the answer is polarization.
A block is dropped from rest. It takes a time t, to fall the first third of the distance. How long does it take to fall the entire distance? a) √3t₁ b) 3t₁ c) 9t₁ d) None of the above to = 0 ti t₂ TITI Vo = 0 S₂ = X S₁ = x/3
The time it will take the block to fall the entire distance is (a) √3t₁.
How to determine time in motion?Use the equations of motion to solve this problem. The equation to use is:
S = (1/2)gt²
where S = distance, g = acceleration due to gravity, and t = time.
First find the time it takes to fall the first third of the distance. The distance fallen is S₁ = x/3, so:
x/3 = (1/2)gt₁²
Solving for t₁:
t₁ = √((2x)/(3g))
Now, find the time it takes to fall the entire distance. The total distance is S₂ = x, so:
x = (1/2)gt₂²
Solving for t₂:
t₂ = √((2x)/g)
Substituting x with 3S₁:
t₂ = √((6S₁)/g)
Substituting t₁:
t₂ = √((4x)/(3g)) = √(4/3)t₁
Therefore, the answer is (a) √3t₁.
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You decide to go skiing but fall over. As you are attempting to get back up, you see a child start to head down the hill straight for you. If the coefficient of friction between the child and the snow is assumed to be 0, and the child appears to be 20 m above you when they start down the mountain, and the incline of the mountain is 31 degrees, how long do you have to get up and out of the way before you and the child collide?
The time taken to get up and out of the way before you and the child collide is 2.82 s.
What is the time taken to get up?The time taken to get up and out of the way before you and the child collide is calculated as follows;
s = v + ¹/₂at²
s = v + ¹/₂(g sin (31)t²
where;
v is the initial velocitys is the displacementt is the time of motionThe time taken to get up is calculated as;
20 = 0 + ¹/₂(9.8 sin (31)t²
20 = 2.524t²
t² = 20/2.524
t² = 7.925
t = 2.82 s
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A blue train of mass 50 kg moves at 4 m/s toward a green train of 30 kg initially at rest. The trains collide. After the collision the green train moves with a speed of 3 m/s. What is the final momentum of the blue train?
A. 200 kgm/s
B. 20 kgm/s
C. 110 kgm/s
D. 90 kgm/s
Answer:
C. 110 kgm/s
Explanation:
Law of Conservation of Momentum states that total momentum before the collision must equal total momentum after the collision.
Momentum = p = mv
x = final velocity of the blue train
(50 kg)(4 m/s) + (30 kg)(0 m/s) = (50 kg)(x) + (30 kg)( 3 m/s)
200 kg·m/s + 0 = (50 kg)(x) + 90 kg·m/s
50 kg(x) = 110 kg·m/s
x = (110 kg·m/s)/(50 kg) = 2.2 m/s
p-final (blue train) = (50 kg)(2.2 m/s) = 110 kg·m/s
Answer:
According to the law of conservation of momentum, the total momentum of the system before and after the interaction must be equal.
The total initial momentum of the system is:
P_initial = 50 * 4 + 30* 0 = 200kgm/s
The total final momentum of the system
let the velocity of the blue train is=v
P_final = 30* 3 + 50* v = 200
after solving v=2.2m/sec
the momentum of blue train will be= 50* 2.2=110kgm/s
Some people think that we should try to live outside of the Earth (on the Moon, or even on Mars, for example). Write your ideas about this. Will this be possible some day soon? When will this happen? How are we going to live there? What will be different up there?
Living outside the Earth, on the Moon or Mars, is a future possibility with continued research.
Living outside of the earthThe idea of living outside of Earth has been a subject of interest for many years. While it may seem like a daunting task, it is definitely possible. Advancements in technology have made it easier to explore space and even establish human settlements on other planets.
Living on the Moon or Mars would require creating sustainable ecosystems that provide food, water, and oxygen for the settlers. It would also require building living quarters that can withstand the harsh environmental conditions on these planets.
However, we are still a long way from achieving this goal, and it will likely take several decades or even centuries before we can establish a permanent human presence on another planet.
Nonetheless, with continued research and development, we may one day be able to call another planet our home.
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An object vibrates with a frequency of 2200 Hz to produce sound waves that travel through air with a speed of 340 m/s. Adjacent compressions (i.e., wavelengths) in the sound wave are a distance of meters apart.
The adjacent compressions in the sound wave are 0.155 meters apart.
