Answer:
a = 640 m/s²
Explanation:
From work-kinetic energy principles,
The net force acting on the second object is the gravitational force and the electric force due to the first object.
So, the gravitational force on the mass is F₁ = Gm₁m₂/r² since m₁ = m₂ = m, U = -Gm²/r²
Also, the electric force on the charge is F₂ = kq₁q₂/r² since q₁ = q₂ = q, U = kq²/r²
The net Force F = ma
So, -F₁ + F₂ = F (F₁ is negative since it is an attractive force in the negative x -direction and F₂ is positive since it is a repulsive force in the positive x- direction)
-Gm²/r² + kq²/r² = ma
ma = -Gm²/r² + kq²/r²
a = (-Gm²/r² + kq²/r²)/m
a = (-G + kq²/m²)m/r²
Since m = 0.250 kg, q = 4.00 μC = 4.00 × 10⁻⁶ C, r = 3.00 cm = 3.00 × 10⁻² m, G = 6.67 × 10⁻¹¹ Nm²/kg², k = 9 × 10⁹ Nm²/C² and a = acceleration of second mass.
Substituting the variables into the equation, we have
a = (m/r²)(-G + k(q/m)²)]
a = (0.250 kg/{3.00 × 10⁻² m}²)(-6.67 × 10⁻¹¹ Nm²/kg² + 9 × 10⁹ Nm²/C²(4.00 × 10⁻⁶ C/0.250 kg)²)
a = (0.250 kg/9.00 × 10⁻⁴ m)(-6.67 × 10⁻¹¹ Nm²/kg² + 9 × 10⁹ Nm²/C²(16 × 10⁻⁶ C/kg)²)]
a = (0.250 kg/9.00 × 10⁻⁴ m)(-6.67 × 10⁻¹¹ Nm²/kg² + 9 × 10⁹ Nm²/C²(256 × 10⁻¹² C²/kg²)]
a = (0.250 kg/9.00 × 10⁻⁴ m)(-6.67 × 10⁻¹¹ Nm²/kg² + 2304 × 10⁻³ Nm²/kg² ]
a = (0.250 kg/9.00 × 10⁻⁴ m)(2.304 Nm²/kg²)
a = 0.576 Nm²/kg /9.00 × 10⁻⁴ m²
a = 0.064 × 10⁴N/kg
a = 64 × 10 N/kg)
a = 640 m/s²
If three forces F1 = 20N, 300NE, F2 = 50N along W, F3 = 40N 500NW act on a body. Find the resultant in magnitude and direction.
Answer:
110N north west
Explanation:
.........
If three forces F1 = 20N, 300NE, F2 = 50N along W, F3 = 40N 500NW act on a body. The resultant in magnitude and direction is 110N north west
What are the types of force ?Force is a quantitative parameter and it is an interaction between two physical bodies such as an object and its environment, there are different types of forces in nature.
it can be defined as pushing or pulling of any object resulting from the object’s interaction or movement, without force the objects can not move
If an object in moving state the it will be either static or motion, the position of the object will only be changed if it is pushed or pulled and The external push or pull upon the object called as Force.
The contact force types are Spring Force, Applied Force, Air Resistance Force, Normal Force, Tension Force, Frictional Force
Non-Contact forces are occur from a distance such as Electromagnetic Force, Gravitational Force, Nuclear Force
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Calculate the force of an object that has a mass of 10kg and an acceleration of 4m/s²
A-40N
B-8N
C-2.5N
D-0.4N
What happens to the body’s immune system when attacked by HIV ?
Answer:
HIV attacks a specific type of immune system cell in the body. It's known as the CD4 helper cell or T cell. When HIV destroys this cell, it becomes harder for the body to fight off other infections.
Explanation:
A 45.0-kg girl is standing on a 168-kg plank. The plank, originally at rest, is free to slide on a frozen lake, which is a flat, frictionless surface. The girl begins to walk along the plank at a constant velocity of 1.55 m/s to the right relative to the plank.
Required:
What is the velocity of the plank relative to the surface of the ice?
Answer:
The speed of the plank relative to the ice is:
[tex]v_{p}=-0.33\: m/s[/tex]
Explanation:
Here we can use momentum conservation. Do not forget it is relative to the ice.
