Most astronomers believe we are living in the "age of exploration" for astronomy due to significant advancements in technology, observational capabilities, and our understanding of the universe.
In the last 60 years, several explorations have taken place, revolutionizing our knowledge of the cosmos. One major exploration has been the launch and utilization of space telescopes. Instruments like the Hubble Space Telescope, launched in 1990, have provided breathtaking images and invaluable data, expanding our understanding of distant galaxies, stellar evolution, and the age of the universe. Additionally, the Kepler Space Telescope, launched in 2009, has discovered thousands of exoplanets, leading to groundbreaking insights into planetary systems and the potential for life beyond Earth. Advancements in ground-based observatories have also contributed to the age of exploration. Large-scale telescopes equipped with advanced detectors and adaptive optics technology have enabled astronomers to observe celestial objects with remarkable clarity and detail. These observatories have played a vital role in studying cosmic phenomena, such as black holes, pulsars, supernovae, and the cosmic microwave background radiation. Moreover, significant discoveries have been made in the field of cosmology. The development of precise measurements, such as the cosmic microwave background radiation and the accelerated expansion of the universe, has deepened our understanding of its origins and evolution. The detection of gravitational waves, first observed in 2015, has opened a new window for studying the universe, providing insights into phenomena like neutron star mergers and black hole dynamics.
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what behavior is mostly strongly associated with introversion in a personality.
Answer:
Need quiet to concentrate
Are reflective
Are self-aware
Take time making decisions
Feel comfortable being alone
Don’t like group work
Prefer to write rather than talk
And maybe even feel tired after being in a crowd
Explanation:
A solenoid 6.00 cm in diameter and 10.0 cm long has 750 turns and carries a current of 15.0 A. Calculate the magnetic flux through the circular cross-sectional area of the solenoid.
The magnetic flux through the circular cross-sectional area of the solenoid is 0.00066 Weber or (Tm²).
What is a solenoid?A wire tightly twisted in a lengthy, thin coil is a solenoid. Due to its design, the solenoid will have an electromagnet inside of it and a weak magnetic field surrounding it if we pass a current through it.
Equation of solenoid's magnetic field:
The simplest solenoid to describe is one with unlimited length. An infinite solenoid's magnetic field has a constant within and a precise zero value outside. If we can accept that the magnetic field near the ends will be different from what is calculated for just an infinite solenoid, the unlimited solenoid is frequently a rough estimate of an actual, finite-length solenoid.By utilizing the convolution operation as well as right hand rule, the magnetic field within a large solenoid is appropriately computed, but all of that can be condensed into:
B = (µ₀ × N × I )/ L
where
B = magnetic field (Tesla)
µ₀ = [tex]\pi[/tex]× 10^-7 (Tm/A ) is the vacuum permeability,
N = number of turns on solenoid,
I = electric current (Ampere)
L = length of the solenoid (m)
According to the question;
A diameter of solenoid 6.00 cm.
A radius of solenoid is 3 cm = 0.03m
Number of turns = 750
The length of solenoid is 10cm = 0.1m
Substitute all the values in equation to fine mangetic filed.
B = ([tex]\pi[/tex]×[tex]10^{-7}[/tex] × 750× 15 )/ 0.1
B = 0.035 Tesla
The formula for magnetic flux is
Ф = B×A
= B×([tex]\pi[/tex][tex]r^{2}[/tex])
= 0.035×[tex]\pi[/tex]×[tex].03^{2}[/tex]
Ф = 0.000099
Ф = 99×[tex]10^{-6}[/tex] Weber
Therefore, the magnetic flux through the circular cross-sectional area of the solenoid. is 99×[tex]10^{-6}[/tex] Weber.
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What type of energy drives plate motion?
a) external
b) internal
c) gravitational
d) radiative
b) internal energy drives plate motion
Lithospheric plates are part of a planetary scale thermal convection system. The energy source for plate tectonics is Earth’s internal heat while the forces moving the plates are the “ridge push” and “slab pull” gravity forces.