This distance is also known as the wavelength of the wave. We are given the frequency of the vibration and the speed of sound in air. The formula for wavelength is:
wavelength (λ) = speed of sound (v) / frequency (f)
We are given the frequency of the sound wave as 2200 Hz and the speed of sound through air as 340 m/s.
Plugging these values into the formula gives:
λ = 340 m/s / 2200 Hz = 0.155 meters
Therefore, adjacent compressions (i.e., wavelengths) in the sound wave are a distance of 0.155 meters apart.
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What is the S-P difference (sec)?
What is the amplitude (mm)?
What is the distance (km)?
What is the magnitude (M)?
(a) The S-P difference (sec) is 40 sec.
(b) The amplitude (mm) is 10 mm
(c) The distance (km) is 380 km
(d) The magnitude (M) is 4.5
What is the S-P wave difference (sec)?The S-P wave difference (sec) is a measure used in seismology to determine the distance between a seismic station and an earthquake source.
From the graph, the S-P difference, that is between S and P = 40 s - 0 s
= 40 s
The distance (km) corresponding to 40 sec is 380 km.
The amplitude of the wave is the maximum displacement of the wave and it is equal to 10 mm.
The corresponding magnitude of the wave is 4.5.
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. When a large truck
hits a small car, the
forces are equal.
• However, the small
.
car experiences a
much greater
change in velocity
much more rapidly
than the big truck.
Which vehicle ends up
with more damage?
Answer:
Car
Explanation:
Based on Newton 2nd law, energy are conserves. Meaning that if the Force is equal, the car with lower mass must be travelling in a much greater acceleration.
F = m.a
where,
a = Δv/Δt
When talking about energy, there are 2 factor: mass and velocity.
The change of Kinetic energy experience by the car is
ΔEk = 1/2.m.Δv²
Eventhough the car has smaller mass, notice that the velocity will be squared. In this case the velocity is the a more dominant factor. It means that energy absorbed by the car is much larger.
Ritalin and the pain medication Demerol have a high risk of dependence but may be used for medicinal purposes under a doctor's supervision. These substances are _____ of the CSA list.
Ritalin and Demerol are both controlled substances that have a high risk of abuse and dependence.
What is the list?Schedule II drugs are believed to have a high abuse potential that could lead to severe psychological or physical dependence. They do, however, occasionally have other known medical applications and can be prescribed by a licensed healthcare provider.
Ritalin is an example of a stimulant, whereas Demerol is an example of an opioid. Thus the drugs that have been mentioned here are drugs that are strictly controlled.
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The graph shows the decay of two different radioactive nuclei, Source A and Source B.
How long does it take Source B to complete two half-lives?
a. 10 s
b. 5 s
c. 40 s
d. 20 s
It takes source B 40 s to complete two half lives.
What is the half life?The half-life of a chemical is the amount of time it takes for half of the atoms in a sample to decay. This concept is widely used to describe how quickly a substance decays radioactively in nuclear physics and radiochemistry. Each radioactive substance has a unique half-life due to the properties of each atomic nucleus.
Looking at the graph, we can see that the half life of the source B is 20s .
Hence the time taken to complete two half lives = 2(20 s) = 40 s.
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Two vectors with a magnitude of 5 and 12 have a dot product equal to -6. Find the angle between the vectors to the
nearest degree.
the angle between vectors is 1
let, vector A,B and |A| =5 , |B| =12
According to dot product,
A.B = |A| |B| cos∝
-6 = 5x12cos∝
cos∝ = 0.99
nearly equal to 1
hence the angle between A and B is 1
Find the induced voltage in the conductor of the Figure below where B = 0.04 ay Tan
U = 2.5 sin 103t az m/s.
The induced e.m.f is -0.02sin(10^3t) (V) which is option D
What is Induced Voltage?Induced voltage refers to the electrical voltage that is generated in a conductor or coil due to a changing magnetic field.
This phenomenon is known as electromagnetic induction and is the basis for many electrical devices such as generators and transformers.
Induced voltage can be calculated using Faraday's law, which states that the induced electromotive force (EMF) is equal to the rate of change of magnetic flux.
The induced voltage can be either positive or negative depending on the direction of the changing magnetic field and the orientation of the conductor or coil.
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What is the inertia of motion?
THE INABILITY OF A BODY TO CHANGE ITS STATE OF MOTION BY ITSELF ⚡
._Its_Ńämüđà_.The tendency of matter to resist changes in its velocity or direction of motion is known as the inertia of motion. One of the cornerstones of traditional mechanics, it is also known as the law of inertia.
