Answer:
Part A
a) F = -16x + 4, b) x = 0.25 m, c) STABLE
Explanation:
Part A
a) Potential energy and force are related
F = [tex]- \frac{dU}{dx}[/tex]- dU / dx
F = - (8 2x -4)
F = -16x + 4
b) The object is in equilibrium when the forces are zero
0 = -16x + 4
x = 4/16
x = 0.25 m
c) An equilibrium position is called stable if with a small change in position, the forces make it return to the initial position, in case the forces make it move away it is called unstable.
In this case there is only one equilibrium point
by changing the position a bit
x ’= x + Δx
we substitute
F ’= - 16 x’ + 4
F ’= - 16 (x + Δx) + 4
F ’= (-16x +4) - 16 Δx
at equilibrium position F = 0
F ’= 0 - 16 Δx
we can see that the body returns to the equilibrium position, therefore it is STABLE
PART B
This is an exercise in body collisions, let's define the system formed by the two bodies in such a way that the forces during the collisions are internal and the moment is conserved
initial instant. Before the shock
p₀ = m v
final instant. After the crash
p_f = (m + M) v_f
We have two possibilities: an elastic collision in which the bodies separate, each one maintaining its plus, and an INELASTIC collision where the neutron is absorbed by the nucleus and the final mass is M '= m + M, in this case they indicate that the collision is elastic
p₀ = pf
mv = mv ’+ M v_f
in the case of the elastic collision, the kinetic energy is conserved
K₀ = K_f
½ m v² = ½ m v’² + ½ M v_f²
we write the system of equations
mv = mv ’+ M v_f (1)
m (v² -v'²) = M v_f ²
m (v - v ’) = M v_f
m (v-v ’) (v + v’) = M v_f
v + v ’= v_f
we substitute in equation 1 and solve
v ’=[tex]\frac{m -M }{m+M } \ vo[/tex]
v_f = [tex]\frac{2m}{m+M} \ v_o[/tex]
the mechanical energy of the neutron is
initial
Em₀ = K = ½ m v²
final moment
Em_f = K + U = ½ m v_f ² + U
U is the energy lost in the collision
total energy is conserved
Em₀ = Em_f
½ m v² = ½ m v_f ² + U
U = ½ m (v² -v_f ²)
U = ½ m [v² - ( [tex]\frac{m-M}{m+M}[/tex] v)² ]
U = ½ m v² [1- ( [tex]\frac{m-M}{m+M}[/tex] )² ]
U = ½ m v2 [ [tex]\frac{2M}{m+M}[/tex]]
U = [tex]\frac{2 mM}{m +M } \ v^2[/tex]
Let's do the same calculations for the nucleus
initial Em₀ = 0
final Em_f = K + U = ½ M v_f ² + U
Em₀ = Em_f
0 = K + U
U = -K
U = - ½ M v_f ²
U = - ½ M [ [tex]\frac{2m}{m+M} \ v[/tex] ]²
U = [tex]\frac{2 m M }{m+M} \ v^2[/tex]
We can see that we obtain the same result, that is, the potential energy lost by the neutron is equal to the potential energy gained by the nucleus.
b) the fraction of energy lost
f = U / Em₀
f = 4 m M / m + M
c) let's calculate the fraction of energy lost in a collision
m = 1.67 10⁻²⁷ kg
M = 12 1.67 10⁻²⁷= 20 10⁻²⁷ kg
f = 4 1.6 20 / (1.6+ 20) 10⁻²⁷
f = 5.92 10⁻²⁷ J
the energy of a fast neutron is greater than 1 eV
Eo = 1 eV (1.67 10⁻¹⁹ J / 1eV) = 1.67 10⁻¹⁹ J
Let's use a direct portion rule if in a collision f loses in how many collisions it loses 0.95Eo
#_collisions = 0.95 Eo / f
#_collisions = 0.95 1.67 10⁻¹⁹ / 5.92 10⁻²⁷
#_collisions = 2.7 10⁷ collisions
What is this?
Picture
Answer:
may be upside down alphabet :"T"
Explanation:
pahelp po ako.