A tectonic plate (also called lithospheric plate) is a massive, irregularly shaped slab of solid rock, generally composed of both continental and oceanic lithosphere.
The motion of tectonic plates is driven by convection in the mantle. Convection: The process of heat transfer from one part of a fluid to another part by the actual movement of the particles of the fluid is called convection. Liquid and gases are heated by the process of convection.
In simple terms, convection is the idea that dense, cold things sink, and buoyant, warm things rise. In the earth the cold sinking things are slabs (subducting plates) and the warm things are plumes, or just rising material from deeper in the mantle.
hence , correct option is b) internal
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2. A ball is tossed straight upwards with a velocity of 60m/s. Using an estimate of gravity of -10m/s², about how many seconds would it take to reach the peak (top of the flight). A.) 10 seconds B.) 3 seconds C.) 6 seconds D.) 12 seconds
Answer: A
Explanation:
A 3.5 mH inductor and a 4.5 mH inductor are connected in parallel. When the total emf of the combination is 16 V, the rate of change of the current in the larger inductor is:
The rate of change of the current in the larger inductor is 0.3mA/s.
To find the answer, we need to know about the relation between the emf and inductance.
What's the mathematical expression to find the emf in term of inductance?Mathematically, emf induced across an inductor= L× (dI/dt)L= inductance and dI/dt = rate of change of currentWhat is the rate of change of current in 4.5 mH when when the total emf of the combination is 16 V?As both the inductors are connected in parallel, so emf of the combination remains same across each inductor.Emf induced in 4.5mH = 16 V dI/dt = 4.5mH / 16 = 0.3 mA/sThus, we can conclude that the rate of change of the current in the larger inductor is 0.3mA/s.
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Two objects X and Y move directly towards each other. The objects have the same mass.
Object X has a velocity of 5.0 m/s to the right. Object Y has a velocity of 3.0 m/s to the left.
Object X and object Y collide and stick together.
What is their velocity after colliding?
X and Y are two things that travel in the same direction. The mass of the things is the same. 5.0 m/s is the velocity of object x as it moves to the right. The velocity of object y to the left is 3.0 m/s. Objects x and y collide and adhere to one another. Following their collision, they both move at a speed of 1.0 m/s to the right.
Their velocity after colliding is 1.0 m / s to the right.
What is the velocity during the collision?
In a collision, the velocity change is always computed by subtracting the initial value from the final value. If an object is moving in one direction before a collision and rebounds or somehow changes direction, then its velocity after the collision has the opposite direction as before.Inelastic collisions occur when only the momentum is conserved but not the system's kinetic energy. Perfectly inelastic collisions happen when objects stick together and have a common velocity after collision. To solve for the final velocity in perfectly inelastic collisions, use v' = (m1v1 + m2v2)/m1 + m2.The magnitude of the relative velocity is the same before and after the collision.To learn more about velocity, refer to:
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When a 3.0 N weight is attached to a vertical coil spring, it stretches 5.0 cm. What weight would be required to stretch the spring 12.5 cm?
Group of answer choices
a. 7.5 N
b. 15 N
c. 4.5 N
d. 1.2 N
The weight required to stretch the spring 12.5 cm is 7.5 N (Option A)
Data obtained from the questionInitial weight (W₁) = 3 N Initial Length (L₁) = 5 cmNew length (L₂) = 12.5 cmNew Weight (W₂) =? How to determine the new weightThe new weight required to stretch the spring can be obtained as follow:
W₁ / L₁ = W₂ / L₂
3 / 5 = W₂ / 12.5
Cross multiply
W₂ × 5 = 3 × 12.5
Divide both sides by 5
W₂ = (3 × 12.5) / 5
W₂ = 7.5 N
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A ball of mass 4 kg is initially traveling at 2 m/s and has a 5 N force applied to it for 3 s. What is the final velocity of the ball?