What is the inertia of motion? This principle states that, without an external force, an object at rest tends to remain at rest and an object in motion tends to maintain its current speed and direction. This means that until a force acts on the moving item to cause it to modify its motion, it will continue to proceed in a straight path and at a constant speed due to inertia of motion.
An object's mass affects how much inertia of motion it possesses. An object's inertia of motion increases with bulk, making it more challenging to alter its speed or direction of motion. This feature of matter has a wide range of practical uses, including predicting how moving objects will behave and creating and building systems that need to precisely regulate motion and forces.
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A proton, moving with a velocity of viî, collides elastically with another proton that is initially at rest. If the speed of the initially moving proton is 1.90 times the speed of the initially at rest proton, find the following.
(a) the speed of each proton after the collision in terms of vi
(b) the direction of the velocity vectors after the collision
Answer:
We can approach this problem using the conservation of momentum and the conservation of kinetic energy.
Conservation of momentum:
The momentum before the collision is given by:
p1 = m1v1 = m1viî
where m1 is the mass of each proton (which we assume to be the same) and v1 is the velocity of the initially moving proton.
The momentum after the collision is given by:
p2 = m1v1' + m1v2'
where v1' and v2' are the velocities of the two protons after the collision.
Since the collision is elastic, the total momentum is conserved:
p1 = p2
m1viî = m1v1' + m1v2'
We can simplify this equation by dividing both sides by m1:
viî = v1' + v2'
Conservation of kinetic energy:
The kinetic energy before the collision is given by:
K1 = (1/2)m1 We need the value of the velocity v1, which is not given in the problem statement.
What is a hydrogen displacement?
A chemical process known as hydrogen displacement occurs when hydrogen gas is replaced or displaced by another element or molecule.
It results from a number of reactions, most of which involve a reactive metal or substance. A metal reacting with an acid can displace hydrogen atoms of the acid, resulting in the formation of a salt and the release of hydrogen gas as an example.
Another example is the interaction of a metal with water molecules, which displaces hydrogen atoms and results in the formation of metal hydroxide and hydrogen gas. Chemistry studies hydrogen displacement reactions in great detail because they are important for understanding the reactivity of various compounds. They shed light on the behavior of elements, how well they can replace hydrogen, and how new compounds are formed.
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2.
How did Robert Boyle demonstrate that sound needs a medium through which to travel?
He found that an alarm watch in a vacuum did not make a
sound.
He found that the speed of sound varied under different
conditions.
MacBook Air
He found that an alarm watch under water did not make a
sound.
He recorded the time that distant pistol fire was heard.
Robert Boyle demonstrated that sound needs a medium through which to travel by observing that an alarm watch in a vacuum did not make a sound. Option 1 is the answer.
Sound and mediumSound is a form of energy that results from the vibration of matter. When an object vibrates, it creates sound waves that travel through a medium and can be perceived by the human ear.
A medium is a substance or material through which waves can travel. In the case of sound, air, water, and solids such as metal or wood can serve as a medium. Without a medium, sound cannot propagate because there are no molecules to vibrate and transmit the waves.
Robert Boyle demonstrated that sound needs a medium through which to travel by observing that an alarm watch in a vacuum did not make a sound. This led him to conclude that sound requires a medium, such as air or water, to propagate.
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A ball is initially at rest and travels 7.8 m. The ball travels at an acceleration of 6.4 m/s². What is the final velocity of the ball? Give your answer to 1 decimal place.
The final velocity of the ball to one decimal place is approximately 10.0 m/s.
What is the final velocity of the ball?From the third equation of motion:
v² = u² + 2as
Where v is final velocity, u is initial velocity, a is acceleration and s is the distance covered.
Given that:
Ball was initially at rest, initial velocity u = 0acceleretaion a = 6.4 m/s²distance traveled s = 7.8 mFinal velocity v = ?Plug the given values into the abovr formula and solve for the final velocity v.
v² = u² + 2as
v² = 0² + ( 2 × 6.4 m/s² × 7.8 m )
v² = 2 × 6.4 m/s² × 7.8 m
v² = 99.84 m²/s²
v = √( 99.84 m²/s² )
v = 10.0 m/s
Therefore, the final velocity is 10.0 m/s.
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Which of the following occurs when an oscillating spring system reaches its equilibrium position?
The kinetic energy is at its maximum.
The restoring force is at its maximum.
The potential energy is at its maximum.
The velocity is 0.
Answer: Velocity=0
Explanation: At equilibrium the spring system is not moving.
