of the length of the vector F and the angle θ, with the components separated by a comma.
Fx, Fy = _____
Answers
Answer:
i would help but im just as confused. sorry.
for an ideal monoatomic gas, the internal energy U os due to the kinetic energy and U=3/2RT per mole.show that cv=3/2R per mole and Cp=5/2RPer mole
Answers
Answer:
i. Cv =3R/2
ii. Cp = 5R/2
Explanation:
i. Cv = Molar heat capacity at constant volume
Since the internal energy of the ideal monoatomic gas is U = 3/2RT and Cv = dU/dT
Differentiating U with respect to T, we have
= d(3/2RT)/dT
= 3R/2
ii. Cp - Molar heat capacity at constant pressure
Cp = Cv + R
substituting Cv into the equation, we have
Cp = 3R/2 + R
taking L.C.M
Cp = (3R + 2R)/2
Cp = 5R/2
What determines a wave’s velocity? a The number of waves per a period of time. b The amplitude of the wave. c The medium it travels through. d How much constructive interference there is.
Answers
Answer:
A
Explanation:
I'm pretty sure that this answer is correct please let me know!
Please Help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
An electron is in motion at 4.0 × 10^6 m/s horizontally when it enters a region of space between two parallel plates, as shown, starting at the negative plate. The electron deflects downwards and strikes the bottom plate. The magnitude of the electric field between the plates is 4.0 x 10^2 N/C and separation between the charged plates is 2.0 cm.
Determine the horizontal distance travelled by the electron when it hits the plate.
Answers
Answer:
Given that
speed u=4*10^6 m/s
electric field E=4*10^3 N/c
distance b/w the plates d=2 cm
basing on the concept of the electrostatices
now we find the acceleration b/w the plates to find the horizontal distance traveled by the electron when it hits the plate.
acceleration a=qE/m=\(1.6*10^{-19}*4*10^3/9.1*10^{-31} =0.7*10^{15}\)=\(7*10^{14}\) m/s
now we find the horizontal distance traveled by electrons hit the plates
horizontal distance
\(X=u[2y/a]^{1/2}\)
=\(4*10^6[2*2*10^{-2}/7*10^{14}]^{1/2}\)
=\(3*10^{-2}\)= 3 cm
What is SI unit of frequency Mcq?.
Answers
The hertz (Hz) is the SI frequency unit named after the German physicist Heinrich Hertz; one hertz means that an event occurs once every second.
What is frequency?The frequency of a repeating event is the number of occurrences per unit of time. It is distinct from angular frequency and is sometimes referred to as temporal frequency. The unit of frequency is hertz, which equals one event per second. The number of waves that pass through a fixed point in a given amount of time is described by frequency. So, if a wave takes half a second to pass, the frequency is 2 per second. The frequency is 100 per hour if it takes 1/100 of an hour.
Here,
The hertz (Hz) is the SI unit of frequency, named after the German physicist Heinrich Hertz; one hertz means that an event occurs once every second.
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A 72.0 kg ice skater is moving at 3.1 m/s on frictionless ice throws a 0.21 kg snowball horizontally at a speed of 28.0 m/s. What is the final velocity of the skater?
Answers
Answer:
the final velocity of the skater after throwing the snowball is 3.17 m/s.
Explanation:
Given;
mass of the ice skater, m₁ = 72 kg
initial velocity of the ice skater, u₁ = 3.1 m/s
mass of the snowball, m₂ = 0.21 kg
initial speed of the snowball, u₂ = 28.0 m/s
Let the final velocity of the skater after throwing the snowball = v
Apply the principle of conservation of linear momentum to determine v;
m₁u₁ + m₂u₂ = v(m₁ + m₂)
72 x 3.1 + 0.21 x 28 = v(72 + 0.21)
229.08 = v(72.21)
v = 229.08 / 72.21
v = 3.17 m/s
Therefore, the final velocity of the skater after throwing the snowball is 3.17 m/s.
A rock is thrown off a 25 m cliff at 60m/s. It was thrown 32° above the ground
How long will the rock be in the air before it hits the ground?
Answers
The rock has a height y at time t according to
y = 25 m + (60 m/s) sin(32°) t - 1/2 gt ²
where g = 9.8 m/s² is the magnitude of the acceleration due to gravity.
Solve for t when y = 0. The quickest way to do this is with the quadratic formula.
0 = 25 m + (60 m/s) sin(32°) t - 1/2 gt ²
t = (-(60 m/s) sin(32°) + √[(60 m/s)² sin²(32°) - 4 (25 m) (-1/2 gt ²)]) / 2
(ignoring the negative root because that would make t negative)
or approximately
t ≈ 7.2 s
Does science support the idea that humans have influenced global warming?
Provide specific examples that show how two knowledgeable individuals with differing opinions might argue.
Answers
Answer:
A: Scientists agree that the earth's rising temperatures are fueling longer and hotter heat waves, more frequent droughts, heavier rainfall, and more powerful hurricanes.
Explanation:
Rain comes down with a velocity of -15 m/s and hits the roof of a car. The mass of rain per second that strikes the roof of the car is 0. 060 kg/s. Assuming that rain comes to rest upon striking the car, find the average force exerted by the rain on the roof
Answers
The average force exerted by the rain on the roof of the car is approximately 0.99N.
