Answer:
Một ô tô có khối lượng m=1000kg đang chạy với vận tốc 18km/h thì hãm phanh.Biết lực hãm là 2000N. Tính quãng đường xe còn chạy thêm trước khi dừng ... Chiếu phương trình của định luật II Newtơn mà →F=m. ... chuyển động ta có F=ma, suy ra gia tốc chuyển động của xe ( với F=2000N) ...
Explanation:
A permanent magnet is pushed into a wire, left there for a while, and then pulled out. During which time does a current run though the wire? A from the time that the magnet is pushed into the coil to the time it is pulled out B while the magnet remains within the coil C while the magnet is moving D only while the magnet is being pulled out of the coil
Answer:
C. while the magnet is moving
Explanation:
Electromagnetic induction implies the production of electric current by mere movement of a magnet with respect to a coil or wire.
In the given question, current would be induced in the wire only when the magnet moves. That is either when the magnet is pushed into a wire, or when pulled out. But no current would flow through the wire when the magnet is left there for a while.
The current is induced because of the motion involved. Thus, the appropriate option is C.
The fact that we can define electric potential energy means that:
A) the electric force is nonconservative
B) the electric force is conservative
C) the work done on a charged particle depends on the path it takes
D) there is a point where the electric potential energy is exactly zero
E) it takes work for the electric force to move from some point a to some other point b and back again
Answer: I'd go with Option B if you're allowed to pick One Option Only.
Option A is wrong. Electric Forces arent Non - Conservative. They're Conservative forces.
Option B: We Can Only Define Potential Energies for conservative Forces/fields✅
Option C is wrong. Since the Electric Force is Conservative... It doesn't depend on the path taken.
Option D... There's a Point where the electric Potential Energy is Zero but the separation Distance Would be large.
E is wrong because the Workdone around a closed path is Zero.
The electric potential energy results from the conservative Coulomb forces.
What is electric potential energy?The electric potential energy is the potential energy that results due to the conservative Coulomb forces and is always associated with the set of two charged particles.
Any object can have electric potential energy by two key elements first is its own charge and the second is its position with respect to the other charged particle.
The electric potential energy-containing only one point charge will be zero. Because there are no other sources of electrostatic force against which an external agent must do work in moving the point charge from infinity to its final position.
Thus the electric potential energy results from the conservative Coulomb forces.
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A man pulls his dog (m=20kg) on a sled with a force of 100N at a 60° angle from the horizontal. What is the horizontal component of the force?
A) 100N
B) 196N
C) 50N
D) 86N
show your work please
Answer:
the horizontal component of the force is 50 N
Explanation:
Given;
force applied by the man, F = 100 N
angle of inclination of the force, θ = 60⁰
mass of the dog, m = 20 kg
The horizontal component of the force is calculated as;
[tex]F_x = F\times cos(\theta)\\\\F_x = 100 \ N \times cos(60^0)\\\\F_x = 100\ N \times 0.5\\\\F_x = 50 \ N[/tex]
Therefore, the horizontal component of the force is 50 N
An elevator lifts a mass=200kg a distance of 20m in 15s. What power does the elevator motor produce? *
A) 20000J
B) 20000W
C) 2666W
D) 600000W
show your work please
Answer:
C. 2666W
Explanation:
m =200kg
h =20m
t =15s
g =10ms^-2
p = mgt/t
=200×20×10/15
=40,000/15
=2666.6
≈2666W
An electron is moving through an (almost) empty universe at a speed of 628 km,/s toward the only other object in the universe — an insulating sphere with a diameter of 4 m and charge density 3nC/m2 on its outside surface. The sphere "captures" the electron, which falls into a circular orbit.
Required:
Find the radius and period of the orbit.