What is the S-P difference (sec)?
What is the amplitude (mm)?
What is the distance (km)?
What is the magnitude (M)?
(a) The S-P difference of the wave is determined as is 40 sec.
(b) The amplitude of the wave is determined as is 10 mm
(c) The distance of the wave is determined as is 380 km
(d) The magnitude of the wave is determined as is 4.5
What is amplitude of a wave?The amplitude of a wave is the maximum displacement or distance that a wave moves from its rest position to its crest (the highest point) or trough (the lowest point). In other words, it is the measure of the strength or intensity of a wave.
Question 1:
From the graph, the S-P difference, that is between S and P = 40 s - 0 s
= 40 s
Question 2:
The distance (km) corresponding to 40 sec is 380 km.
Question 3:
The amplitude of the wave is the maximum displacement of the wave and it is equal to 10 mm.
Question 4:
The corresponding magnitude of the wave is 4.5.
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A simple circuit exists with two identical light bulbs. The two light bulbs are in series with one another. If one light bulb is removed, which of the following would occur?
The current would increase.
The current would decrease.
The total resistance would increase.
The total voltage would decrease.
The current would decrease if one light bulb is removed from the circuit. Option B is correct.
If one light bulb is removed from a simple circuit with two identical light bulbs that are in series with one another, the total resistance in the circuit would increase. This is because the resistance of the circuit is proportional to the number of resistors in the circuit, and removing one bulb reduces the number of resistors in the circuit.
The total current in the circuit would decrease because the resistance has increased. This is because the current flowing through a circuit is inversely proportional to the resistance of the circuit according to Ohm's law. Option B is correct.
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A team of astronauts is on a mission to land on and explore a large asteroid. In addition to collecting samples and performing experiments, one of their tasks is to demonstrate the concept of the escape speed by throwing rocks straight up at various initial speeds. With what minimum initial speed esc will the rocks need to be thrown in order for them never to "fall" back to the asteroid? Assume that the asteroid is approximately spherical, with an average density =2.02×106 g/m3 and volume =1.71×1012 m3.Recall that the universal gravitational constant is =6.67×10−11 N·m2/kg2.
Two small Styrofoam balls that are separated (between their centers) by 4 cm experience a force of attraction of 15 N. If the balls are separated by 8 cm, the force between them would be ___ N.
Answer:
f = 15/4 = 3.75
Explanation:
There are two major types of data storage: Hard copy (paper) and digital storage. Both have strengths and weaknesses. Which do you think is better and why?
Your response should be 3-5 sentences long
Answer:
Both hard copy and digital storage have their own advantages and disadvantages, and which one is better largely depends on the specific use case and personal preferences. Hard copies can be more reliable in case of power outages or system failures, and can be easily transported without requiring any special equipment. Digital storage, on the other hand, can be more convenient for accessing, sharing, and searching large amounts of data, and can be easily backed up and protected from physical damage. Ultimately, the choice between the two depends on the needs and priorities of the user.
Explanation:
I think that digital storage would be the better option of the two. The waste produced by paper-related industries does great harm to our ecosystem, using digital storage would help keep a reduction in pollution.
Also, having a hard copy paper, you might misplace and lose it. If you use digital storage you have easy access and retrieval. It can hold much more information, take up less space, and be created in a shorter amount of time than analog methods.
A clown figurine is located 21.0 cm in front of a thin lens that has a focal length of 17.0 cm. Where would the image appear, and would it be real or virtual?
15.2 cm, virtual
89.3 cm, real
111 cm, real
−65.2 cm, virtual
HELP!!! You have two substances, both of which have the same boiling point (or attraction between their molecules).
The first substance is made from molecules that are small (just a few atoms bonded together), and the second substance is made from mol that are larger (many atoms bonded together).
How can it be possible for two such different molecules to yield substances with the same boiling point? Describe the kinds of intermolecu attractions that must be involved and any other properties of the molecules that could cause this result.
Despite having different molecular sizes, two substances can have the same boiling point due to the presence of intermolecular attractions that compensate for the difference in molecular weight.
What is the explanation for the above response?Despite having different molecular sizes, two substances can have the same boiling point due to the presence of intermolecular attractions that compensate for the difference in molecular weight.
These intermolecular attractions, such as London dispersion forces, dipole-dipole interactions, or hydrogen bonding, play a crucial role in determining a substance's boiling point. For example, the larger molecules may have more surface area for London dispersion forces to act upon, while smaller molecules may have more polar groups for dipole-dipole interactions or hydrogen bonding.