[tex]m_{g}v_{g}+m_{p}v_{p}=0[/tex] (1)
Where:
m(g) is the mass of the girlm(p) is the mass of the plankv(g) is the speed of the girlv(p) is the speed of the plankNow, as we have relative velocities, we have:
[tex]v_{g/b}=v_{g}-v_{p}=1.55 \: m/s[/tex] (2)
v(g/b) is the speed of the girl relative to the plank
Solving the system of equations (1) and (2)
[tex]45v_{g}+168v_{p}=0[/tex]
[tex]v_{g}-v_{p}=1.55[/tex]
[tex]v_{p}=-0.33\: m/s[/tex]
I hope it helps you!
A 9.00 g bullet is fired horizontally into a 1.20 kg wooden block resting on a horizontal surface. The coefficient of kinetic friction between block and surface is 0.20. The bullet remains embedded in the block, which is observed to slide 0.390 m along the surface before stopping.
Required:
What was the initial speed of the bullet?
Answer:
The initial speed of bullet is "164 m/s".
Explanation:
The given values are:
mass of bullet,
[tex]m'=9.00 \ g[/tex]
or,
[tex]=0.009 \ kg[/tex]
mass of wooden block,
[tex]m=1.20 \ kg[/tex]
speed,
[tex]s=0.390 \ m[/tex]
Coefficient of kinetic friction,
[tex]\mu=0.20[/tex]
As we know,
The Kinematic equation is:
⇒ [tex]v^2=u^2+2as[/tex]
then,
Initial velocity will be:
⇒ [tex]u=v^2-2as[/tex]
[tex]=v^2-2 \mu gs[/tex]
On substituting the given values, we get
⇒ [tex]u=\sqrt{0-2\times 0.20\times 9.8\times 0.390}[/tex]
[tex]=\sqrt{-1.5288}[/tex]
[tex]=1.23 \ m/s[/tex]
As we know,
The conservation of momentum is:
⇒ [tex]mu=m'u'[/tex]
or,
⇒ Initial speed, [tex]u'=\frac{mu}{m'}[/tex]
On substituting the values, we get
⇒ [tex]=\frac{1.20\times 1.23}{0.009}[/tex]
⇒ [tex]=\frac{1.476}{0.009}[/tex]
⇒ [tex]=164 \ m/s[/tex]
which is an example of a scientist using a mathematical model to describe the weather?
A. The scientist finds an equation that predicts how long a rainstorm will last.
B. The scientist says that a lightning bolt is like a long snake.
C. The scientist uses cotton balls to represent clouds, and grass to represent the ground.
D. The scientist thinks of a cloud as a giant ball of cotton candy.
(its A)
Answer:
The scientist finds an equation that predicts how long the rainstrom will last.
Explanation:
I just answered it :)
As you rise upwards in the atmosphere air pressure___
Answer:
Gases - Water vapor, Nitrogen, Oxygen etc. Describe what happens to air pressure as you rise upwards in the atmosphere. What causes this change in air pressure? As altitude increases, air pressure will decrease As altitude increases the gas molecules that make up the air spread further apart
Answer: As you rise upwards in the atmosphere, air pressure decreases
Explanation: Because there are fewer molecules in the air, the air has a lower density, which results in a drop in air pressure. At different altitudes, the air is not the same. The area close to the earth is denser. As we rise, it continues to thin out. As a result of more air nearby, there is also increased air pressure. The weight and pressure of the air also continue to reduce as the volume of air does.
Astronomy Question
Who thinks Venus is the hottest planet instead of the lava planet?
say aye or nay
Answer:
AYE
Explanation:
A current loop ABCDA consists of a metal rod. a resistor R, and a pair of conducting rails separated by a distance d. The rod has a weight mg and it is falling with an instantaneous speed v. There is a constant magnetic field B which is perpendicular to the paper and directed into the paper. Find the direction of the induced current through the resistor It. A to B B to A 0 What is the magnitude of the induced current? If B = 3.6T, d = 7m, m = 4.7kg, R = 8.2 ohm, and g = 9.8 m/s2 . find the terminal velocity. (When the terminal velocity is readied, there is no net force on the rod, so the magnetic force is equal and opposite to the weight of the rod.) Answer in units of m/s.