Answer:
r = 2,026 10⁹ m and T = 2.027 10⁴ s
Explanation:
For this exercise let's use Newton's second law
F = m a
where the force is electric
F = [tex]k \frac{q_1q_2}{r^2}[/tex]
Acceleration is centripetal
a = v² / r
we substitute
[tex]k \frac{q_1q_2}{r^2} = m \frac{v^2}{r}[/tex]
r = [tex]k \frac{q_1q_2}{m \ v^2}[/tex] (1)
let's look for the charge in the insulating sphere
ρ = q₂ / V
q₂ = ρ V
the volume of the sphere is
v = 4/3 π r³
we substitute
q₂ = ρ [tex]\frac{4}{3}[/tex] π r³
q₂ = 3 10⁻⁹ [tex]\frac{4}{3}[/tex] π 4³
q₂ = 8.04 10⁻⁷ C
let's calculate the radius with equation 1
r = 9 10⁹ 1.6 10⁻¹⁹ 8.04 10⁻⁷ /(9.1 10⁻³¹ 628 10³)
r = 2,026 10⁹ m
this is the radius of the electron orbit around the charged sphere.
Since the orbit is circulating, the speed (speed modulus) is constant, we can use the uniform motion ratio
v = x / t
the distance traveled in a circle is
x = 2π r
In this case, time is the period
v = 2π r /T
T = 2π r /v
let's calculate
T = 2π 2,026 10⁹/628 103
T = 2.027 10⁴ s
You are a venture capitalist that is asked to invest in a startup company that claims it will be able to launch tiny "micro space probes" into space at close to the speed of light using a massive electromagnetic rail gun system2. You are cynical about their cost estimates and decide to analyze the problem in more detail before you invest in their company. Neglect air resistance for this worksheet.
1. A typical payload they claim to launch will weigh 1 kilogram and be accelerated to 90% the speed of light. How much electrical energy will the rail gun require to launch the probe, assuming it is 20% efficient at converting electrical energy to projectile kinetic energy?
2. Given that typical electrical costs are about 5 cents/MJ, how much would this launch cost? Would you invest in this company?
43. You are also concerned about safety. What happens if this projectile were to hit an airplane that is flying overhead and dissipate all of its kinetic energy in the collision? To give you a sense of scale, a large nuclear explosion generates about 1015 J of energy.
4. The system must be able to launch probes to all parts in the sky and must be transportable on a ship. Assume that the railgun is mounted on a frigate-class navy ship (weight = 4,000 metric tons).
a. Will the recoil momentum of the ship be relativistic? Justify your argument.
b. At what speed will the ship recoil after it launches a probe? Do you think that this is a problem for the ship?
Answer:
1. 5.825 × 10¹⁷ J
2. i. $ 29.125 billion ii. I would not invest in the company
3. A nuclear reaction would occur if the payload hits an airplane flying overhead and dissipates all its kinetic energy in the collision.
4. a i. The momentum will not be relativistic
ii. This is because objects with large masses do not move at relativistic speeds
b i. 155 m/s
ii. This speed wouldn't be a problem for the ship.
Explanation:
1. A typical payload they claim to launch will weigh 1 kilogram and be accelerated to 90% the speed of light. How much electrical energy will the rail gun require to launch the probe, assuming it is 20% efficient at converting electrical energy to projectile kinetic energy?
The kinetic energy of the payload is K = (γ - 1)mc² where m = mass of payload = 1 kg, c = speed of light = 3 × 10⁸ m/s and γ = 1/√(1 - β²) where β = 0.9 (since the payload moves at 90 % speed of light)
So, K = (γ - 1)mc²
= (1/√(1 - β²) - 1)mc²
= (1/√(1 - (0.9)²) - 1) × 1 kg × (3 × 10⁸ m/s)²
= (1/√(1 - 0.81) - 1) × 1 kg × (3 × 10⁸ m/s)²
= (1/√0.19 - 1) × 1 kg × (3 × 10⁸ m/s)²
= (1/0.436 - 1) × 1 kg × (3 × 10⁸ m/s)²
= (2.294 - 1) × 1 kg × (3 × 10⁸ m/s)²
= 1.294 × 1 kg × 9 × 10¹⁶ m²/s²
= 11.65 × 10¹⁶ kgm²/s²
= 1.165 × 10¹⁷ J
Let E be the total electrical energy of the rail gun. Since 20 % of this energy is converted to kinetic energy of the payload, we have
20 % of E = K
0.2E = K
E = K/0.2
= 1.165 × 10¹⁷ J/0.2
= 5.825 × 10¹⁷ J
2 Given that typical electrical costs are about 5 cents/MJ, how much would this launch cost? Would you invest in this company?
i. how much would this launch cost?