1. Which of the following terms refers to energy in motion?
A. kinetic energy C. potential energy
B. light energy D. thermal energy
2. Which of the following is a type of energy gained due to its position?
A. kinetic energy C. gravitational potential energy
B. light energy D. thermal energy
3. How do you get the total mechanical energy of an object in a closed system?
A. Get the sum of the initial and final kinetic energy.
B. Get the sum of the initial and final potential energy.
C. Get the sum of the kinetic energy and the potential energy.
D. Get the difference between the kinetic energy and the potential energy.
4. Which of the following is the best set up to observe the conservation of mechanical energy?
A. A cart rolling down a wooden ramp.
B. A wooden block falling in a vacuum.
C. A volleyball falling from a tall building.
D. a paper plane being launched from a tower.
5. A big rock was dropped from the third floor of a building. What happens to the kinetic energy of the ball as it falls?
A. The rock’s kinetic energy increases.
B. The rock’s kinetic energy decreases.
C. The rock’s kinetic energy remains the same.
D. The rock’s kinetic energy cannot be identified.
6. A heavy metallic ball was rolled up on a frictionless ramp. What happens to the gravitational potential energy of the ball as it rolls up the ramp?
A. The ball’s gravitational potential energy increases.
B. The ball’s gravitational potential energy decreases.
C. The ball’s gravitational potential energy remains the same.
D. The ball’s gravitational potential energy cannot be identified.
7. A 2kg ball is elevated up a building, how much is its potential energy 10m from the ground?
A. 5J C. 98J
B. 20J D. 196J
For items 8 to 10, refer to the illustration below. A ball is dropped at point W and travels along a frictionless path to reach point Z.
8. At which point does the ball has greatest gravitational potential energy?
A. W C. Y
B. X D. Z
9. At which point does the ball has greatest kinetic energy?
A. W C. Y
B. X D. Z
10. What happens to the total mechanical energy of the ball as it travels from point W to point Z?
A. The total mechanical energy increases.
B. The total mechanical energy decreases.
C. The total mechanical energy remains the same.
D. The total mechanical energy cannot be determined.
For items 11 to 12, refer to the illustration below. A pendulum swings back and forth from its highest position to its lowest position and vice versa.
11. As a pendulum swings from its highest to lowest position, what happens to its gravitational potential energy and kinetic energy?
A. Both its GPE and KE increases.
B. Both its GPE and KE decreases.
C. Its GPE decreases but KE increases.
D. Its GPE increases but KE decreases.
12. What happens to the total mechanical energy of the bob as it swings back and forth if only force acting on it is the gravitational force?
A. The total mechanical energy increases.
B. The total mechanical energy decreases.
C. The total mechanical energy remains the same.
D. The total mechanical energy cannot be determined.
Four ball of masses 0.5 kg, 1 kg, 2 kg, and 5 kg were dropped simultaneously on top of a building with the height of 20 m. Ignoring the air resistance, the four balls reach the ground at the same time.
13. Which of the following balls has the greatest gravitational potential energy on top of the building?
A. The ball with the mass of 5 kg.
B. The ball with the mass of 2 kg.
C. The ball with the mass of 0.5 kg.
D. All the balls have the same potential energy.
14. Which of the following balls has the least kinetic energy on top of the building?
A. The ball with the mass of 5kg.
B. The ball with the mass of 1kg.
C. The ball with the mass of 0.5kg.
D. All the balls have the same kinetic energy.
15. Which of the following balls has the greatest total mechanical energy?
A. The ball with the mass of 2kg.
B. The ball with the mass of 1kg.
C. The ball with the mass of 0.5kg.
D. All the balls have the same total mechanical energy
A squirrel jumps into the air with a velocity of 4 m/s at an angel of 50 degrees. What is the maximum height reached by the squirrel?
Answer:
Explanation:
Assuming the squirrel is jumping off the ground, here's what we know but don't really know...
v₀ = 4.0 at 50.0°
So that's not really the velocity we are looking for. We are dealing with a max height problem, which is a y-dimension thing. Therefore, we need the squirrel's upward velocity, which is NOT 4.0 m/s. We find it in the following way:
[tex]v_{0y}=4.0sin(50.0)[/tex] which gives us that the upward velocity is
v₀ = 3.1 m/s
Moving on here's what we also know:
a = -9.8 m/s/s and
v = 0
Remember that at the very top of the parabolic path, the final velocity is 0. In order to find the max height of the squirrel, we need to know how long it took him to get there. We are using 2 of our 3 one-dimensional equations in this problem. To find time:
v = v₀ + at and filling in:
0 = 3.1 - 9.8t and
-3.1 = -9.8t so
t = .32 seconds.