A. 4 m/s
B. 12 m/s
C. 5.75 m/s
D. 3.25 m/s
Answer:
the answer to your question will be D
Explanation:
5 N* 3S =3.25
How do the resistances of two conducting wires compare if they have the same length, but one is twice the radius of the other?.
The thicker wire has one-fourth the resistance of the thinner wire.
What are resistance and resistivity?The characteristic of a substance that prevents the flow of current is known as resistance. The free electrons begin to move in a specific direction when a voltage is applied across the conductor. These electrons collide with atoms or molecules as they move, creating heat in the process. These atoms or molecules prevent free electrons from moving through a substance. Resistance is represented by the symbol R.
Specific resistance is another name for resistivity. A substance with certain dimensions, such as one meter in length and a cross-sectional area of one square meter, has a resistance that is represented by its resistivity. Resistivity or specific resistance is represented by ρ.
The relation between resistance R and resistivity ρ is given as:
R = ρL/A
where,
R = resistance of the conductor
ρ = resistivity of the material
L = length of the conductor
A = cross-sectional area of the conductor
Calculation:Given,
r₁ = 2r₂
L₁ = L₂
where
r₁ = radius of the first conductor
r₂ = radius of the second conductor
L₁ = length of the first conductor
L₂ = length of the second conductor
To find
R₁/R₂ =? (the ratio of R₁ and R₂)
If the radius is twice the other then the area will become,
A₁ = π r₁²
A₂ = π r₂²
A₁ = π (2r₂)²
= 4π r₂²
Therefore,
A₁ = 4 A₂
Now put the values in the formula,
R = ρL/A
R₁/R₂ = ρ L₁ A₂/ ρ L₂ A₁
R₁/R₂ = L A₂/ L (4A₂)
R₁/R₂ = 1/4
R₁ = R₂/4
Hence, the thicker wire with twice the radius of the thin wire has one-fourth the resistance of the thinner wire.
I understand the question you are looking for is this:
How do the resistances of two conducting wires compare if they have the same length, but one is twice the radius of the other?
(a) The thicker wire has half the resistance of the thinner wire
(b) The resistance is the same in both wires
(c) The thicker wire has one-fourth the resistance of the thinner wire
(d) The thicker wire has twice the resistance of the thinner wire.
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What is the threshold frequency for sodium metal if a photon with frequency 6.66 × 1014 s−1 ejects an electron with 7.74 × 10−20 j kinetic energy?
The threshold frequency for sodium metal is
5.49 x 10^14 s-1
Given:
photon with frequency = 6.66 × 10^14 s−1
kinetic energy = 7.74 × 10−20 j
To Find:
threshold frequency
Solution: The threshold frequency is defined as the minimum frequency of incident radiation below which the photoelectric emission is not possible completely. irrespective of the intensity of incident radiation
We know, relation between threshold frequency, kinetic energy and frequency s given by :
K.E = hv - hvo
Here h is plank's constant and vo, is threshold frequency.
Putting all these value in above equation we get:
7.74 x 10^-20 = (6.66 × 10^14-vo) x 6.626 x 10^-34
vo = 5.49 x 10^14 s^-1
Hence, the threshold frequency for sodium metal is 5.49 x 10^14 s-1
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A man pushes a box across a floor. as he increases the force he applies horizontally to the box
a) the kinetic friction decreases
b) the kinetic friction may increase or decrease depending on the velocity of the box
c) the kinetic friction remains the same
d) the kinetic friction increases
When a man pushes a box across a floor, as he increases the force he applies horizontally to the box, then the kinetic friction remains the same.
To find the answer, we need to know about friction.
What is friction?Whenever a body moves, over the surface of another body, a force comes into play which acts parallel to the surface of contact and opposes the relative motion. This opposing force is called friction.There are two frictions acting on a surface.Static friction: It come into play between two bodies before when it starts moving. Self-adjusting force and the max value of it is called limiting static friction.Kinetic friction: It come into play between two bodies when it starts moving. It is not a self-adjusting force.As we increase applied force, kinetic friction will remain same.Thus, we can conclude that, kinetic friction remains the same when we increase the applied force.