To calculate the average force wielded by rain on the auto's roof, we may use the force formula, F = ma, where F is the force, m is the mass, and an is the acceleration. In this script, the mass of rain falling on the auto's roof each second is0.060 kg/s.
Assuming that the rain comes to a stop when it hits the machine, we may assume that the rain's acceleration is equal to its haste, which is-15 m/s. Using the data handed, we can cipher the force wielded by rain on the auto's roof as follows
F = ma
F = 0.060 kg/s × (-15 m/s)
F = -0.9 N
Therefore, the average force exerted by the rain on the roof of the car is 0.9 N.
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what is the speed of a wave has a wavelength of 0.5 m/s and a frequency of 2 hz?
Answers
Answer: The equation that relates wavelength and frequency for electromagnetic waves is: λν=c where λ is the wavelength, ν is the frequency and c is the speed of light.
10/0.5=20 meter.
Explanation:
The speed of a wave has a wavelength of 0.5 m/s and a frequency of 2 hz is 0.25 m.
What is wave ?Wave is is a disturbance in a medium that carries energy as well as momentum . wave is characterized by amplitude, wavelength and phase. Amplitude is the greatest distance that the particles are vibrating. especially a sound or radio wave, moves up and down. Amplitude is a measure of loudness of a sound wave. More amplitude means more loud is the sound wave.
Wavelength is the distance between two points on the wave which are in same phase. Phase is the position of a wave at a point at time t on a waveform.
There are two types of the wave longitudinal wave and transverse wave.
Longitudinal wave : in which, vibration of the medium (particle) is parallel to propagation of the wave. Sound wave is a longitudinal wave.
Transverse wave : in which, vibration of the medium (particle) is perpendicular to propagation of the wave. Light wave is a Transverse wave.
The relation between velocity, frequency and wavelength is,
c = λν
Where λ is wavelength, ν is frequency and c is velocity.
Given,
c = 0.5 m/s
ν = 2 hz
λ = ?
Putting all the values in the equation,
0.5 = 2λ
λ = 0.5/2 = 0.25 m
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when using the ziehl-neelsen acid-fast stain, acid-fast cells are ____and nonacid-fast cells are _____.
Answers
In the Ziehl-Neelsen acid-fast stain, acid-fast cells are stained bright red, while nonacid-fast cells are stained blue or counterstained with a contrasting color.
The Ziehl-Neelsen acid-fast stain is a technique commonly used in microbiology to differentiate acid-fast bacteria from nonacid-fast bacteria. Acid-fast cells, such as those of the Mycobacterium genus which includes the causative agent of tuberculosis, have a unique cell wall composition that makes them resistant to decolorization by acid-alcohol. As a result, when the stain is applied, acid-fast cells retain the primary stain (carbol fuchsin) and appear bright red under a microscope.
Nonacid-fast cells, on the other hand, do not have the same cell wall composition and are susceptible to decolorization. After the application of acid-alcohol, nonacid-fast cells lose the primary stain and are subsequently counterstained with a contrasting color, often methylene blue. This counterstain allows them to be visualized as blue or a different color, differentiating them from the acid-fast cells.
By employing the Ziehl-Neelsen acid-fast stain, microbiologists can effectively distinguish acid-fast bacteria from nonacid-fast bacteria, aiding in the identification and diagnosis of specific bacterial infections, particularly those caused by acid-fast pathogens.
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What is the momntum of a football player that has a mass of 50 kg and
a velocity of 3m/s? *
Answers
Answer:
150 kg.m/sExplanation:
The momentum of an object can be found by using the formula
momentum = mass × velocity
From the question we have
momentum = 50 × 3 = 150
We have the final answer as
150 kg.m/sHope this helps you
what is the magnitude of the train's angular acceleration after it is released?
Answers
The magnitude of the train's angular acceleration after it is released cannot be determined without additional information, such as the train's mass, the radius of the curve it is on, and the forces acting on it.
Angular acceleration is the rate at which the angular velocity of an object changes with respect to time.
To calculate the magnitude of the angular acceleration, one would need to know specific details about the train and the forces acting on it, such as its mass, the radius of the curve it is on, and any external forces affecting its motion.
Summary: To determine the train's angular acceleration after it is released, additional information about the train and the forces acting on it is needed.
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if an nfl football has a mass of 430 g. what is the velocity of the system after the catch? assume both are moving to the right, and round your answer to two decimal points.
Answers
To determine the velocity of the system after the catch, we need to consider the concept of momentum conservation. The momentum of an object is the product of its mass and velocity.
Given that the mass of the NFL football is 430 g, we need to convert it to kilograms:
Mass = 430 g = 0.43 kg
Let's assume the football is caught by a receiver who is also moving to the right. Since both the football and the receiver are moving in the same direction, their velocities will have the same sign.
The momentum before the catch is zero since the football is in motion and the receiver is stationary. After the catch, the momentum of the system should still be zero to conserve momentum.
Using the equation for momentum:
Momentum = Mass × Velocity
Since the momentum before the catch is zero, the momentum after the catch should also be zero. Therefore, the product of the mass and velocity of the football and the receiver should sum up to zero.
0 = (Mass of football × Velocity of football) + (Mass of receiver × Velocity of receiver)
Given the mass of the football and assuming the mass of the receiver is unknown, we cannot determine the exact velocity of the system after the catch without additional information.
Therefore, without the mass or velocity of the receiver provided, we cannot calculate the velocity of the system after the catch.
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