Since the total energy required is E = 5.825 × 10¹⁷ J = 5.825 × 10¹¹ MJ and it costs 5 cent/MJ. So the total cost of energy will be total energy rate = 5.825 × 10¹¹ MJ × 5 cent/MJ = 29.125 × 10¹¹ = 2.9125 × 10¹² cents. Converting this to dollars, we have 2.9125 × 10¹² cents/100 cents/dollar = 2.9125 × 10¹⁰ dollars = 29.125 × 10⁹ dollars = 29.125 billion dollars = $ 29.125 billion
ii. Would you invest in this company?
I would not invest in the company
3. You are also concerned about safety. What happens if this projectile were to hit an airplane that is flying overhead and dissipate all of its kinetic energy in the collision? To give you a sense of scale, a large nuclear explosion generates about 1015 J of energy.
Since the kinetic energy of the payload is 1.165 × 10¹⁷ J and a nuclear explosion generates about 10¹⁵ J of energy, then a nuclear reaction would occur if the payload hits an airplane flying overhead and dissipates all its kinetic energy in the collision.
4. The system must be able to launch probes to all parts in the sky and must be transportable on a ship. Assume that the rail gun is mounted on a frigate-class navy ship (weight = 4,000 metric tons).
a. Will the recoil momentum of the ship be relativistic? Justify your argument.
i. Will the recoil momentum of the ship be relativistic?
The momentum will not be relativistic.
ii. Justify your argument.
This is because objects with large masses do not move at relativistic speeds. Since the speed cannot be relativistic, its momentum which is the product of mass and speed is non-relativistic
b. At what speed will the ship recoil after it launches a probe? Do you think that this is a problem for the ship?
i. At what speed will the ship recoil after it launches a probe?
Since the total energy of the payload E' = K + mc² = 1.165 × 10¹⁷ J + 1 kg × (3 × 10⁸ m/s)² = 1.165 × 10¹⁷ J + 1 kg × 9 × 10¹⁶ m²/s² = 11.65 × 10¹⁶ J + 9 × 10¹⁶ J = 20.65 × 10¹⁶ J
Also, E'² = (pc)² + (mc²)² where p = momentum of payload
So, making p subject of the formula, we have
(pc)² = E'² - (mc²)²
pc = √[E'² - (mc²)²]
p = √[E'² - (mc²)²]/c
substituting the values of the variables into the equation, we have
p = √[E'² - (mc²)²]/c
p = √[(20.65 × 10¹⁶ J)² - 1kg × (3 × 10⁸ m/s²)²]/3 × 10⁸ m/s
p = √[(20.65 × 10¹⁶ J)² - (1kg × 9 × 10⁸ m²/s²)²]/3 × 10⁸ m/s
p = √[426.4225 × 10³² J² - 81 × 10³² J²]/3 × 10⁸ m/s
p = √[345.4225 × 10³² J²]/3 × 10⁸ m/s
p = 18.59 × 10¹⁶/3 × 10⁸ m/s
p = 6.20 × 10⁸ kgm/s
From the law of conservation, this momentum of the payload equals the momentum of recoil of the ship.
So, p = m'v where m' = mass of navy ship = 4,000 metric tons = 4,000 × 1000 kg = 4 × 10⁶ kg and v = speed of navy ship
So, v = p/m'
= 6.20 × 10⁸ kgm/s ÷ 4 × 10⁶ kg
= 1.55 × 10² m/s
= 155 m/s
ii. Do you think that this is a problem for the ship?
Since the ship's speed is 155 m/s, which is small for an object with such a large mass, this speed wouldn't be a problem for the ship.
A pitcher throws a curveball that reaches the catcher in 0.61 s. The ball curves because it is spinning at an average angular velocity of 350 rev/min (assumed constant) on its way to the catcher's mitt. What is the angular displacement of the baseball (in radians) as it travels from the pitcher to the catcher
Answer:
22.36 rad
Explanation:
Applying,
ω = θ/t.............. Equation 1
Where ω = angular velocity, θ = angular displacement of the baseball, t = time
make θ the subject of the equation
θ = ωt............... Equation 2
From the question,
Given: ω = 350 rev/min = 350(0.10472) = 36.652 rad/s, t = 0.61 s
Substitute these values into equation 1
θ = 0.61(36.652)
θ = 22.36 rad
Hence the angular displacement of the baseball is 22.36 rad
a 50kg skater on level ice, has built up her speed to 30km/h. how far will she coast before sliding friction dissipates her energy?