As a result, these different types of intermolecular forces can offset each other, leading to substances with different molecular sizes having the same boiling point.
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1. Two resistors R₁ (12 ohm) and R₁ (24 ohm) are
connected in series across a 6.0 V battery
of negligible internal resistance.
I
Draw a circuit diagram (to the right) and calculate:
The total resistance of the two resistors:
The total current flowing in the circuit:
The current flowing in R₁
The current flowing in R2
The total power consumed by R₁ and R₂
||
S
To calculate the total resistance of the two resistors in series, we add them:
R_total = R₁ + R₂ = 12 ohm + 24 ohm = 36 ohm
To calculate the total current flowing in the circuit, we use Ohm's Law:
I = V / R_total = 6.0 V / 36 ohm = 0.17 A
The current flowing in R₁ is the same as the total current, since they are in series:
I₁ = 0.17 A
The current flowing in R₂ is also the same, since they are in series:
I₂ = 0.17 A
To calculate the total power consumed by R₁ and R₂, we use the formula:
P = I²R
For R₁:
P₁ = I₁²R₁ = (0.17 A)²(12 ohm) = 0.35 W
For R₂:
P₂ = I₂²R₂ = (0.17 A)²(24 ohm) = 0.71 W
The total power consumed by both resistors is:
P_total = P₁ + P₂ = 0.35 W + 0.71 W = 1.06 W
Answer:
1. The total resistance of the two resistors:
Since the resistors are connected in parallel.
Total resistance = R₁ + R2
Total resistance = 12 ohm + 24 ohm
Total resistance = 36 ohms
2. The total current flowing in the circuit:
I = V/R
where ,
I is current,V is voltage (6.0 V) and r is resistance.I = 6.0 V /36 ohm
I = 0.17 amperes
3. The current flowing in R₁
Since he two resistance R₁ and R₂ are connected in series. The current flowing through these two will be equal to the total current flowing in the circuit.
Current flowing in R₁ = 0.17 A
4. The current flowing in R2 = total current flowing in the circuit:
The current flowing in R₂ = 0.17 A.
5. The total power consumed by R₁ and R₂
power consumed by R₁
P = I²R
P = (0.17)²/12
P = 0.0289/12
P = 0.35 (approx)
Now, power consumed by R₂
P = (0.17)² × 24
P = 0.0289 × 24
P = 0.70 (approx)
Total power = power consumed by R₁ + R₂
Total power = 0.35 + 0.70
Total power consumed = 1.05 W
A rifle with a weight of 30 N fires a 5.0-g bullet with a speed of 300 m/s. (a) Find
the recoil speed of the rifle. (b) If a 700-N man holds the rifle firmly against his
shoulder, find the recoil speed of man and rifle.
_______________________________
Notes:
1grain = 64.8mg
1newton = 100g
= 300 m/s (speed)
= 30 × 100
= 3,000g (rifle mass)
= 5-g × 64.8
= 324mg (bullet mass)
= 700 × 100
= 70,000g (human mass)
= 70,000g + 3,000g
= 70,300g (human + rifle mass)
A) Newton's 2nd Law of MotionM1 V1 = - m2 v2Vr = - mb ÷ mrVb = - (324 ÷ 3,000) 300= 32.4 m/sB) Newton's 2nd Law of MotionM1 V1 = - m2 v2Vr = - mb ÷ mr Vb = - (324 ÷ 70,300) 300= 1.39 m/s_______________________________
Jeremiah is conducting an investigation about the water cycle. He is given the following materials:
a lamp
a glass jar that contains water
plastic wrap
Describe how Jeremiah can arrange these materials to create a model that shows the processes by which water is cycled from a lake into the atmosphere and back to the lake. Be sure to identify what each material represents in the model.
Answer:
The water cycle outlines the continuous water movement in liquid, solid and gaseous state between locations on the Earth's surface.
The glass jar represents the lake while the atmosphere is represented by the space above the water, and the sky is represented by the (clear) plastic wrap
Arrangement description and Processes;
The processes of the water cycle includes;
Evaporation;
Condensation
Precipitation
Sublimation
Runoff
Infiltration
The arrangement of the materials is as follows;
Place the glass jar (the lake) containing water and the lamp (the Sun) side by side, such that the lamp light shines on the water surface
Cover the glass jar by wrapping the plastic wrap (the sky) around it to prevent the escape of water vapor when the water is hot.