Answer:
a) [tex]\vec{d} =B-A[/tex]
b) [tex]I=\frac{B*v*d*\sin 90 \textdegree}{R}[/tex]
c) [tex]v \approx 0.6m/s[/tex]
Explanation:
From the question we are told that
Magnetic field strength [tex]B=3.6T[/tex]
Distance traveled [tex]d=7m[/tex]
Mass [tex]m=4.7 kg[/tex]
Resistance [tex]r=8.2 ohm[/tex]
Gravitational acceleration [tex]g=9.8m/s^2[/tex]
[tex]\theta =90 \textdegree[/tex] Because of perpendicularity
a)
Generally the direction of the current will be given as
[tex]\vec{d} =B-A[/tex]
Because it opposes increases of magnetic flux
b)
Generally the equation for induced EMF [tex]E[/tex] is mathematically given as
[tex]E=B*v*d*\sin \theta[/tex]
[tex]E=B*v*d*\sin 90 \textdegree[/tex]
Generally the equation for induced current [tex]I[/tex] is mathematically given as
[tex]I=E/R[/tex]
[tex]I=\frac{B*v*d*\sin 90 \textdegree}{R}[/tex]
c)
Generally the the equation for force F at terminal speed is mathematically given as
[tex]F=mg[/tex]
[tex]mg=B*I*d*\sin 90 \textdegree[/tex]
[tex]mg=B*(\frac{B * v * d }{R}) *d[/tex]
[tex]v=\frac{m*g*R}{B^2*D^2}[/tex]
[tex]v=\frac{4.7*9.8*8.2}{3.6^2*7^2}[/tex]
[tex]v=0.59475m/s[/tex]
[tex]v \approx 0.6m/s[/tex]
Black holes result from
Answer:
supernova explosion or death of massive star
Explanation:
"Most black holes form from the remnants of a large star that dies in a supernova explosion."
A 1.0μF capacitor with an initial stored energy of 0.50 J is discharged through a 1.0MΩ resistor. (a) What is the initial charge on the capacitor? (b) What is the current through the resistor when the discharge starts? Find an expression that gives, as a function of time t, (c) the potential difference V C across the capacitor, (d) the potential difference V R across the resistor, and (e) the rate at which thermal energy is produced in the resistor.
Answer:
A) q_o = 0.001 C
B) I = 0.001•e^(-t)
C) V_c = 1000e^(-t)
D) V_r = 1000e^(-t)
E) P = e^(-2t) watts
Explanation:
A) We are given;
Initial stored energy; U_o = 0.5 J
Capacitance; C = 1.0μF = 1 × 10^(-6) F
To find the charge, we will use the formula for energy in capacitors which is given by;
U = q²/2C
Thus, since we are dealing with initial energy, U is U_o and q is q_o
Making q the subject, we have;
q_o = √2CU_o
q_o = √(2 × 1 × 10^(-6) × 0.5)
q_o = 0.001 C
B) The charge as a function of time is expressed as;
q = q_o•e^(-t/RC)
Now the current is gotten by differentiating the charge function. Thus;
I = (q_o/RC)•e^(-t/RC)
Where;
R is Resistance = 1.0MΩ = 1 × 10^(6) Ω
C is capacitance = 1 × 10^(-6) F
(q_o/RC) is the initial current = 0.001/(1 × 10^(6) × 1 × 10^(-6))
(q_o/RC) = 0.001 A
Thus;
I = 0.001•e^(-t/(1 × 10^(6) × 1 × 10^(-6)))
I = 0.001•e^(-t)
C) Formula for potential difference across the capacitor is;
V_c = IR
I = 0.001•e^(-t)
R = 1 × 10^(6) Ω
Thus;
V_c = 1 × 10^(6) × 0.001•e^(-t)
V_c = 1000e^(-t)
D) Potential difference across the resistor will be the same as that across the capacitor because the resistor is connected in parallel to the capacitor.
Thus;
V_r = V_c = 1000e^(-t)
E) rate at which thermal energy is produced is basically the power.