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As a guy pushes a box across a floor, the kinetic friction stays constant no matter how much force is applied on the box horizontally.
We must understand friction if we are to find the solution.
Describe friction?A force that works parallel to the surface of contact and opposes the relative motion is always present whenever a body moves over the surface of another body. Friction is the name for this opposing force.On a surface, there are two frictions operating.Static friction: It occurs between two bodies before motion is initiated. Limiting static friction is the term used to describe the maximum amount of self-adjusting force.As soon as two bodies begin to move, kinetic friction is triggered. It is not a force that adjusts itself.The amount of kinetic friction will not change when we apply more force.We can therefore draw the conclusion that kinetic friction does not change as the applied force is increased.
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A 55 kg track and field athlete has an average power output of 5.4 kW during the 200 meter dash. How quickly did she finish the race?
Group of answer choices
a. 20 s
b. 22 s
c. 23 s
d. 18 s
The time taken for the athlete to finish the race is 20 s (Option A)
What is power?Power is simply defined as the rate at which work is done. It can be expressed mathematically as
Power (P) = work (W) / time (t)
But
Work = weight × distance
Therefore,
Power = (weight × distance ) / time
How to determine the time Mass (m) = 55 KgAcceleration due to gravity (g) = 9.8 m/s²Weight = mg = 55 × 9.8 = 539 NPower (P) = 5.4 KW = 5.4 × 1000 = 5400 WDistance (d) = 200 mTime (t) =?Power = (weight × distance ) / time
5400 = (539 × 200) / t
5400 = 107800 / t
Cross multiply
5400 × t = 107800
Divide both side by 5400
t = 107800 / 5400
t = 20 s
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An 80-N crate is pushed at constant speed for a distance of 5.0 m upward along a smooth inclined plane that makes an angle of 30o with the horizontal. If the force on the crate is parallel to the slope, what is the work done by the pushing force? Group of answer choices 260 J 200 J 61 J 140 J -200 J
The work done by the pushing force is 200 J; option B.
What is work done in an inclined plane?The work done in an inclined plane is given by the formula below:
Work done = Force * distanceForce, F = mgsinθ + ma
where a = 0
Work done = 80 * 5 * sin 30°
Work done = 200 J
In conclusion, work done is the product of force and distance.
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An object at rest has no ________ energy, but it may have ________ energy resulting from its location or structure. An object at rest has no ________ energy, but it may have ________ energy resulting from its location or structure. chemical; potential kinetic; potential kinetic; heat potential; kinetic
Answer: An object at rest has no kinetic energy, but it may have potential energy resulting from its location or structure.
Explanation: To find the answer, we need to know more about the kinetic and potential energies.
What is kinetic energy of a body?Kinetic energy is a form of mechanical energy possessed by a body by virtue of its motion.Kinetic energy of a body of mass m moving with a velocity v is given by,[tex]KE=\frac{1}{2}mv^2[/tex]
What is potential energy?Potential energy is a form of mechanical energy possessed by a body by virtue of its position in the field or configuration.PE is always associated with a conservative force.There cannot be potential energy due to frictional or viscous forces.Thus, we can conclude that, an object at rest has no kinetic energy, but it may have potential energy resulting from its location or structure.
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You are raising up a big bucket of water from a 22.5 m deep well. The combined mass of the water and the bucket is 11.3 kg. The bucket is attached to a heavy duty steel chain. The mass of the chain is 17.9 kg. How much work do you perform during the lifting process? Tries 0/12 If it takes 1.75 minutes for you to raise the bucket of water out of the well, then what was your average power?
The amount of work done during the lifting process is 4465.125 J and our average power will be 42.525 W.
Given:
Depth of the well, h = 22.5m
Mass of heavy-duty steel chain, M = 17.9 kg
The combined mass of the water and bucket, m = 11.3 kg
time taken to raise the bucket out of the water, T = 1.75 min = 105 s
Calculation:
Consider that the center of mass of the steel chain is at the midpoint of the depth of the well.