Answer:
belpw
Explanation:
The distance prior to the sliding friction dispersing her energy would be:
- The distance will remain unaffected by the sliding friction i.e. 354m
As we know, When Sliding friction dissolves her energy, leading her Kinetic Energy to turn 0 on coming to the state of rest. So,
[tex]1/2 mv^2 - 1/2 mu^2 = -W[/tex] (∵ Work in -ve denotes it is done opposite to friction)
Given that,
m(mass) [tex]= 50 kg[/tex]
v(velocity) [tex]= 30 km/hr[/tex] or [tex]8.33 m/s[/tex]
The coefficient of Kinetic Friction [tex]= 0.01[/tex]
g(gravitational force) [tex]= 9.8 m/s^2[/tex]
Initial Velocity(u) [tex]= 30[/tex] × [tex]1000/3600 m/s[/tex]
[tex]= 8.33 m/s[/tex]
Now by employing the provided values,
[tex]F =[/tex] μ[tex]mg[/tex]
[tex]= (0.01) (50) (9.8)[/tex]
[tex]= 4.9[/tex]
∵ [tex]F = 4.9 N[/tex]
By using the above expression, we will find the distance;
[tex]1/2 mv^2 - 1/2 mu^2 = -W[/tex]
⇒ [tex]1/2 (50) (0)^2 - 1/2 (50) (8.33)^2 = -4.9(S)[/tex]
⇒ [tex]1734.7225 = 4.9S[/tex]
⇒ [tex]S = 1734.7225/4.9[/tex]
∵ [tex]S = 354 m[/tex]
Because [tex]1/2 mv^2 - 1/2 mu^2 = -W[/tex] [tex]= -[/tex] μmgS
⇒ [tex]S = (u^2 - v^2)[/tex]/2μ[tex]g[/tex]
Thus, the distance will remain unaffected by the sliding friction i.e. 354m
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the oscillation of pendulum is ...... motion
Answer:
A simple pendulum consists of a ball (point-mass) m hanging from a (massless) string of length L and fixed at a pivot point P. When displaced to an initial angle and released, the pendulum will swing back and forth with periodic motion.
On a day when the speed of sound is 345 m/s, a 440 Hz tuning fork causes a tube closed at one end to vibrate in the second harmonic. How long is the tube?
Answer:
Length = 3.136 meters
Explanation:
Given the following data;
Speed = 345 m/s
Frequency = 440 Hz
To find how long is the tube;
First of all, we would determine the wavelength;
Wavelength = speed/frequency
Wavelength = 345/440
Wavelength = 0.784 m
Next, we would determine how long is the tube using the formula;
[tex] Length = \frac {2n - 1}{4} * wavelength [/tex]
Substituting into the formula, we have;
[tex] Length = \frac {2*1 - 1}{4} * 0.784 [/tex]
[tex] Length = \frac {2 - 1}{4} * 0.784 [/tex]
[tex] Length = \frac {1}{4} * 0.784 [/tex]
Length = 3.136 meters
HELP PLSS I CANT FAIL!!!
Elements from Period 3 of the periodic table are highlighted. Which element
is a metalloid?
A. Sodium
B. Argon
C. Sulfur
D. Silicon
A 5.0-kg solid cylinder of radius 0.25 mis free to rotate about an axle that runs along the cylinders length and passes through its center. A thread wrapped around the cylinder is weighed down by a mass of 2.0 kg so as to unwrap and make the cylinder rotate as this mass falls. Ignore any friction in the axle. If there is no slippage between the thread and the cylinder, and the cylinder starts from rest (a) Calculate the velocity of the block after it has fallen a distance of 2.0m. Give your answer in m.s (b) Calculate the total work done by the rope on the cylinder after the block has fallen a distance of 2.0 m. Give your answer in Joule.