Thus;
P = (V_r)²/R
P = (1000²e^(-2t))/1 × 10^(6)
P = e^(-2t) watts
Rank the following objects by their accelerations down an incline (assume each object rolls without slipping) from least to greatest:
a. Hollow Cylinder
b. Solid Cylinder
c. Hollow Sphere
d. Solid Sphere
Answer:
acceleration are
hollow cylinder < hollow sphere < solid cylinder < solid sphere
Explanation:
To answer this question, let's analyze the problem. Let's use conservation of energy
Starting point. Highest point
Em₀ = U = m g h
Final point. To get off the ramp
Em_f = K = ½ mv² + ½ I w²
notice that we include the kinetic energy of translation and rotation
energy is conserved
Em₀ = Em_f
mgh = ½ m v² +1/2 I w²
angular and linear velocity are related
v = w r
w = v / r
we substitute
mg h = ½ v² (m + I / r²)
v² = 2 gh [tex]\frac{m}{m+ \frac{I}{r^2} }[/tex]
v² = 2gh [tex]\frac{1}{1 + \frac{I}{m r^2} }[/tex]
this is the velocity at the bottom of the plane ,, indicate that it stops from rest, so we can use the kinematics relationship to find the acceleration in the axis ax (parallel to the plane)
v² = v₀² + 2 a L
where L is the length of the plane
v² = 2 a L
a = v² / 2L
we substitute
a = [tex]g \ \frac{h}{L} \ \frac{1}{1+ \frac{I}{m r^2 } }[/tex]
let's use trigonometry
sin θ = h / L
we substitute
a = g sin θ \ \frac{h}{L} \ \frac{1}{1+ \frac{I}{m r^2 } }
the moment of inertia of each object is tabulated, let's find the acceleration of each object
a) Hollow cylinder
I = m r²
we look for the acerleracion
a₁ = g sin θ [tex]\frac{1}{1 + \frac{mr^2 }{m r^2 } }[/tex]1/1 + mr² / mr² =
a₁ = g sin θ ½
b) solid cylinder
I = ½ m r²
a₂ = g sin θ [tex]\frac{1}{1 + \frac{1}{2} \frac{mr^2}{mr^2} }[/tex] = g sin θ [tex]\frac{1}{1+ \frac{1}{2} }[/tex]
a₂ = g sin θ ⅔
c) hollow sphere
I = 2/3 m r²
a₃ = g sin θ [tex]\frac{1}{1 + \frac{2}{3} }[/tex]
a₃ = g sin θ [tex]\frac{3}{5}[/tex]
d) solid sphere
I = 2/5 m r²
a₄ = g sin θ [tex]\frac{1 }{1 + \frac{2}{5} }[/tex]
a₄ = g sin θ [tex]\frac{5}{7}[/tex]
We already have all the accelerations, to facilitate the comparison let's place the fractions with the same denominator (the greatest common denominator is 210)
a) a₁ = g sin θ ½ = g sin θ [tex]\frac{105}{210}[/tex]
b) a₂ = g sinθ ⅔ = g sin θ [tex]\frac{140}{210}[/tex]
c) a₃ = g sin θ [tex]\frac{3}{5}[/tex]= g sin θ [tex]\frac{126}{210}[/tex]
d) a₄ = g sin θ [tex]\frac{5}{7}[/tex] = g sin θ [tex]\frac{150}{210}[/tex]
the order of acceleration from lower to higher is
a₁ <a₃ <a₂ <a₄
acceleration are
hollow cylinder < hollow sphere < solid cylinder < solid sphere
Why would citizens need to be wary of debris on the road?
A student rubbed two balloons with a piece of wool. What will happen when the balloons are
brought near each other?
Attract
Repel
Answer:
# ICSE board exam 2021
Explanation:
# ICSE board exam 2021
# ICSE board exam 2021
# ICSE board exam 2021
examples of transfer of energy
Answer:
by radiation
by heating
electrically
mechanically
Which wave has the longest wavelength?
A. A
B. B
C. C
D.D
Answer:
In my opinion, ''A" would be the longest wavelength.
A –5 μC charge is placed 2 mm from a +3 μC charge. Find the force between the two charges?
