The speed of the approaching smaller fish before lunch is 6m/s.
What is the speed?The entire distance that an object travels in a predetermined amount of time is the definition of speed.
Given that the speed v₁ of big fish is 1 m/s and mass m₁ is 6kg. The mass m₂ of small fish is 1 kg.
Both fish have linear momentum of,
p₁ = m₁v₁ + m₂v₂
Where,
p₁ is the initial linear momentum
v₂ is the speed of the small fish.
Since both fish are traveling in the same direction and v is their ultimate meeting velocity, the final linear momentum will be given as,
p₂ = (m₁ + m₂) v
Linear momentum is held constant hence,
p₁ = p₂
m₁v₁ + m₂v₂ = (m₁ + m₂) v
The fish's final speed will be zero because they stopped moving., so
m₁v₁ + m₂v₂ = 0
v₂ = - m₁v₁/m₂
v₂ = -6×1/1
v₂ = -6
The negative symbol indicates that the tiny fish are swimming against the current.
The speed of the approaching smaller fish before lunch is 6m/s.
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L=0.7m
m=2kg
Calculate the frequency of the pendulum
According to the given data the frequency of the pendulum is 0.595 Hz.
What is frequency and Hz?Frequency is defined as the rate of changes in current direction per second. It is given in hertz (Hz), an internationally recognised unit of measurement. One cycle per second is equal to one hertz. Cycles per second are represented by the unit hertz (Hz). A cycle is a full cycle of an opposing current or voltage wave.
What makes frequency important?The time rate of change observed in cyclical and periodic phenomena, such as mechanical motion, audio signals (sound), radio waves, and light, is specified by the frequency, an essential parameter in science and engineering.
Briefing:Calculate the period of oscillations formula is
T = 2π√(L/g)
T = 2 * π * √(0.7/9.80665)
T= 1.678 s
Then the frequency as the reciprocal of the period
f = 1/T
f =1/1.678
f = 0.595 Hz.
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cepheid stars are useful to astronomers as indicators of group of answer choices white-dwarf star behavior. the mechanics of eclipsing variable stars. distance, particularly to stars in our galaxy and to nearby galaxies. stars with very high speed motion.
Option b cepheid stars are useful to astronomers as indicators of distance, particularly to stars in our Galaxy and to nearby galaxies.
An astronomer is a scientist who focuses on the stars, planets, galaxies and other extraterrestrial natural phenomena. The study of astronomy includes everything in the cosmos that is outside of our solar system. This includes celestial bodies that we can see with our unaided eyes, such as the Sun, Moon, planets, and stars. Additionally, it contains celestial bodies like distant galaxies and minute particles that we can only see with telescopes or other tools. On a more urgent level, astronomy aids in our research into how to extend the survival of our species. Studying the Sun's impact on Earth's climate and how it will effect weather, water levels, etc., for instance, is crucial. The broad discipline of natural science known as astronomy is concerned with celestial objects, such as those in the solar system, galaxies, and extragalactic objects. The majority of the fieldwork participants are students who specialize in this broad discipline.
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a small sphere is launched horizontally with a speed v0 toward a target a horizontal distance d away. the sphere lands on the target that is at height h below the height from which the sphere was launched. if the sphere were launched again, but with a speed 2v0 , how high above the target would the sphere have to be launched horizontally to hit the same target, still a horizontal distance d away? responses
The sphere has to be launched 4 times the initial height, h, to hit the same target.
What is the time of motion of the first sphere?The time taken for the first sphere to hit the target is calculated as follows;
d = V₀t₁
where;
V₀ is the initial horizontal velocityd is the horizontal distance travelled by the spheret is the time of motiont₁ = d/V₀
The height travelled by the ball;
h = ¹/₂gt₁²
t₁² = 2h/g
t₁ = √(2h/g)
The time of motion of the second sphere when it is launched at a speed of 2V₀.
t₂ = d/2V₀
t₂ = ¹/₂(d/V₀)
t₂ = ¹/₂(t₁)
The height of fall of the second sphere;
¹/₂(t₁) = √(2h/g)
[¹/₂(t₁)]² = 2h/g
t₁²/4 = 2h/g
t₁² = 4(2h/g)
Thus, the height the sphere need to be launched in order to hit the same target is determined by applying kinematic equation.