Answer:
157n is the correct answer
Describe how the constant electric potential from the battery drives the charges in the conducting wire in your own words.
Explanation:
It is known that charges tend to move from a higher potential towards lower potential. As a result, charges tend to move from a positive terminal to negative terminal of the battery.
For example, at a certain height water is stored in a water tank. This height is correspondent to the constant potential and water contained is the charge present in the battery.
When a pipe is connected from the tank to the ground then water will start moving towards the ground and similarly if a conducting wire is connected across the battery then charge will also begin to flow in the same direction which is called current.
The phrase "hot air rises" describes which type of heat transfer?
A. Conduction
B. Insulation
C. Convection
D. Radiation
Answer:
Option C
Explanation:
C. Convection...
The phrase 'hot air rises'describe the convection as a type of heat transfer therefore the correct answer is option C.
It is the type of heat transfer in which the heat is transferred from the bulk motion of the particles of liquid and gases due to the presence of temperature gradient.
The hot air rises is one of the best example of convection currents
The boiling water is also an example of convection heat transfer process in which the hot water rises to the top of the surface due to the bulk molecular movement of convection current .
The hot air rides is the bulk movement of the gas molecules because of the presence of the temperature gradients resulting in the varied density of air ,the hot air rising to the surface have less density as compared to the air settling near the surface ,the convection current phenomenon is responsible for the phrase "hot air rises" ,therefore the correct option is the option C.
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QUESTION 24
2 point
A man travels 40 km eastwards, then 40 km to the south before finally travelling
10 km west. At the end of his journey the magnitude of his displacement is
The ejection seat has an acceleration of 8gees (8xgravity or ~80m/s/s). He has a mass of 70kg. The total force on him from the chair/rocket would be.
A) (80m/s/s)(70kg)=5600N
B) (80m/s/s)(70kg)=5600N + Fg = 5600N+(70kg)(9.8N/kg)~5600N+700N=6300N
C) (80m/s/s)(70kg)=5600N - Fg = 5600N+(70kg)(9.8N/kg)~5600N-700N=4900N
D) I need the time
Answer:
B) (80m/s/s)(70kg)=5600N + Fg = 5600N+(70kg)(9.8N/kg)~5600N+700N=6300N
Explanation:
The total force by the chair is given by the following formula:
[tex]F = m(g+a)[/tex]
where,
F = Force = ?
m = mass of person = 70 kg
g = value of acceleration dueto gravity = 9.81 m/s²
a = acceleration of ejection seat = 8g = 80 m/s²
Therefore,
[tex]F = mg+ma \\F = (70\ kg)(9.8\ m/s^2)+(70\ kg)(80\ m/s^2)\\F = 6300 N[/tex]
Therefore, the correct option is:
B) (80m/s/s)(70kg)=5600N + Fg = 5600N+(70kg (9.8N/kg)~5600N+700N=6300N
A 10,000J battery is depleted in 2h. What power consumption is this? *
A) 5000W
B) 3W
C) 1.4W
D) 20000W
show your work please
Answer:
C) 1.4W
Explanation:
Given;
energy of the battery, E = 10,000 J
duration of the battery, t = 2 hours
The power consumption of the battery is calculated as;
[tex]Power = \frac{Energy}{time} \\\\Power = \frac{10,000}{2 \times 3600 } \\\\Power = 1.4 \ J/s = 1.4 \ W[/tex]
Therefore, the power consumption of the battery is 1.4 W
A ceramic tile measuring 50 cm x50cm has been designed to bear a pressure of 40 N/in . Will it with stand a force of 5 N?
Answer:
The ceramic tile will stand the force of 5 N.
Explanation:
Step 1: Calculate the area (A) of the ceramic tile
We will use the formula for the area of a square.
A = 50 cm × 50 cm = 2500 cm²
Step 2: Convert "A" to in²
We will use the conversion factor 1 in² = 6.45 cm².
2500 cm² × 1 in²/6.45 cm² = 3.9 × 10² in²
Step 3: Calculate the pressure (P) exerted by a force (F) of 5 N
We will use the following expression.
P = F/A
P = 5 N / 3.9 × 10² in² = 0.013 N/in²
Since the pressure exerted would be less than the maximum pressure resisted (40 N/in²), the ceramic tile will stand the force of 5 N.