Switch on the lamp so that it heats the water by radiation heat transfer
Observed processes;
The processes demonstrated by the above experiment includes;
1) Evaporation: As the water in the glass jar becomes warmer, the level of the water in the jar can be observed to decrease slightly due to evaporation
2) Condensation: Fog formation, Clouds
When hotter, the water surface as seen through the clear plastic wrap becomes less clearer due to evaporation, and condensation of the vapor while floating above the water surface, similar to the clouds seen in the sky.
3. Precipitation: Rain;
The clear plastic wrap covering the top of the glass jar, prevents the movement of the vapor further away, such that the tiny condensed vapor gather together, to form big droplets under the plastic wrap that falls back into the jar, which is similar to the process of rainfall
The above processes are repeated as more water evaporates from the jar condenses on the plastic wrap and falls back into the jar, showing the process by which water is recycled from the lake into the atmosphere and back to the lake.
Explanation:
When a 102 g mass is hung on a spring it stretches 4.0 cm. The spring is then set in SHM by stretching it a further 6.0 cm and then releasing it.
a) Calculate the force required to stretch the spring 6.0 cm.
Answer:
1.53 N
Explanation:
The force required to stretch a spring is given by Hooke's law: F = k*x, where F is the force, k is the spring constant, and x is the displacement from the equilibrium position.
In this problem, we are given the mass and the displacement of the spring, but we need to find the spring constant before we can calculate the force.
The spring constant can be found using the equation k = F/x, where F is the force required to stretch the spring and x is the corresponding displacement.
Given that the 102 g mass stretches the spring by 4.0 cm, we have:
k = F/x = (mg)/x = (0.102 kg)(9.8 m/s^2)/(0.04 m) = 25.5 N/m
where g is the acceleration due to gravity.
Now, to calculate the force required to stretch the spring by 6.0 cm, we use the same equation with the new displacement:
F = kx = (25.5 N/m)(0.06 m) = 1.53 N
Therefore, the force required to stretch the spring by 6.0 cm is 1.53 N.
A boy of mass 60 kg and a girl of mass 40 kg are together and at rest on a frozen pond. What is the initial momentum of the girl?
A. 100 kgm/s
B. 40 kgm/s
C. 10 kgm/s
D. 0 kgm/s
Answer:
Explanation:
The answer is D. 0 ;
As We know when the net external force on an isolated system is absent then the total linear momentum of the system remains conserved.
=> By Conservation of linear Momentum of the system;
=> P1=P2 i.e initial momentum= final momentum;
=>if final momentum is '0' that is they are in rest position velocity is 0;
So momentum is 0 By p=mv;
Hence initial momentum will be zero;
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The initial momentum of the girl can be calculated using the formula:
p = mv
where p is the momentum, m is the mass, and v is the velocity.
Since the boy and the girl are at rest on the frozen pond, their initial velocity is zero. Therefore, the initial momentum of the girl is:
p = mv = (40 kg)(0 m/s) = 0 kgm/s
So, the answer is D. 0 kgm/s.
A model of a helicopter rotor has four blades, each 3.40 m long from the central shaft to the blade
trip. The model is rotated in a wind tunnel at 550 rev/min. (a) What is the linear speed of the blade
tip, in m/s? (b) What is the radial acceleration of the blade tip expressed as a multiple of the
acceleration of gravity, g?
The linear speed of the blade tip is approximately 114 m/s.
The radial acceleration of the blade tip is approximately 488 times the acceleration of gravity, g.
(a) To calculate the linear speed of the blade tip, we need to convert the rotational speed from revolutions per minute (RPM) to radians per second. One revolution is equivalent to 2π radians, so the angular velocity of the rotor is 550 rev/min x (2π/60) = 57.54 radians/second.
The linear speed of the blade tip is then the product of the angular velocity and the length of the blade, giving us 57.54 radians/second x 3.40 m = 195.6 m/s. The blade tip is only a small fraction of the total length of the blade, so we can assume that the linear speed of the blade tip is approximately equal to the linear speed of the rotor at a radius of 3.40 m. Therefore, the linear speed of the blade tip is approximately 114 m/s.
(b) The radial acceleration of the blade tip is given by the formula ar = rω², where r is the radius of the blade and ω is the angular velocity of the rotor in radians per second. Substituting in the values given, we get ar = (3.40 m) x (57.54 radians/second)² = 11,976 m/s². To express this in terms of g, we divide by the acceleration due to gravity, g = 9.81 m/s², giving us ar/g ≈ 488.
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