Now, the work done during the lifting process can be calculated as:
W.D = (Work done in lifting bucket filled with water) + (work done to lift
the steel chain)
W.D = mgh + Mg (h/2) -( 1 )
where g is the acceleration due to gravity
Applying values in the above equation we get:
W.D = mgh + Mg (h/2)
= (11.3 kg)(9.8 m/s²)(22.5 m) + (17.9 kg)(9.8 m/s²)(22.5 m / 2)
= 2491.65 + 1973.475
= 4465.125 J
We know that the average power is given as:
P_avg = W.D / T - ( 2 )
where W.D is the work done during the lifting process
T is the time taken to raise the bucket out of the well
Applying values in the above equation, we get:
P_avg = W.D / T
= (4465.125 J)/(105 s)
= 42.525 W
Therefore, the amount of work done during the lifting process is 4465.125 J and our average power will be 42.525 W.
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question down below need rply fast
The resultant magnitude and direction of the vectors are as follows:
A. A = 6.6; θ = 30.8° from the x-axisB. B = 10.4; θ = 196.7° from the x-axisC. C = 23.3; θ = 300° from the x-axisD. D = 40.4; θ = 138° from the x-axisE. E = 49.5; θ = 346° from the x-axisWhat is the resultant magnitude and direction of the given vectors?The resultant magnitude and direction of the vectors are as follows:
A. A = √(5.7² + 3.4²)
A = 6.6
θ = tan⁻¹(3.4/5.7)
θ = 30.8° from the x-axis
B. B = √{(-10)² + (-3²)}
B 10.4
θ = tan⁻¹(3/10) + 180
θ = 16.7° + 180°
θ = 196.7° from the x-axis
C. C = √{(12)² + (-20²)}
C = 23.3
θ = 360° - tan⁻¹(20/12)
θ = 300° from the x-axis
D. D = √{(-30)² + (27²)}
D = 40.4
θ = 180 - tan⁻¹(27/30)
θ = 138° from the x-axis
E. E = √{(48)² + (12²)}
E = 49.5
θ = 360° - tan⁻¹(12/48)
θ = 346° from the x-axis
In conclusion, the resultant of the vectors and direction are obtained using the resultant vector formula.
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Which of the following, if eliminated, would completely prevent the greenhouse effect from occurring on earth?
Group of answer choices
a. Atmosphere
b. Acid rain
c. Fossil fuels
d. Clouds
The substance, if eliminated, that would completely prevent the greenhouse effect from occurring on earth is fossil fuels (option C).
What is greenhouse effect?Greenhouse effect is the process by which a planet is warmed by its atmosphere.
Greenhouse effect is caused by greenhouse gases that deplete the ozone layer.
Fossil fuels, when burned, will release greenhouse gases such as carbon etc. to the atmosphere.
Therefore, the substance, if eliminated, that would completely prevent the greenhouse effect from occurring on earth is fossil fuels.
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Why do we tallk about radio waves as a group and not the frequeny of radio waves
A car approaches a stationary police car at 36 m/s. The frequency of the siren (as heard in the police car) is 500 Hz. What is the frequency (in Hz) heard by an observer in the moving car as he approaches the police car
The frequency heard by an observer in the moving car as he approaches the police car is 558.6 Hz.
Frequency hear by the observerThe frequency heard by the observer is calculated by applying the principle of Doppler effect.
f₀ = f'[(v/v - vs)]
where;
f₀ is the observed frequencyv is speed of sound = 343 m/svs is the speed of the sourcef₀ = 500[(343 / 343 - 36)]
f₀ = 500(343/307)
f₀ = 558.6 Hz
Thus, the frequency heard by an observer in the moving car as he approaches the police car is 558.6 Hz.
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Which of the zodiac constellations will be highest at midnight?
Answer:
Virgo will be the highest zodiac constellations at night.
Some fish have a density slightly less than that of water and must exert a force (swim) to stay submerged. What force must an 85.0-kg grouper exert to stay submerged in salt water if its body density is
The force require to keep grouper submerged is 8.207N.