What is the direction of a vector with an x component of -12 m and a y component of -15 m?
Answer:
[tex]51.34^{\circ}[/tex]
Explanation:
Given that,
x component of a vector = -12 m
The y component of a vector = -15 m
We need to find the direction of a vector. The direction of a vector is given by :
[tex]\tan\theta=\dfrac{y}{x}[/tex]
Put all the values,
[tex]\tan\theta=\dfrac{-15}{-12}\\\\\theta=\tan^{-1}(\dfrac{-15}{-12})\\\\\theta=51.34^{\circ}[/tex]
So, the direction of vector is [tex]51.34^{\circ}[/tex] to x component.
Una persona en la tierra tiene una masa de 70[kg]. Calcule: a) Su fuerza peso en la tierra. b) Su fuerza peso en la luna (considere que la aceleración gravitatoria en la luna es de 1.62 [m/s²]) *
Answer:
a. El peso = 686 Newton
b. El peso = 113.4 Newton
Explanation:
Dados los siguientes datos;
Masa = 70 kg
Aceleración debida a la gravedad en la luna = 1,62 m/s² una.
a. Para encontrar la fuerza-peso en la Tierra;
Sabemos que la aceleración debida a la gravedad es igual a 9,8 m/s² en el planeta Tierra.
El peso se puede definir como la fuerza que actúa sobre un cuerpo o un objeto como resultado de la gravedad.
Matemáticamente, el peso de un objeto viene dado por la fórmula;
[tex] Peso = mg [/tex]
Dónde;
m es la masa del objeto.
g es la aceleración debida a la gravedad.
Substituting into the formula, we have;
El peso = 70 * 9.8
El peso = 686 Newton
b. To find weight on moon;
Weight = mass * acceleration due to gravity on moon
Weight = 70 * 1.62
Weight = 113.4 Newton
Mary applies a force of 73 N to push a box with an acceleration of 0.48 m/s^2. When she increases the pushing force to 84 N, the box's acceleration changes to 0.64 m/s^2. There is a constant friction force present between the floor and the box.
Required:
a. What is the mass of the box?
b. What is the coefficient of kinetic friction between the floor and the box?
Answer: [tex]68.75\ kg, 0.06[/tex]
Explanation:
Mary applies a force of 73 N to create an acceleration of [tex]0.48\ m/s^2[/tex]
When She increases force to 84 N, it creates an acceleration of [tex]0.64\ m/s^2[/tex]
Friction opposes the motion of box
[tex]\Rightarrow 73-f=m\times 0.48\quad \ldots(i)\\\Rightarrow 84-f=m\times 0.64\quad \ldots(ii)[/tex]
Subtract (i) from (ii)
[tex]\Rightarrow 11=m(0.64-0.48)\\\Rightarrow m=68.75\ kg[/tex]
Therefore friction is
[tex]\Rightarrow f=73-68.75\times 0.48\\\Rightarrow f=73-33\\\Rightarrow f=40\ N[/tex]
Here, friction is kinetic friction which is given by
[tex]\Rightarrow f=\mu_kmg\\\Rightarrow 40=\mu_k 68.75\times 9.8\\\Rightarrow \mu_k=0.061[/tex]
There are only two charged particles in a particular region. Particle 1 carries a charge of 3q and is located on the negative x-axis a distance d from the origin. Particle 2 carries a charge of -2q and is located on the positive x-axis a distance d from the origin.
Required:
Where is it possible to have the net field caused by these two charges equal to zero?
Answer:
The net field will be the sum of the fields created by each charge.
where the charge Q in a position r' is given by:
E(r) = k*Q/(r - r')^2
Where k is a constant, and r is the point where we are calculating the electric field.