Now that we know how long it took him to get to the max height, we use that in our next one-dimensional equation:
Δx = [tex]v_0t+\frac{1}{2}at^2[/tex] and filling in:
Δx = [tex]3.1(.32)+\frac{1}{2}(-9.8)(.32)^2[/tex] and using the rules for adding and subtracting sig fig's correctly, we can begin to simplify this:
Δx = .99 - .50 so
Δx = .49 meters
a ball is launched upward at an angle from the ground. which way does its acceleration point at the top?
For a ball that is launched upward at an angle from the ground, the direction of its acceleration at the top of the projectile curve is downwards.
Acceleration of the ball at the topAs the ball is projected upward its acceleration points upwards until the ball reaches the maximum height or top of the projectile path.
At the top of the projectile path, its acceleration start pointing downwards.
Thus, for a ball that is launched upward at an angle from the ground, the direction of its acceleration at the top of the projectile curve is downwards.
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Answer:
vertical
Explanation:
The search for black holes involves searching for The search for black holes involves searching for Group of answer choices single stars that emit large amounts of X-rays. a stellar core greater than 3 solar masses large spherical regions from which no light is detected. pulsars with periods less than one millisecond. pulsars that are orbited by planets.
Answer:
Large spherical regions from which no light is detected
Explanation:
A black hole is an object that has an extremely high density such that it possesses very powerful gravitational force that prevents the escape of all objects including light from it, and consumes nearby objects.
Due to the power of the gravitational force of a black hole, at the center, objects are infinitesimally compressed resulting in the inapplicability of the concept of space and time and the location is known as a singularity
Therefore, the search for black holes involves searching for large spherical regions from which no light is detected.
A system has a pressure of 5 N/m2
If a force of 2000N is applied, what is the area that the force is applied to?
Give the units.
400 m2
Explanation:
Pressure = Force ÷ Area
5 N/m2 = 2000 N ÷ A
A = 2000 N ÷ 5
= 400 m2
If a force of 2000N is applied, the area that the force is applied to is 400 m²
What is force?The word "force" has a specific meaning in science. At this level, calling a force a push or a pull is entirely appropriate. A force is not something an object "has in it" or that it "contains."
One thing experiences a force from another. There are both living things and non-living objects in the concept of a force.
The amount of force applied to a certain region is referred to as pressure. The force per unit area is called pressure. F in this condensed version of the equation stands in for the force, which is expressed in newtons.
Given that the pressure of 5 N/m²
Force is 2000N
Pressure = Force ÷ Area
5 N/m² = 2000 N ÷ A
A = 2000 N ÷ 5 = 400 m²
Therefore, the area that the force is applied to is 400 m².
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what is gamma rays brust
Explanation:
A gamma - Ray Brust (GRB) is often the brightest source in the sky, often brighter than everything else combined.Answer:
A solenoid is a type of electromagnet, the purpose of which is to generate a controlled magnetic field through a coil wound into a tightly packed helix. The coil can be arranged to produce a uniform magnetic field in a volume of space when an electric current is passed through it.
An object 2cm high is placed 3cm in front of a concave lens of focal length 2cm, find the magnification?
Answer:
0.4
Explanation:
A concave lens is a diverging lens, so it will always have a negative focal length. Image distance is always negative for a concave lens because it forms virtual images.
From the lens formula;
1/f = 1/u+ 1/v
- 1/2 = 1/3 - 1/v
1/v = 1/3 + 1/2
v= 6/5
v= 1.2 cm
Magnification = image distance/object distance
Magnification = 1.2cm/3cm
Magnification = 0.4
How did the English bill of rights impact the colonists views of government?  A. It established a process by which people could petition the government. B.It stated that freedom of religion should be respected by the government. C. It declared people’s freedom of political speech. D. It asserted that a rulers power are limited by a separate branch of government.