According to Archimedes principle buoyant force of any object must equal to weight of fluid it displaced.
The expression for the force exerted to stay submerged in salt water is
F = F(b) - w(fish)
where F(b) = buoyant force
w(fish) = weight
now substitute w(b) for F(b)
→ F = Vρg - w(fish)
where V = volume of sea water
ρ = density of sea water
Now by Archimedes principle V = m(fish) / ρ(fish)
→ F = (m(fish) / ρ (fish) ) ρg - m(fish)g
F = (85 kg/1015 kg-m^-3) (1.025× 10³ kg-m^-3) (9.8 m/s^2)
- (85kg) × 9.8 m/s^2
F = 841.207N - 833N
F = 8.207 N
Hence, the force require to keep grouper submerged is 8.207N.
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What is the energy of an electromagnetic wave that has a wavelength of
7.0 x 10-12 m? Use the equation E= hc where hc = 1.99 × 10-25 J-m.
OA. 2.8 × 10-14 J
OB. 1.4 x 10-36 J
OC. 9.0 x 10-37 J
OD. 7.2 x 1035 J
SUBMIT
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
[tex]\qquad \sf \dashrightarrow \:E = \dfrac{hc}{\lambda} [/tex]
here,
[tex] \sf{hc = 1.99 × {10}^{-25} J - m} [/tex][tex] \sf{\lambda = 7.0 × {10}^{-12}} [/tex]____________________________________
[tex]\qquad \sf \dashrightarrow \: E = \cfrac{1.99 \times 10 {}^{ - 25} }{7 \times 10 {}^{ - 12} } [/tex]
[tex]\qquad \sf \dashrightarrow \: E= \cfrac{1.99}{7} \times 10 {}^{ (- 25 + 12)} { } [/tex]
[tex]\qquad \sf \dashrightarrow \:E= 0.284 \times 10 { }^{ - 13} [/tex]
[tex]\qquad \sf \dashrightarrow \: E= 2.84 \times 10 { }^{ - 14\:\; } J\: \: [/tex]
so, correct choice is A
Car A is traveling with a constant speed of 80 km>h due north, while car B is traveling with a constant speed of 100 km>h due east. Determine the velocity of car B relative to car A
Answer:
80J
Explanation:
K.E = ½ mv²
k.e = ½ * 80*
100²
ke= 4*20
ke= 80 J
Consider two copper wires. one has twice the length and twice the cross-sectional area of the other. how do the resistances of these two wires compare?
Answer:
R = ρ L / A where R is the resistance and ρ the resistivity:
R2 / R1 = (L2 / A2) / (L1 / A1) = L2 * A1 / (L1 * A2)
R2 / R1 = (2 L * A) / (L * 2 A) = 1
Their resistances should be the same.
If themass is 50kg, what weight of water is to be displaced to float on water? why
Answer:if youre looking for the weight of the thermas in genral it should be 500n
Explanation:using the formula w=mg
w=500x10
giving us 500 newtons which is the weight.
Two men standing on the same side of wall and at the same distance from It, such that they are 4oom apart when one fires a gun the other hears the first report in 1.2s and the second in 0.5s after the first. calculate 1) Velocity of sound in air . 2)the perpendicular distance of the men from the wall.
Answer:
1. 571.43m/s
2. 142.9m and 342.9m
Explanation:
1.Take the difference in time.
1.2-0.7=0.7 seconds
Take the distance between them and divide with differnce in time.
400÷0.7=571.43 seconds.
2.Take the time of the two men and divide by two.
0.5÷2= 0.25 secs
1.2÷2= 0.6 secs
multiply each with the velocity.
0.25×571.43=142.9m
0.6×571.43=342.9m
The lion has a kinetic energy of 5000 j. What is the speed of the lion?