Then for the charge 3q, in the position r₁ = (-d, 0, 0) the electric field will be:
E₁(r) = k*3q/(r - r₁)^2
While for the other charge of -2q in the position r₂ = (d, 0, 0)
The electric field is:
E₂(r) = -k*2*q/(r - r₂)^2
Then the net field at the point r is:
E(r) = E₁(r) + E₂(r) = k*3q/(r - r₁)^2 + -k*2*q/(r - r₂)^2
E(r) = k*q*( 3/(r - r₁)^2 - 2/(r - r₂)^2)
Then if the we want to find the points r = (x, y, z) such that:
E(r) = 0 = k*q*( 3/(r - r₁)^2 - -k*2*q/(r - r₂)^2)
Then we must have:
0 = ( 3/(r - r₁)^2 - 2/(r - r₂)^2)
Also remember that the distance between two points:
(x, y, z) and (x', y', z') is given by:
D = √( (x - x')^2 + (y - y)^2 + (z -z')^2)
Then we can rewrite:
r - r₁ = √( (x - (-d))^2 + (y - 0 )^2 + (z -0)^2)
= √( (x + d))^2 + y^2 + z^2)
and
r - r₂ = √( (x - d)^2 + (y - 0 )^2 + (z -0)^2)
= √( (x - d))^2 + y^2 + z^2)
Replacing that in our equation we get:
0 = ( 3/(√( (x + d))^2 + y^2 + z^2))^2 - -k*2*q/(√( (x - d))^2 + y^2 + z^2))^2)
0 = (3/((x + d))^2 + y^2 + z^2) - 2/ (x - d))^2 + y^2 + z^2)
We want to find the values of x, y, z such that the above equation is true.
2/ (x - d))^2 + y^2 + z^2) = (3/((x + d))^2 + y^2 + z^2)
2*[((x + d))^2 + y^2 + z^2] = 3*[(x - d))^2 + y^2 + z^2]
2*(x + d)^2 + 2*y^2 + 2*z^2 = 3*(x - d)^2 + 3*y^2 + 3*z^2
2*(x + d)^2 - 3*(x - d)^2 = 3*y^2 + 3*z^2 - 2*y^2 - 2*z^2
2*(x + d)^2 - 3*(x - d)^2 = y^2 + z^2
2*x^2 + 2*2*x*d + 2*d^2 - 3*x^2 + 3*2*x*d - 3*d^2 = y^2 + z^2
-x^2 + 10*x*d - d^2 = y^2 + z^2
we can rewrite this as:
- ( x^2 - 10*x*d + d^2) = y^2 + z^2
now we can add and subtract 24*d^2 inside the parenthesis to get
- ( x^2 - 10*x*d + d^2 + 24*d^2 - 24*d^2) = y^2 + z^2
-( x^2 - 2*x*(5d) + 25d^2 - 24d^2) = y^2 + z^2
-(x^2 - 2*x*(5d) + (5*d)^2) + 24d^2 = y^2 + z^2
The thing inside the parenthesis is a perfect square:
-(x - 5d)^2 + 24d^2 = y^2 + z^2
we can rewrite this as:
24d^2 = y^2 + z^2 + (x - 5d)^2
This equation gives us the points (x, y, z) such that the electric field is zero.
Where we need to replace two of these values to find the other, for example, if y = z = 0
24d^2 = (x - 5d)^2
√(24d^2) = x - 5d
√24*d = x - 5d
√24*d + 5d = x
so in the point (√24*d + 5d, 0, 0) the net field is zero.
.Use Newton's third law to describe the forces that are exerted by the falling egg and the ground. Explain how the use of the straws in the design affects the forces
Answer:
Newton's third law states that for every action, there is an equal and opposite reaction. That means when you exert a force on an object, the object exerts a force back on you. ... Using shock-absorbing materials can help reduce the amount of force exchanged between the ground and the egg.
Explanation:
I hope it helps you
When one of the tall straws hits the ground, the energy is transferred to the center of the pyramid and then to the egg, but as the middle straw is connected to the outer surface of the egg, energy enters trying to make the egg rotate. This is governed by Newton's third law.
What is Newton's third law?If an object exerts a force on another object, then another object must exert a force of equal magnitude and opposite direction back on first object.
What are examples of Newton's third law?Examples of Newton's third law are:
A swimmer moves forward by pushing off the side of pool. This way, the wall pushes in opposite direction and giving acceleration.
Another example is rockets move forward by expelling gas backward at high velocity. This means the rocket exerts a large backward force on the gas in the rocket combustion chamber, and the gas therefore exerts a large reaction force forward on the rocket. This reaction force is called thrust.