Answer:
C. It declared people’s freedom of political speech.
Explanation:
The English bill of rights limited the king's power and increased the power of the population. This is because after the declaration of rights, the king should take into account the will of the people so that he could be kept in power. On that occasion, the people should have understood that the king was not an absolute liber and that they had more political freedom to express when they felt the country was not being managed properly. This freedom was also given to the colonists, making them see themselves as an active factor within English politics and not a subordinate factor to the king.
Look at the distance-time graph below. It shows Angela's journey as she walks to the end of the road and back. The end of the road is 40 m away. After how many seconds did she arrive back where she started?
Answer:
Explanation:
If the distance to the end of the road was 40 m, and she traveled back to where she started, she traveled a total distance of 80 m. It took her 100 seconds to travel the 80 m.
Based on the given distance-time graph, the number of seconds that Angela used to go to the end of the road and arrive back is 100 seconds.
How long did Angela take?The end of the road is 40m and coming back is also 40 m. The total distance is:
= 40 + 40
= 80m
The graph shows that to walk 80 meters, Angela took a 100 seconds because the line on the graph ends at 80 m and 100 seconds.
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Which forms of energy determine temperature: translational kinetic energy, rotational kinetic energy, vibrational kinetic energy, or all of these
oh this question seems to be difficult I don't think I can answer this
What is the name of the Egyptian sun god, usually depicted as a hawk-headed man with a solar disk and cobra on his head
Answer: Re-Horakhty
Explanation:
He has a human body and a falcon head, he has a crown in form of a disk with a cobra on his head. Ra-Horakhty was thought of as the god of the rising sun.
A glass tube in the shape of a letter J has the shorter limb sealed and the longer limb open. Mercury is poured into the tube until the levels in either limb is the same when the tube is vertical.In this position, the length of the air column in the sealed limb is 6.3cm.More mercury is then poured into the tube until the length of the trapped air column is 42cm.Calculate the difference in the levels of mercury in the limbs if a nearby mercury barometer reads 75.0cm and the reading of a nearby thermometer has not changed?
Answer:
35.4 cm
Explanation:
We have that when the level of mercury on either limb is the same, the pressure of the trapped air, P₁ = Atmospheric pressure
Also the initial height of the mercury in the tube = The reading of the barometer = 75.0 cm
The initial length of the air column, l₁ = 6.3 cm
The final length of the air column, l₂ = 4.2 cm (The length is expected to decrease due to compression)
The volume, V = l × A
Where;
A = The cross sectional area of the tube
Therefore, the volume of the air column is directly proportional to the length of the air column
∴ V ∝ l
According to Boyles law, we have;
P₁·V₁ = P₂·V₂
Where;
P₁ = The initial pressure in the air column before more mercury is added
V₁ = The initial volume occupied by the air in the air column
P₂, and V₂ are the final pressure and volume of the air column respectively
Given that V = l·A, we can write;
P₁·l₁·A = P₂·l₂·A
P₂ = P₁·l₁·A/(l₂·A) = P₁·l₁/(l₂) = P₁ × 6.3/4.2 = 1.5·P₁
The pressure in the air column after more mercury is added, P₂ = 1.5 × P₁
P₁ = Atmospheric pressure, therefore;
The pressure in the air column after more mercury is added, P₂ = 1.5 × Atmospheric pressure
Pressure = h·ρ·g
Where;
ρ = The density of the substance
g = The acceleration due to gravity
h = The height of the column of the fluid
Given that the density and the gravitational force, can be taken as constant, we have that the pressure of the fluid is directly proportional to the height of the fluid column
Therefore, when the pressure doubles, the height of the fluid column doubles, and when the factor of increase is 1.5, we have;
The final level of the mercury, h₂ = 1.5·h₁ = 1.5×75 cm = 112.5 cm
The initial length of the closed end of the J tube, [tex]h_{closed1}[/tex] = 6.3 cm + 75 cm = 81.3 cm
The final length of the mercury in the closed end, [tex]h_{closed2}[/tex] = 81.3 cm - 4.2 cm = 77.1 cm
The difference in the level of mercury, Δh = h₂ - [tex]h_{closed2}[/tex]
∴ Δh = 112.5 cm - 77.1 cm = 35.4 cm
The difference in the levels of mercury in the limbs, Δh = 35.4 cm
How much current flows in the circuit if two resistors of 6 connected in parallel are
supplied with potential difference of 12 volts?