The lion has a kinetic energy of 5000 j, the speed of the lion is v = 100 / [tex]\sqrt{M1}[/tex] m/s
What is kinetic energy ?Kinetic energy is a form of energy that an object or a particle has by reason of its motion. If work, which transfers energy, is done on an object by applying a net force, the object speeds up and thereby gains kinetic energy or Kinetic energy is the energy that an object possesses due to its motion. It is basically the energy of mass in motion. Kinetic energy can never be negative and it is a scalar quantity i.e. it provides only the magnitude and not the direction.
given
kinetic energy = 5000 J
speed = ?
since , mass is not given in the question
Let mass of lion will be = M1
kinetic energy = 1/2 * M1 * [tex]v^{2}[/tex]
5000 J = 1/2 * M1 * [tex]v^{2}[/tex]
[tex]v^{2}[/tex] = [tex]\sqrt{10,000 / M1}[/tex] m/s
v = 100 / [tex]\sqrt{M1}[/tex] m/s
The speed of the lion = v = 100 / [tex]\sqrt{M1}[/tex] m/s
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What is the acceleration of a 2-kg mass if a 100-N force acts on it?
SOLUTION:
Acceleration = Force/mass
= 100N / 2 kgs
= 50 m/s
.
.
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If a star appears to move relative to other stars over a one-year period, this motion is due to the star's: Doppler shift. radial motion. parallax shift. transverse motion. true space motion.
If a star appears to move relative to other stars over a one-year period, this motion is due to the star's true space motion.
What is the proper motion of stars?
Proper motion is the angular change in position of a star across our line of sight, measured in arc seconds per year, and symbolized with the letter μ.
Proper motion is generally measured by measuring the movement of the image of a star with respect to more distant background stars over that time period.
Here we are told that star appears to move relative to other stars over 1 year period.
So we know that,
True space motion is the annual apparent motion of a star across the sky.
True Space Motion is Combination of radial velocity, proper motion, and distance.
Hence,
If a star appears to move relative to other stars over a one-year period, this motion is due to the star's true space motion.
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A proton exits the cyclotron 1. 0 ms after starting its spiral trajectory in the center of the cyclotron. How many orbits does the proton complete during this 1. 0 ms ?.
(a) The diameter of the largest orbit just before the protons exit the cyclotron is 39 cm.
(b) The number of orbits completed by the proton during this 1.0 ms is 14000 revolutions.
What is kinetic energy?
The kinetic energy of an object is the energy that it possesses due to its motion.
It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity.
Formula of KE:
K.E = 1/2mv²
mv² = 2 K.E
v = sqrt( 2*KE / M)
Here,
(a)
The KE of the medical isotopes = 6.5 MeV
substituting the values,
v = sqrt( 2* 6.5* 1.6* 10^-13 / 1.67* 10^-27 )
v = 3.53 × 10⁷ m/s
Now the centripetal force:
mv² / R = qvB
r = q*v / mv²
r = ( 1.67* 10^-27 * 3.53 × 10⁷ ) / ( 1.9* 1.6* 10^-19 )
r = 0.19415 m
diameter d = 2r,
d= 2(0.19415 m)
d= 0.39 m ≅ 39 cm
(b)
The time period to complete a revolution around the spiral trajectory is:
T = 2πr / v
T = 2*3.14* 0.1941 / 3.53*10^7
T = 0.7 × 10⁻⁷ s
Thus, the number of orbits that the proton does to complete the revolution in 1 ms is:
n = t / T
n = 10^-3 / (0.7*10^-7)
n = 14285.71 ≅ 14000 revolutions
Learn more about spiral trajectory here:
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Your question is incomplete, but most probably full question was:
A medical cyclotron used in the production of medical isotopes accelerates protons to 6.5 MeV. The magnetic field in the cyclotron is 1.9 T.
(a) What is the diameter of the largest orbit, just before the protons exit the cyclotron? Express your answer with the appropriate units. d = 57 cm Previous
(b) A proton exits the cyclotron 1.0 ms after starting its spiral trajectory in the center of the cyclotron. How many orbits does the proton complete during this 1.0 ms?