Helicopters similarly create lift by pushing air down, thereby experiencing an upward reaction force. Birds and airplanes also fly by exerting force on air in a direction opposite to that of whatever force they need. For example, the wings of a bird force air downward and backward in order to get lift and forward motion.
To learn more about Newton's third law here
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We say that evaporation is a cooling process. (a) What cools and what warms? We say that condensation is a warming process. (b) What warms and what cools?
Answer:
a liquid warms gas cools
b solid piece warms and liquid cools
human activities that interfere with distribution of natural resources are contributing to the increase of earthquake risk.
Answer:
Changes in climate conditions, especially the warming of global temperatures increases the likelihood of weather-related natural disasters. ... This is most visible when seen through changes in the intensity and frequency of droughts, storms, floods, extreme temperatures and wildfires.
A 0.277 kg bat is flying 4.25 m/s.
It then doubles its velocity.
How much KE did it gain?
Answer:
7.51
Explanation:
The mass of the bat is given to us as:
m = 0.277 kg
,
and its initial velocity is:
v
i = 4.25 m/s
When the velocity is doubled, the new value becomes:
v f = 4.25 m/s × 2 = 8.5 m/s
.
The formula for kinetic energy is:
K
=
1
2
m
v
2
.
The change in kinetic energy is:
Δ K = 1 /2( m ) ( v2 f − v 2 i ) = 1 2 ( 0.277)
10-2.5=7.5J
7.51 J
.
The bat gained 7.51 joules.
What is the electric field 3.9 m from the center of the terminal of a Van de Graaff with a 6.60 mC charge, noting that the field is equivalent to that of a point charge at the center of the terminal
Answer:
the electric field is 3.91 x 10⁶ N/C
Explanation:
Given the data in the question;
Electric field at a point due to point charge is;
E = kq/r²
where k is the constant, r is the distance from centre of terminal to point where electric field is, q is the excess charge placed on the centre of terminal of Van de Graff,a generator
Now, given that r = 3.9 m, k = 9.0 x 10⁹ Nm²/C², q = 6.60 mC = 6.60 x 10⁻³ C
so we substitute into the formula
E = [(9.0 x 10⁹ Nm²/C²)( 6.60 x 10⁻³ C)] / ( 3.9 )²
E = 59400000 / 15.21
E = 3.91 x 10⁶ N/C
Therefore, the electric field is 3.91 x 10⁶ N/C
A 92-kg man climbs into a car with worn out shock absorbers, and this causes the car to drop down 4.5 cm. As he drives along he hits a bump, which starts the car oscillating at an angular frequency of 4.52 rad/s. What is the mass of the car ?A) 890 kg
B) 1900 kg
C) 920 kg
D) 990 kg
E) 760 kg
Answer:
the mass of the car is 890 kg
Explanation:
Given;
mass of the man, m = 92 kg
displacement of the car's spring, x = 4.5 cm = 0.045 m
acceleration due to gravity, g = 9.8 m/s²
The spring constant of the car,
f = kx
where;
f is the weight of the man on the car = mg
mg = kx
k = mg/x
k = (92 x 9.8) / 0.045
k = 20,035.56 N/m
The angular speed of car, ω, when the is inside is given as 4.52 rad/s
The total mass of the car and the man is calculated as;
[tex]\omega = \sqrt{\frac{k}{m} } \\\\\omega^2 = \frac{k}{m} \\\\m = \frac{k}{\omega^2} = \frac{20,035.56}{(4.52)^2} = 980.7 \ kg[/tex]
The mass of the car alone = 980.7 kg - 92 kg
= 888.7 kg
≅ 890 kg
Therefore, the mass of the car is 890 kg
Prepare a stock available at home following the procedure you learned in this lesson. Have a picture of the finished product and a narration on how you do it
Answer:
NO, 1. is stocks
2. is also stocks
bouquit GARNI IS NUMBER 3
NUMBER 4 IS ACID PRODUCTS
number 5 is brown stock
Explanation:
stocks are bones
A certain electric stove has a 16 Ω heating element. The current going through the element is 15 A. Calculate the voltage across the element.
The voltage across the element is = 240 V
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