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Cocoa is made from _______. a. cacao beans b. cacao leaves c. the meat of the cacao fruit d. milk, butter, sugar and cacao fruit please select the best answer from the choices provided a b c d
The correct option is (a) Cocoa beans are used to make cocoa.
Cocoa bean shapes during manufacture The dried and fully fermented seed of Theobroma cacao, usually known as the cocoa bean or simply cocoa, is where cocoa solids and cocoa butter are extracted.
The dried, fully fermented cacao grain known as Theobroma is what is commonly referred to as a cacao bean or a cocoa bean. Solids, a mixture of nonfat substances, and cocoa butter, or lard, can be extracted from Theobroma cacao. The chocolate and meals from Mesoamerica were made from these cacao beans. As a result, cacao beans are used to create chocolate.
Hence, cocoa is made from cocoa beans.
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a ten-loop coil having an area of 0.23 m2 and a very large resistance is in a 0.047-t uniform magnetic field oriented so that the maximum flux goes through the coil. the coil is then rotated, so the flux goes to zero in 0.34 s. what is the magnitude of the emf induced in the coil during the 0.34 s?
The magnitude of electromotive force is 0.32 volts.
We need to know about the electromotive force of induction to solve this problem. The emf induction appears when there is any change in magnetic flux. The magnitude of emf can be determined by
ε = N dΦ / dt
where N is coil turns, ε is electromotive force, dΦ is change in magnetic flux and dt is time interval.
From the question above, the parameters given are
B = 0.047 T
dt = 0.34 s
N = 10
A = 0.23 m²
Find the change in magnetic flux
dΦ = (B . A)
dΦ = ( 0.047 . 0.23 )
dΦ = 0.01081 Tm²
By substituting the given parameters, we can calculate electromotive force
ε = N . dΦ / dt
ε = 10 . 0.01081 / 0.34
ε = 0.32 volt
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An experiment was performed to determine how the amount of coffee grounds could affect the taste of coffee. The same amount and type of water, the same perking time, and the same electrical sources were used. What is a constant?
A constant in the experiment performed to determine how the amount of coffee grounds could affect the taste of coffee is amount of water.
What is constant in an experiment?Experiment is a test under controlled conditions made to either demonstrate a known truth, examine the validity of a hypothesis, or determine the efficacy or likelihood of something previously untried.
An experiment is conducted using variables such as;
Independent variableDependent variableControlled variable or constantA controlled variable or constant is a factor that is kept constant in a series of experiments in which other factors are varied.
According to this question, in an experiment that was performed to determine how the amount of coffee grounds could affect the taste of coffee, the same amount and type of water, the same perking time, and the same electrical sources were used.
This suggests that the amount of water is a constant in this experiment.
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A student learns that a certain comet in the solar system is considered a short-period comet. Based on this knowledge, what is the student most justified in concluding?.
A student learns that a certain comet in the solar system is considered a short-period comet The comet originates in the Kuiper belt is the student most justified in concluding.
The Sun and the things that circle it make up the gravitationally bound solar system. It was created 4.6 billion years ago when a massive interstellar molecular cloud collapsed because to gravity. The Sun is the system's primary mass source, while Jupiter is home to the majority of the system's leftover mass. Our Sun is called Sol after the Latin word for Sun, "solis," and anything connected to the Sun is referred to as "solar" as a result. The only known example of a habitable planet, the only star we can see up close, and the only planets we can explore with spacecraft are all found in the Solar System. Understanding the genesis and evolution of planets depends on solar system study.
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in a computational model of the energy loss of a house, if the energy flux increases and the total area insulated increases, what happens to the energy loss of the house?
The energy loss can increase or decrease.
In modern houses and systems, insulation is created to maintain heat and reduce losses.
P = ( AΔT ) / R
P is the heat flow, A is the insulated area, T is the temperature difference, and R represents the correlation between the insulation's thermal conductivity and thickness.
In this instance, they suggest that both the flow and the isolated area are growing. We have numerous options.
In this instance, the flow grows faster than the isolated area, increasing heat loss.