Answer:
4 A
Explanation:
Firstly we need to calculate the equivalent resistance. Since, two resistors of 6 connected in parallel, so equivalent resistance will be given by,
[tex]\longrightarrow[/tex] 1/R = 1/R1 + 1/R2
[tex]\longrightarrow[/tex] 1/R = (1/6 + 1/6) Ω
[tex]\longrightarrow[/tex] 1/R = (1 + 1)/6 Ω
[tex]\longrightarrow[/tex] 1/R = 2/6 Ω
[tex]\longrightarrow[/tex] R = 6/2 Ω
[tex]\longrightarrow[/tex] R = 3 Ω
We know that,
[tex]\longrightarrow[/tex] V = IR
V denotes p.d (12V)I denotes currentR denotes resistance (3 Ω)[tex]\longrightarrow[/tex] 12 = I × 3
[tex]\longrightarrow[/tex] 12 ÷ 3 = I
[tex]\longrightarrow[/tex] 4 Ampere = I
A screw Jack whose pitch is 2mm is used to raise a bus of mass 900kg through height of 20cm. The length of the Tommy of the Tommy of the jack is 40cm. Calculate the velocity ratio of the machine
R= 40cm —> R= 0.4 m
P= 2mm —> P= 0.002 m
[tex]V.R = \frac{2πR}{p} = \frac{2 \times 3.14 \times 0.4}{0.002} = 1256[/tex]
I think this is the answer
I hope I helped you
Good luck ^_^
As the motor speeds up, the value of current decreases because of A. Friction loss B. Increase in resistance C. Increase in back emf D. All mentioned above
Answer:
C. Increase in back emf
Explanation:
As the current through the field winding decreases the field strength also decreases and the back-emf is reduced, as a result the motor speeds up.
When the motor begins to speed-up, an additional back EMF is generated due to induction which reduces armature current. This also results in reduced strength of the field flux. The back emf generated is not enough to reduce the armature current which could stop the acceleration of the motor and the motor further accelerates.
Does this equation show that transmutation has taken place during decay?
Why or why not?
Ni – S.Ni+y
A. No, because there is conservation of the number of atoms as well
as the number of nucleons.
B. No, because high-energy electromagnetic waves are emitted.
C. Yes, because the numbers of nucleons and atoms are conserved.
D. Yes, because nickel atoms remain nickel atoms with the same
number of neutrons.
Answer:
Maybe A is the correct answer
You can see stars brighter than magnitude +6 with your naked eye under dark sky conditions, and you can also see the full moon at magnitude –13. (You can glance at the Sun, which is at magnitude –27, but you can't safely look at the Sun.) Given these limits, what is the dynamic range of the naked eye?
During an Apollo lunar landing mission, the command module continued to orbit the Moon at an altitude of about 112 km . How long did it take to go around the Moon once?
Express your answer using three significant figures and include the appropriate units.
T=2 Hours 6 Minutes 33.53 Seconds
The acceleration of the car with two washers added to the string would be
Answer:
[tex]a=0.33\ m/s^2[/tex]
Explanation:
For washer 2,
v₁ = 0.13 m/s
v₂ = 0.36 m/s
t₁ = 1.92
t₂ = 2.61
We need to find the acceleration of waster 2.
[tex]a=\dfrac{v_2-v_1}{t_2-t_1}\\\\a=\dfrac{0.36-0.13}{2.61-1.92}\\\\a=\dfrac{0.23}{0.69}\\\\a=0.33\ m/s^2[/tex]
So, the acceleration of washer 2 is [tex]0.33\ m/s^2[/tex].
Answer:
.33
Explanation:
help please correct answer i will mark brainliest
Answer:
19.21ms-¹
Explanation:
that is the solution above
Mike is serving the volleyball for the second time in a volleyball game. If the ball leaves his hand with twice the velocity it had on the first serve, its horizontal range R would be:
Answer:
His new horizontal range is 4 times his initial range.
Explanation:
Since Mike serves the ball with velocity, u, his horizontal range is
R = u²sin2Ф/g where Ф is the angle between u and the horizontal.