Answer:
-33750 N
Explanation:
Use coulomb's law: [tex]\frac{k(q1)(q2)}{r^{2} } = \frac{(9x10^{9})(-5x10^{-6})(3x10^{-6})}{0.002^{2} } = -33750 N[/tex]
In general, the time it takes from when in interstellar cloud fragment first begins collapsing until it gives birth to a main-sequence star is In general, the time it takes from when in interstellar cloud fragment first begins collapsing until it gives birth to a main-sequence star is shorter for less massive stars. about the same for all stars. dependent on the rotation rate of the star. longer for less massive stars.
Answer:
longer for less massive stars.
Explanation:
A star is a giant astronomical or celestial object that is comprised of a luminous sphere of plasma, binded together by its own gravitational force.
It is typically made up of two (2) main hot gas, Hydrogen (H) and Helium (He).
Some of the examples of stars are Canopus, Sun (closest to the Earth), Betelgeus, Antares, Vega etc.
Generally, the time taken for the collapse of an interstellar cloud fragment to the period (time) when a main-sequence star is given birth to, is usually longer for less massive stars.
This ultimately implies that, stars that are not so massive or big in size are transformed from interstellar cloud fragment to a main-sequence star is lesser.
Time taken from, when in interstellar cloud fragment first begins collapsing until it gives birth to a main-sequence star is longer for less massive stars.
What is interstellar cloud fragment?The process of Interstellar cloud fragment results the development into the stars.
The formation of stars is takes place within the highly dense concentration of the interstellar gases and the dust. These interstellar gases and the dust forms the molecular or interstellar clouds.
Here, in these molecular clouds the gases are present like helium, CO, hydrogen in major amount. Now this clouds started to collapse due to their own weight and density, and the formation of star is started.
Here, the H₂ atoms, which are fused forms helium atoms, to their core to form the main-sequence star.
In general, the time it takes from when in interstellar cloud fragment first begins collapsing until it gives birth to a main-sequence star. The time required to form the main-sequence star is lesser than the star which has big size.
Hence, the time taken from, when in interstellar cloud fragment first begins collapsing until it gives birth to a main-sequence star is longer for less massive stars.
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A forward horizontal force of 12 N is used to pull a 240-N crate at constant velocity across a
horizontal floor. The coefficient of friction is:
Explanation:
[tex]let \: coefficient \: of \: friction \: be \: \gamma \\ from \: third \: law \: of \: solid \: friction \\friction \: force = \gamma \times normal \: reaction \\ F = \gamma R \\ but \: R = mg = 240N \\ \gamma = \frac{ F}{R} \\ \gamma = \frac{12}{240} \\ \gamma = \frac{1}{20} [/tex]
molecules , like hormones , are made up of which of the following
A. cells
B. Atoms
C. Tissues
D. Organs
Answer:
atoms
Explanation:
Hormones are derived from amino acids or lipids. Amine hormones originate from the amino acids tryptophan or tyrosine. Larger amino acid hormones include peptides and protein hormones. Steroid hormones are derived from cholesterol.
What is another example of convection
Answer:
boiling water - When water heats, the heat from the burner is transferred to the container, heating the water at the bottom. This hot water rises, creating a circular motion, as colder water descends to replace it.
The sun is made up mostly of
gas material.
liquid material.
solid material.
plasma material.
The sun is made up mostly of plasma material. Option D
Plasma is considered the fourth state of matter, distinct from gases, liquids, and solids. It is a highly ionized gas consisting of charged particles, including electrons and ions. The sun is primarily composed of plasma due to the extremely high temperatures and intense energy present in its core.
The sun's core has a temperature of about 15 million degrees Celsius (27 million degrees Fahrenheit), which is hot enough to strip electrons from atoms, creating a plasma state. The high temperature and pressure cause hydrogen atoms to undergo nuclear fusion, resulting in the release of vast amounts of energy in the form of light and heat.
This fusion process involves the conversion of hydrogen nuclei (protons) into helium nuclei, releasing enormous energy in the process. The intense heat and pressure within the sun's core sustain this fusion reaction, powering the sun and providing the energy that is radiated out into space as sunlight.
Plasma is an electrically conductive state of matter, meaning it can carry electric currents. The sun's plasma exhibits complex dynamics, including the generation of magnetic fields, solar flares, and coronal mass ejections.
In summary, the sun is primarily composed of plasma material due to the extreme temperatures and intense energy within its core. The plasma state allows for nuclear fusion to occur, releasing the immense energy that sustains the sun's radiative output.