The quantity of insulation needed to increase (R) will cause the heat flow to grow by the same amount as the isolated area while keeping losses constant
Losses will reduce if the rate of heat transfer increases more slowly than the area that is insulated.
The two rises in this instance suggest that the heat requests may increase or decrease.
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If a tenth planet were to be discovered with a sidereal period of 125 years, what would be the radius or the orbit (distance from the Sun)? In your answer you need to have the number in the first blank and the correct abbreviated units in the second blank.
From the computation and the use of the Kepler's law, the period of the orbit is period of the orbit is 25 AU.
What is Kepler's law?The term Kepler's law has to do with the relationship between the relationship between the period of the satellite and the radius of the orbit in which the satellite is found.
According to the Kepler's law, we know that the square of the period of the satellite is directly proportional to the cube of the radius of the orbit. Having said this, we need to find the radius of the orbit and we have been told from the question as we have it above that the period of the satellite that is under consideration is 125 years.
Now;
T^2 = r^3
Given that;
T = period
r = radius of the orbit
Then;
r = T^2/3
r = (125)^2/3
r = 25 Au
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Laser light passing through two small slits produces a bright fringe centered at the midpoint on a distant screen because?.
Laser light passing through two small slits produces a bright fringe centered at the midpoint on a distant screen because the light waves travel the same distance from each slit to the midpoint.
Considering that light is composed of both electric and magnetic fields, it often acts as an electromagnetic wave. Magnetic fields oscillate perpendicularly to the wave propagation direction and are perpendicular to one another. They are called transverse waves as a result of this. The following are a few traits of light:
When dealing with light waves, the sine waveform is used. One complete sweep from 0 to 360 degrees makes up the waveform's period. The wavelength and frequency of light waves are two crucial properties. The wavelength is the distance separating the wave's peaks. Light waves have wavelengths that are on the order of nanometers.
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Minerals and vitamins are called
Answer:
micronutrients.
Explanation:
what is the maximum speed with which a 1200- kgkg car can round a turn of radius 95.0 mm on a flat road if the coefficient of static friction between tires and road is 0.60?
The maximum speed will be 0.74m/s
What is friction force?Friction, the force that resists a solid object from sliding or rolling over another. Frictional forces, such as the traction required to walk without slipping, can be beneficial, but they also present significant resistance to motion. About 20% of a car's engine power is expended to overcome the frictional forces of moving parts.
The speed that corresponds to the maximum centripetal force (Fₓ) that could be provided by the friction is given as:
f = Fₓ
f = μN is the friction force. where, μ is the coefficient of static friction and this is the maximum force the friction can provide.
Fₓ = mv²/r
N = mg (flat road)
Thus:
μ mg = mv²/r
So, according to the given question:
μ = 0.60
m = 1200kg
r = 95.0 mm or 95×10⁻³m
μ mg = mv²/r
0.60 × 9.8 = v²/ 95×10⁻³
v² = 558.6 ×10⁻³
v = 0.74m/s
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what is the maximum speed (umax) that the missile could achieve in level flight? (hint: (1) when thrust is equal to the drag, there is no acceleration which means maxi speed. we assumed no drag, so it means when maxi speed is reached, the thrust is 0. (2) at this point, air reaches its maximum temperature, and no fuel injection is needed.) b) what would the velocity be of the gas exiting the nozzle (i.e., ue) at this maximum operating flight speed? c) sketch (qualitatively) the ramjet cycles for both cases (u
a) maximum speed (umax) that the missile could achieve in level flight = 2123 m/s
b) velocity of the gas exiting the nozzle (i.e., ue) at this maximum operating flight speed = 2120 m/s
The direction of a body or object's movement is defined by its velocity. In its basic form, speed is a scalar quantity. In essence, velocity is a vector quantity. It is the speed at which distance changes. It is the displacement change rate.
Given data:
Pressure ratio = 45.5
TSFC = 5.27 * 10⁻⁵ kg/N
Cp = 1150 J/Kg
Wair = 25.5
Ta = 240K
Δhe = 4.4 KJ/kg
Tmax = 2200 K
(a) Maximum speed (Umax):
Ramjet's energy equation:
T₀₂ = Ta + (μ² / 2μ)
[tex]Umax = \sqrt{2Cp (Tmax - Ta})[/tex]
[tex]Umax = \sqrt{2* H50(2200 - 240)}\\ \\Umax = \sqrt{2 * 1150 * 1960}[/tex]
Therefore, Umax = 2123 m/s
(b) Velocity of exiting gas (Ue)
No fuel is provided, thus air expands back to its initial speed i.e., (Ue = U)
The specific thrust = [1 + f] Ue - U = 0
Therefore, Ue = 2120 m/s
(c) T-S diagram of Ramjet cycle:
The T-S schematics for Ramjet at U < Umax and U = Umax are based on the aforementioned two components ( 'a' and 'b')
Ramjets' maximum operating speed is significantly constrained by their maximum operating temperature.
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A car of mass 20kg moving with a velocity of 16m/s collide with a pedestrian moving at a velocity of 0.5m/s in the same direction calculate the magnitude of their common velocity if they move together after collision
The magnitude of their common velocity if they move together after collision is 12.9 m/s.
What is the final velocity after collision?
The final velocity after collision is calculated by applying the principle of conservation of linear momentum as shown below.
m₁u₁ + m₂u₂ = v(m₁ + m₂)
where;
m₁ is the mass of the carm₂ is the mass of the pedestrianu₁ is the initial velocity of the caru₂ is the initial velocity of the pedestrianv is the their common velocity after collision(20)(16) + (5)(0.5) = v(20 + 5)
322.5 = 25v
v = 322.5/25
v = 12.9 m/s
Thus, the car and the pedestrian moved together after the collision suggestion an inelastic collision.
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The complete question is below:
A car of mass 20kg moving with a velocity of 16m/s collide with a pedestrian moving at a velocity of 0.5m/s in the same direction calculate the magnitude of their common velocity if they move together after collision if the mass of the pedestrian is 5 kg.
If a car of mass 20 kg with a velocity of 16 m/s collides with a pedestrian, then the magnitude of common velocity, if they move after the collision of masses, is 12.9 m/s.
What is Collision?Any situation in which two or more bodies quickly exert forces on one other is referred to be a collision. The most common usage of the word "collision" relates to instances where two or more objects collide violently, while the scientific usage of the word does not refer to the amount of force involved.
According to the question, the given values are :
Mass of the car, m = 20 kg
The velocity of the car, u₁ = 16 m/s
The velocity of the pedestrian, u₂ = 0.5 m/s.
m₁ u₁ + m₂ u₂ = v (m₁ + m₂)
(20) × (16) + (5) × (0.5) = v(20 + 5)
322.5 = 25 × v
v = 322.5/25
v = 12.9 m/s
Hence, the magnitude of common velocity is 12.9 m/s.
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The complete question is :
A car of mass 20 kg moving with a velocity of 16 m/s collides with a pedestrian moving at a velocity of 0.5 m/s in the same direction, calculate the magnitude of their common velocity if they move together after a collision if the mass of the pedestrian is 5 kg.
an electron moves from one point a to point b. while moving, the electron remains on an equipotential surface created by nearby charges. what can you say about the speed of the electron as it moved?
At initial speed must the quarter back through the ball for it to reach the reciver.
What is initial speed
The initial speed is the velocity at which motion start.
Sol-
The horizontal velocity is Vi*cos38.6and the vertical velocity is Vi*sin38.6
horizontal
28.4=Vi*cos38.6 time find time in terms of Vi.
Vertical
hf=hi+Vi*sin38.6*t -1/2 g t^2
now hf=hi=0
so
0=Vi*sin 38.6-1/2 g t and put the expression you got for t, then solve for Vi. You will encounter the need for one trig identity.
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Show how you got the answer, please
Question:
A wave with a frequency of 14 Hz has a wavelength of 3 meters. At what speed with this wave travel?
Answer:
42m/s
Explanation:
v= λf
Frequency of wave: f= 14Hz
the wavelength of the wave: λ=3m
speed of wave: s=?
speed = frequency * wavelength
s = 14 * 3 = 42 m/s.
You push with 310N of force to move a 25 kg box across the floor. If the coefficient of kinetic friction between the box and the floor is .21, what is the net force on the box?
The net force will be the difference between the applied force and frictional force which is 258.6 N
What is Force ?Force can be simply defined as push or pull. It is the product of mass and acceleration. It is a vector quantity and it is measured in Newton.
If you push with 310N of force to move a 25 kg box across the floor. If the coefficient of kinetic friction between the box and the floor is .21
The normal force N on the box = mg
N = mg
N = 25 × 9.8
N = 245 N
The frictional force f = μN
where μ = coefficient of friction
f = 0.21 × 245
f = 51.45 N
The net force on the box = F - f
Where F = force applied
f = frictional force
Net force = 310 - 51.45
Net force = 258.6 N
Therefore, the net force on the box is 258.6 N
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Victor is using his Geiger-counter to record the amount of radiation that is leaking into the soil from a nearby nuclear disposal site. This radiation decreases by the square of the distance from the source. If he starts measurements 100 m from the disposal site how close will he need to stand if he hopes to measure soil with 4 times the radiation?
According to inverse square proportionality, measuring 4 times more radiation will require Victor to _____ his distance. Victor will need to stand _____ m from the disposal site.
If Victor starts measurements 100 m from the disposal site, he needs to stand 50 m from the source if he hopes to measure soil with 4 times the radiation.
I = 1 / r²
I = Intensity
r = Distance
At a distance of 100 m from the source,
I = 1 / 100²
I = 1 / 10000
I = [tex]10^{-4}[/tex] J / m² s
Four times this radiation will have an intensity of,
I = 4 * [tex]10^{-4}[/tex] J / m² s
4 * [tex]10^{-4}[/tex] = 1 / d²
d² = 1 / 4 * [tex]10^{-4}[/tex]
d² = 0.25 * [tex]10^{4}[/tex]
d = √ 25 * 10²
d = 5 * 10
d = 50 m
Therefore, he needs to stand 50 m from the source
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A soccer ball is kicked upward from a height of 6 ft with an initial velocity of 96 ft/s. How high will it go? Use -32 ft/s? forthe acceleration caused by gravity. Ignore air resistance.
Given,
The initial height of the soccer ball, h₁=6 ft
The initial velocity of the ball, u=96 ft/s
The acceleration due to gravity, g=-32 ft/s
When the ball reaches the maximum height, its velocity will reduce to zero.
Thus the velocity of the ball when it is at its maximum height is v=0 ft/s
From the equation of motion,
[tex]v^2-u^2=2gh_2[/tex]Where h₂ is the total height covered by the ball from its initial height to reach its maximum height.
On substituting the known values,
[tex]\begin{gathered} 0-96^2=2\times-32\times h_2 \\ \Rightarrow h_2=\frac{-96^2}{2\times-32} \\ =144\text{ ft} \end{gathered}[/tex]Thus the maximum height reached by the ball is,
[tex]\begin{gathered} H=h_1+h_2 \\ =6+144 \\ =150\text{ ft} \end{gathered}[/tex]Thus the maximum height reached by the ball is 150 ft.
josh and taylor, standing face-to-face on frictionless ice, push off each other, causing each to slide backward. josh is much bigger than taylor. after the push, which of the two is moving faster?
After the push, Taylor will be moving faster because he has a smaller mass.
What is the force applied by each person?The force exerted by each person is determined by applying Newton's second law of motion.
F = ma
where;
m is the mass of the persona is the acceleration of the personThe force applied by each person depends on the mass and acceleration.
mass of Josh > mass of Taylor
Since Josh has a greater mass, he will be able impact more force on Taylor causing Taylor to move faster after the push.
Thus, the speed of each person after the push, depends on the force received by each person at the opposite end.
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A golfer takes three strokes to putt a golf ball into a hole. On the first stroke, the ball moves 5.1 m due east. On the second, it moves 1.8 m at an angle 20° north of east. On the third, it moves 0.50 m due north. If the golfer had instead hit the ball directly into the hole on the first stroke, what would have been the magnitude (in m) and direction of the ball's displacement? Give the direction as a positive angle measured counterclockwise from due east.
The three strokes to put the golf ball into a hole is given. we have to find the overall displacement of the golf ball and its direction measured counterclockwise due east. So, we take due east as 0°, north as 90°, and so on.
For 1st stroke, the ball moves 5.1m due east means 5.1m at 0°.
The displacement along x- direction for 1st stroke = 5.1m × cos 0° = 5.1m, and y-displacement = 5.1m × sin 0° = 0m.
For 2nd stroke, the ball moves 1.8m at an angle 20° north of east.
Its x-displacement = 1.8m × cos (20°) = 1.691m, and y-displacement = 1.8m × sin (20°) = 0.6156m.
For third stroke, the ball moves 0.50m due north, means 0.50m by 90°.
Its x-displacement = 0.5m × cos (90°) = 0m, and y-displacement = 0.5m × sin(90°) = 0.5m.
The overall x- and y- displacements of the ball are:
x = 5.1 + 1.691 + 0 m = 6.791 m, and
y = 0 + 0.6156 + 0.5 m = 1.1156 m, respectively.
And its direction is θ = y/x = 1.1156 ÷ 6.791 = 0.164° due east.
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HELP!
Emily is riding her skateboard down the sidewalk at 2 m/s when she suddenly hits a rock, causing the skateboard to stop. According to Newton's first law of motion, what happens to Emily?
a
Emily accelerates forward.
b
Emily moves forward at 2 m/s.
c
Emily moves forward at less than 2 m/s.
d
Emily stops with her skateboard.
Answer: (b)
Explanation:
According to the law of conservation of momentum.
B. Emily moves forward at 2 m/s.
the shape of an atomic orbital is associated with group of answer choices the spin quantum number (ms). the principal quantum number (n). the angular momentum quantum number (l). the magnetic quantum number (ml). the magnetic and spin quantum numbers, together.
The shape of an atomic orbital is associated with the principal quantum number (n).
Why do atoms have orbitals?
The wave character of the electrons (or electron pairs) in an atom is described by atomic orbitals, which are mathematical functions. They provide a method for calculating the likelihood that an electron will be located in a particular area surrounding the atom's nucleus. An atom can have any number of orbitals, according to the quantum atomic model.
Why do a wave's orbitals affect the shape of the wave?The function of the wave will therefore be determined by the distance from the nucleus and not by its direction. Any particle's orbital shrinks in size but maintains a spherical geometry as its center quantum number drops.
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The velocity of a wagon increases from 3 m/s to 9 m/s as it
accelerates uniformly down a hill. The average velocity of the
wagon is
m/s.
Answer:
6 m/s
Explanation:
The equation that relates time, distance, and acceleration is:
a = (vf - vi)/t
where a is acceleration (m/s^2), time is time (seconds) and vf and vi are the initial (vi) and final (vf) velocities (m/s).
Average velocity is (vf + vi)/2
We are given that:
vi = 3 m/s
vf = 9 m/s
Average velocity for the wagon is thus:
is (9 + 3)/2 = 6 m/s
a car rounds an unbanked curve of radius 86 m. if the coefficient of static friction between the road and car is 0.51, what is the maximum speed (in m/s) at which the car can traverse the curve without slipping?
The maximum speed at which the car can transverse the curve without slipping is 20.7 m/s.
What is speed and what would be the maximum speed for the car not to slip?Speed is a scalar quantity which represents the distance travelled per unit time during the motion of the body.Here in the question is given radius 86 meters, and coefficient of static friction 0.51 and the car needs to transverse the curve without slipping.So we will use the formula v = ( u x g x r )^1/2 = 0.51 x 86 x 9.8. Here g will be taken as 9.8m/s^2 .Multiplying we will get the value 429.786 and square root of this would be 20.7 , so the velocity or the maximum speed of the car would 20.7 m/s at which car can transverse without slipping.To know more about speed visit:
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What conditions must be met in order for work to be done?
Check all that apply.
A. The applied force must make the object move.
B. At least part of the applied force must be in the same direction as
the movement of the object.
c. The output force must be greater than the input force.
D. The work must be greater than the momentum. you
Answer: B) force must be in the same direction as movement
Explanation:
the large blade of a helicopter is rotating in a horizontal circle. the length of the blade is 7.99 m, measured from its tip to the center of the circle. find the ratio of the centripetal acceleration at the end of the blade to that which exists at a point located 6.16 m from the center of the circle.
The ratio of the centripetal acceleration at the end of the blade to that which exists at a point located 6.16 m from the centre of the circle: 1.29
Centripetal acceleration is given by :
a = ω2R
where,
ω is the angular speed
R is the distance of the point from the centre
Let the point at the tip be A and that at distance 6.16 m from centre be B
Distance of point A from centre (RA) = 7.99 m
Distance of point B from centre (RB) = 6.16 m
Centripetal acceleration at A (aA) = ω2RA = 7.99ω2
Centripetal acceleration at B (aB) = ω2RB = 6.16ω2
The ratio (aA/aB) = 7.99/6.16 = 1.29
What is centripetal acceleration ?
centripetal acceleration is defined as the motion characteristic of an object moving along a circular path. Any object moving in a circle whose acceleration vector points towards the centre of that circle is called centripetal acceleration. You must have seen various examples of medium acceleration in your daily life. When you drive a car around a circle, your car experiences an average acceleration, and the average acceleration is also observed by a satellite orbiting the Earth. Middle means towards the centre.
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A force of 10 n stretches a particular spring by 2 cm. How far would a 20 n force stretch that same spring?.
x2 = 4cm.
20N stretches the same spring 4cm.
What is Hooke's law?The displacement or size of a deformed object is directly proportional to the deforming force or load for relatively small deformations.The spring constant k, is a measure of the spring's stiffness. It varies depending on the spring and material. The greater the spring constant, the stiffer the spring and more difficult to stretch.The force exerted on the spring, F1 = 10N
In the spring, 1st stretch, x1 = 2cm
The force exerted on the spring, F2 = 20N
In the spring, 2ns stretch, x2 = ?
We have to find x2,
The spring constant value for the same spring must be the same. Hooke's law expresses the relationship between force and spring constant as follows:
F=kx.
F1/x1 = F2/x2
By substituting values,
10 / 2 = 20 / x2
x2 = 40/10
x2 = 4cm
As a result, the 20 N force stretches by 4 cm.
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help plssss
Your car is traveling at an initial speed of Vo. At t = 0, you start increasing your speed at a constant acceleration. After 20s, the speed of the car is 54 km/ h, after 60 s — 108 km/ h.
a) What was your acceleration?
b) What was your initial speed?
c) What was the speed after 40s?
Given Data:
The applied acceleration is constant.
speed of the car after time,t1 = 20s, is V1= 54 km/h = 15 m/s
speed of the car after time,t2 = 60s, is V2= 108 km/h = 30m/s
we use the formula, V = Vo + a x t
where, Vo is the initial speed, a is the acceleration(constant),
t is the time taken by the object.
a) Acceleration = rate of change of speed with time = V2 - V1 / t2 - t1
a = 30-15/60-20
a = 15/40 = 0.375 m/[tex]{s^{2} }[/tex]
b) Initial speed, Vo = V1 - a x t1
= 15 - 0.375 x 20
= 7.5 m/s
c) Speed after 40 s, V = Vo + a x t, t = 40s
= 7.5 + 0.375 x 40
= 22.5 m/s
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A student throws a rock upwards. The rock reaches a maximum height 2.4 seconds after it is released.
How fast was the rock thrown?
From Kinematics, the equation for final velocity is
v = [tex]v_{0}[/tex] +at
where [tex]v_{0}[/tex] is the initial velocity, 'a' is the acceleration of the rock, and t is the time taken.
Given, that the rock is thrown upwards and it takes time t = 2.4s to reach a maximum height. So, its acceleration is a= -g= -9.8 m/[tex]s^{2}[/tex] and final velocity is v = 0m/s. To find initial velocity of the rock, rearrange above velocity equation.
⇒[tex]v_{0}[/tex] = v - at
⇒[tex]v_{0}[/tex] = 0 - (-9.8m/[tex]s^{2}[/tex] × 2.4s)
∴ [tex]v_{0}[/tex] = 23.52 m/s.
Thus, the rock was thrown with a velocity 23.52 m/s.
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