Now, if on his second serve, the ball leaves his hand with twice the velocity of his initial serve, the new velocity is v = 2u.
So, the new range R' = v²sin2Ф/g
R' = (2u)²sin2Ф/g
R' = 4u²sin2Ф/g
Since R = u²sin2Ф/g,
R' = 4u²sin2Ф/g
R' = 4R
So, his new horizontal range is 4 times his initial range.
The burner in a hot air balloon adds 6400 J of heat to the balloon while the ballon expands. As the balloon expands, it does 3100 J of work on the surrounding air. What is the internal change in thermal energy of the balloon?
Answer:
the change in the internal energy of the balloon is 3,300 J
Explanation:
Given;
heat gained by the balloon system, Q = 6,400 J
work done on the surrounding air by the balloon, W = 3,100 J
The change in the internal energy of the system is calculated from the first law of thermodynamics;
ΔU = Q - W
where;
ΔU is the change in the internal energy of the balloon;
ΔU = 6,400 J - 3,100 J
ΔU = 3,300 J
Therefore, the change in the internal energy of the balloon is 3,300 J
The electric potential energy of an electric dipole is ______ when the dipole is aligned with an electric field. The electric potential energy of an electric dipole is ______ when the dipole is aligned with an electric field. most positive most negative zero infinite undefined
Answer:
Most negative
Explanation:
The electric potential energy of a dipole U = -pEcosθ where p = dipole moment, E = electric field and θ = angle between p and E.
When the electric dipole is aligned with the electric field, the angle between p and E is 0°. That is θ = 0°.
So, U = -pEcosθ
U = -pEcos0°
U = -pE
which is the most negative value it can have.
So, the electric potential energy of an electric dipole is most negative when the dipole is aligned with an electric field.
So, most negative is the answer.
Why does An apple, potato, and onion all taste the same if you eat them with your nose plugged
Your mass is 80 kg on Earth. What would your MASS
be on Planet Roethler, which has twice as much
gravity as on Earth?
40 kg
160 kg
80 kg
Mass doesn't change. It doesn't matter where you are.
If your mass is 80 kg when you're on Earth, then your mass is 80 kg. It doesn't matter where you are, where you used to be, or where you're going tomorrow.
Do you believe in aliens? And if so, what's your reasoning for believing in them?
Answer:
I believe in aliens but I do not think everyone should. I started to believe in aliens since the US government said they would be taking extraterrestrial life seriously. They will be in our lives sooner or later, so we shouldn't be ignoring their presence. I believe them because surveys show that nearly half of Americans believe that aliens have visited the Earth, either in the ancient past or recently. That percentage has been increasing. Belief in alien visitation is greater than belief that Bigfoot is a real creature, but less than belief that places can be haunted by spirits. Also there have been a lot of UFO sightings, and a Navy Jet has a video of that as well. These small things is just hard to ignore, and they make me and hopefully others believe in aliens.
a wave in which particles of the medium vibrate at right angles to the direction that the wave travels is called?
Explanation:
Longitudinal waves are waves in which the vibration of the medium is parallel to the direction the wave travels and displacement of the medium is in the same (or opposite) direction of the wave propagation. Mechanical longitudinal waves are also called compressional or compression waves, because they produce compression and rarefaction when traveling through a medium, and pressure waves, because they produce increases and decreases in pressure.
Answer:
In transverse waves, particles of the medium vibrate to and from in a direction perpendicular to the direction of energy transport.
Explanation:
hope it will help u
Principles What are the advantages of total reflecting prism over plane mirror?
Answer:
There is no significant energy loss in the total internal reflection and the reflected ray has entire light wave energy so that a brighter image is formed, but some energy in the plane mirror is absorbed inside and thus energy loss.
Explanation:
Advantages
If the light is reflected from the total prism, the entire light is completely reflected internally. But only about 90% of the incident light is reflected from the mirror of the plane. Consequently, reflected light intensity is more in the prism than light reflected in the plane mirror. There are no more reflections in the prism as in the plane mirror in its entirety. In the case of a total prism as in the plane mirror, the image is not reversed laterally. It requires no silvering, one of the benefits.The Sun's energy comes from which nuclear reaction?
Answer:
the sun energy comes from nuclea fution