Option D
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If the length of the standing wave below is 2 meters, what is the wavelength of the standing
wave? *
Answer:
fffffgggggggggggggghhh
An AC circuit has resistor, capacitor and inductor connected in series. It is
connected to a voltage supply at resonant frequency. If the frequency of the
voltage supply is reduced, which of the following quantities will be reduced? *
Answer:
Z = (R^2 + X^2)^1/2
At the resonant frequency, the quantity X equal zero and
w L - 1 / (w * C) equals zero where w is omega the angular frequency
Some types of bacteria contain chains of ferromagnetic particles parallel to their long axis. The chains act like small bar magnets that align these magnetotactic bacteria with the earth's magnetic field. In one experiment to study the response of such bacteria to magnetic fields, a solenoid is constructed with copper wire, 1.0 mmmm in diameter, evenly wound in a single layer to form a helical coil of length 40 cmcm and diameter 12 cmcm. The wire has a very thin layer of insulation, and the coil is wound so that adjacent turns are just touching. The solenoid, which generates a magnetic field, is in an enclosure that shields it from other magnetic fields. A sample of magnetotactic bacteria is placed inside the solenoid. The torque on an individual bacterium in the solenoid’s magnetic field is proportional to the magnitude of the magnetic field and to the sine of the angle between the long axis of the bacterium and the magnetic-field direction.
What current is needed in the wire so that the magnetic field experienced by the bacteria has a magnitude of 150μT?
a. 0.095 A
b. 0.12 A
c. 0.30 A
d. 14 A.
Answer:
the required current is 0.12 A
Option b) 0.12 A is the correct answer
Explanation:
Given the data in the question,
to determine the current needed in the wire, we use the following relation;
B = μ₀n[tex]I[/tex]
[tex]I[/tex] = B / μ₀n
where μ₀ is the magnetic constant ( 4π × 10⁻⁷ T.m/A )
n is the number of turns ( 1 / 1mm[tex]\frac{10^{-3}m}{1 mm}[/tex]) = 1000 m⁻¹
B is magnitude ( 150μT ( [tex]\frac{10^{-6}m}{1uT}[/tex]) )
so we substitute
[tex]I[/tex] = [ 150μT ( [tex]\frac{10^{-6}m}{1uT}[/tex]) ] / [ ( 4π × 10⁻⁷ T.m/A ) × 1000 m⁻¹ ]
[tex]I[/tex] = [ 0.00015 ] / [ 0.00125 ]
[tex]I[/tex] = 0.12 A
Therefore, the required current is 0.12 A
Option b) 0.12 A is the correct answer
Pls Help Me with this problem
Answer:
explanation
Explanation:
1 = C
2 = A
3 = D
4 = E
5 = B
Two rubber bullets (each of the same mass) are fired at the same velocity towards two different blocks of equal mass. One block is made of clay and the bullet gets stuck in it, the clay block bullet begins to move in the direction the bullet was fired. The other block is made of aluminum and the bullet bounces off the block, the aluminum block also begins to move in the direction the bullet was fired. Which block (clay or aluminum) will move with greater velocity after being struck by the bullet
Answer:
Aluminum board will move with a higher velocity
Explanation:
The velocity of the block will be higher when the impulse imparted by the bullet is higher.
In case of bullet bouncing off, the impulse imparted on the aluminum board is high and hence, it will move with a high velocity as compared to that of the clay board.
What are the two main types of defense that teams employ?
O Front and Back
O Person and Zone
O Goal and Midline.
Thing
Answer:
they employ front and Back defenses
Explanation:
there are the most positions in these types
Two balloons become equally charged once they are rubbed against each other. If the force between the balloons is 6.2 * 10^23 N, what would happen to the force if the charge were to triple on one of the balloons?
A) the force would triple
B) the force would become one-nineth
A solid, uniform cylinder with mass 8.35kg and diameter 15.0cm is spinning with angular velocity 250rpm on a thin, frictionless axle that passes along the cylinder axis. You design a simple friction-brake to stop the cylinder by pressing the brake against the outer rim with a normal force. The coefficient of kinetic friction between the brake and rim is 0.338. What must the applied normal force be to bring the cylinder to rest after it has turned through 5.05 revolutions?
Answer:
354
Explanation: