Answer:
The peak electric field is [tex]E_o = 3593.6 V/m[/tex]
Explanation:
From the question we are told that
The power is [tex]P = 1.2 \ kW = 1.2 *10^{3} \ W[/tex]
The cross-sectional area is [tex]A = 700 \ cm^2 = 700 *10^{-4} \ m^2[/tex]
Generally the average intensity of the microwave is mathematically represented as
[tex]I = \frac{c * \epsilon _o * E_o^2 }{2}[/tex]
Where [tex]c[/tex] is the speed of light with value [tex]c = 3.0 *10^{8} \ m/s[/tex]
and [tex]\epsilon_o[/tex] is the permitivity of free space with value [tex]\epsilon_o = 8.85*10^{-12} \ m^{-3} \cdot kg^{-1}\cdot s^4 \cdot A^2[/tex]
also [tex]E_o[/tex] is the peak electric field.
Now making [tex]E_o[/tex] the subject [tex]E_o = \sqrt{\frac{2 * I }{ c * \epsilon _o } }[/tex]
But this intensity of the microwave can also be represented mathematically as
[tex]I = \frac{ P }{A }[/tex]
substituting values
[tex]I = \frac{ 1.2 *10^{3} }{700 *10^{-4} }[/tex]]
[tex]I = 17142.85 \ W/m^2[/tex]
So
[tex]E_o = \sqrt{\frac{2 * 17142.85 }{ 3.0*10^{8}] * 8.85*10^{-12} } }[/tex]
[tex]E_o = 3593.6 V/m[/tex]
The peak electric field of the microwave is 3,593.1 V/m.
The given parameters;
power of the wave, P = 1.2 kW = 1,200 Warea of the plane, A = 700 cm²The intensity of the wave is calculated as follows;
[tex]I = \frac{P}{A} \\\\I = \frac{1,200}{700 \times 10^{-4}} \\\\I = 17,142.86 \ W/m^2[/tex]
The peak electric field is calculated as follows;
[tex]E_o = \sqrt{\frac{2I}{c \varepsilon _o} } \\\\E_o = \sqrt{\frac{2\times 17,142.86}{3\times 10^8 \times 8.85 \times 10^{-12}} } \\\\E_o = 3,593.1 \ V/m[/tex]
Thus, the peak electric field of the microwave is 3,593.1 V/m.
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A wire carries current in the plane of this screen toward the top of the screen. The wire experiences a magnetic force toward the right edge of the screen. Is the direction of the magnetic field causing this force
Answer:
The direction of the magnetic field causing this force is
In the plane of the screen and towards the bottom of the egde
Explanation:
This is by applying Fleming s right hand rule which explains that
When a conductor such as a wire attached to a circuit moves through a magnetic field, an electric current is induced in the wire due to Faraday's law of induction. The current in the wire can have two possible directions. Fleming's right-hand rule gives which direction the current flows.
The right hand is held with the thumb, index finger and middle finger mutually perpendicular to each other (at right angles), as shown in the diagram.[1]
The thumb is pointed in the direction of the motion of the conductor relative to the magnetic field.
The first finger is pointed in the direction of the magnetic field. (north to south)
Then the second finger represents the direction of the induced or generated current within the conductor (from the terminal with lower electric potential to the terminal with higher electric potential, as in a voltage source)
Two unknown resistors are connected together. When they are connected in series their equivalent resistance is 15 Ω. When they are connected in parallel, their equivalent resistance is 3.3 Ω. What are the resistances of these resistors?
Explanation:
Let x and y are two unknown resistors. When they are connected in series their equivalent resistance is 15 Ω. When they are connected in parallel, their equivalent resistance is 3.3 Ω.
For series combination,
[tex]x+y=15[/tex] ......(1)
For parallel combination,
[tex]\dfrac{1}{x}+\dfrac{1}{y}=3.3[/tex] ....(2)
We need to find the resistances of these resistors. Solving equation (1) and (2) we get :
x = 0.29 and y = 14.7
Hence, the resistances of these resistors are 0.29 ohms and 14.7 ohms.
A 7.0-kg shell at rest explodes into two fragments, one with a mass of 2.0 kg and the other with a mass of 5.0 kg. If the heavier fragment gains 100 J of kinetic energy from the explosion, how much kinetic energy does the lighter one gain?
Answer:
39.94m/s.Explanation:
Kinetic energy is expressed as KE = 1/2 mv² where;
m is the mass of the body
v is the velocity of the body.
For the heavier shell;
m = 5kg
KE gained = 100J
Substituting this values into the formula above to get the velocity v;
100 = 1/2 * 5 * v²
5v² = 200
v² = 200/5
v² = 40
v = √40
v = 6.32 m/s
Note that after the explosion, both body fragments will possess the same velocity.
For the lighter shell;
mass = 2.0kg and v = 6.32m/s
KE of the lighter shell = 1/2 * 2 * 6.32²
KE of the lighter shell = 6.32²
KE of the lighter shell= 39.94m/s
Hence, the lighter one gains a kinetic energy of 39.94m/s.
The gain in the kinetic energy of the smaller fragment is 249.64 J.
The given parameters;
Mass of the shell, m = 7.0 kgMass of one fragment, m₁ = 2.0 kgMass of the second fragment, m₂ = 5.0 kgKinetic energy of heavier fragment, K.E₁ = 100 JThe velocity of the heavier fragment is calculated as follows;
[tex]K.E = \frac{1}{2} mv^2\\\\mv^2 = 2K.E\\\\v^2 = \frac{2K.E}{m} \\\\v= \sqrt{\frac{2K.E}{m} } \\\\v = \sqrt{\frac{2 \times 100}{5} }\\\\v = 6.32 \ m/s[/tex]
Apply the principle of conservation of linear momentum to determine the velocity of the smaller fragment as;
[tex]m_1 u_1 + m_2 u_2 = v(m_1 + m_2)\\\\-6.32(5) \ + 2u_2 = 0(7)\\\\-31.6 + 2u_2 = 0\\\\2u_2 = 31.6\\\\u_2 = \frac{31.6}{2} \\\\u_2 = 15.8 \ m/s[/tex]
The gain in the kinetic energy of the smaller fragment is calculated as follows;
[tex]K.E_2 = \frac{1}{2} mu_2^2\\\\K.E_2 = \frac{1}{2} \times 2 \times (15.8)^2\\\\K.E_2 = 249.64 \ J[/tex]
Thus, the gain in the kinetic energy of the smaller fragment is 249.64 J.
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For the cellar of a new house, a hole is dug in the ground, with vertical sides going down 2.10 m. A concrete foundation wall is built all the way across the 8.90 m width of the excavation. This foundation wall is 0.189 m away from the front of the cellar hole. During a rainstorm, drainage from the street fills up the space in front of the concrete wall, but not the cellar behind the wall. The water does not soak into the clay soil. Find the force that the water causes on the foundation wall. For comparison, the weight of the water is given by 2.10 m ✕ 8.90 m ✕ 0.189 m ✕ 1000 kg/m3 ✕ 9.80 m/s2 = 34.6 kN.
Answer:
The force on the foundation wall is [tex]F_f = 191394 \ N[/tex]
Explanation:
From the question we are told that
The depth of the hole's vertical side is [tex]d = 2.10 \ m[/tex]
The width of the hole is [tex]b = 8.90 \ m[/tex]
The distance of the concrete wall from the front of the cellar is [tex]c = 0.189 \ m[/tex]
Generally the area which the water from the drainage covers is mathematically represented as
[tex]A = d * b[/tex]
substituting values
[tex]A = 2.10 * 8.90[/tex]
[tex]A = 18.69 \ m^2[/tex]
Now the gauge pressure exerted on the foundation wall is mathematically evaluated as
[tex]P_g = \rho * d_{avg} * g[/tex]
Here is the average height foundation wall where the pressure of the water is felt and it is evaluated as
[tex]d_{avg} = \frac{h_1 + h_2 }{2}[/tex]
where [tex]h_1[/tex] at the height at bottom of the hole which is equal to [tex]h_1 = 0[/tex]
and [tex]h_2[/tex] is the height at the top of the hole [tex]h_2 = d = 2.10[/tex]
[tex]d_{avg} = \frac{0 + 2.10 }{2}[/tex]
[tex]d_{avg} = 1.05[/tex]
Where [tex]\rho[/tex] is the density of water with constant value [tex]\rho = 1000 \ kg/m^3[/tex]
substituting values
[tex]P_g = 1000 * 1.05 * 9.8[/tex]
[tex]P_g = 10290 \ Pa[/tex]
Then the force exerted by the water on the foundation wall mathematically represented as
[tex]F_f = P_g * A[/tex]
substituting values
[tex]F_f = 10290 * 18.69[/tex]
[tex]F_f = 191394 \ N[/tex]
A 0.2 kg rubber ball is dropped from the window of a building. It strikes the sidewalk below at 30 m/s and rebounds at 20 m/s. The magnitude of the change in momentum of the ball as a result of the collision with the sidewalk is _______.
Answer:
10 kgm/s
Explanation:
Change in momentum: This can be defined as the product of mass and change in velocity. The S.I unit of change in momentum is Kgm/s.
From the question,
ΔM = m(v-u)...................... Equation 1
Where ΔM = change in momentum, u = initial velocity, v = final velocity.
Note: Let upward direction be negative, and downward direction be positive.
Given: m = 0.2 kg, v = -20 m/s, u = 30 m/s
Substitute into equation 1
ΔM = 0.2(-20-30)
ΔM = 0.2(-50)
ΔM = -10 kgm/s.
The negative sign shows that the change in momentum is Upward
The magnitude of the change in momentum of the ball as a result of the collision with the sidewalk is -10 kg-m/s.
Given data:
The mass of rubber ball is, m = 0.2 kg.
The initial speed of ball is, u = 30 m/s.
The final rebounding speed of ball is, v = - 20 m/s ( Negative sign shows that during the rebounding, the ball changes its direction)
The momentum of any object is defined as the product of mass and change in velocity. The S.I unit of momentum is Kg-m/s. And the expression for the change in momentum is given as,
[tex]p= m ( v-u)[/tex]
Solving as,
[tex]p= 0.2 \times ( -20-30)\\\\p=-10 \;\rm kg.m/s[/tex]
Thus, we can conclude that the magnitude of the change in momentum of the ball as a result of the collision with the sidewalk is -10 kg-m/s.
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A generator rotates at 95 Hz in a magnetic field of 0.025 T. It has 550 turns and produces an rms voltage of 170 V and an rms current of 60.0 A.
Required:
a. What is the peak current produced?
b. What is the area of each turn of the coil?
Answer:
Peak current= 84.86 A
Area of each turn = 0.029 m^2
Explanation:
The peak value of current can be obtained from Irms= 0.707Io. Where Io is the peak current.
Hence;
Irms= 60.0A
Io= Irms/0.707
Io = 60.0/0.707
Io= 84.86 A
Vrms= 0.707Vo
Vo= Vrms/0.707= 170/0.707 = 240.45 V
From;
V0 = NABω
Where;
Vo= peak voltage
N= number of turns
B= magnetic field
A= area of each coil
ω= angular velocity
But ω= 2πf = 2×π×95= 596.9 rads-1
Substituting values;
A= Vo/NBω
A= 240.45/550×0.025×596.9
A= 0.029 m^2
A person can survive a feet-first impact at a speed of about 12 m/s (27 mi/h) on concrete, 15 m/s (34 mi/h) on soil, and 34 m/s (76 mi/h) on water. What is the reason for the different values for different surfaces
Answer:
Different surfaces have different impact force during collision which depends on the time it takes the person to come to rest after collision.
Explanation:
Given;
speed on concrete = 12 m/s (27 mi/h)
speed on soil = 15 m/s (34 mi/h)
speed on water = 34 m/s (76 mi/h)
The impact force on this person during collision is rate of change of momentum;
[tex]F = \frac{\delta P}{\delta t}[/tex]
During collision, the force exerted on this person depends on how long the collision lasts; that is, how long it takes for this person to come to rest after collision with each of the surfaces.
The longer the time of collision, the smaller the force exerted by each.
It takes shorter time for the person to come to rest on concrete surface than on soil surface, also it takes shorter time for the person to come to rest on soil surface than on water surface.
As a result of the reason above, the force exerted on the person during collision by the concrete surface is greater than that of soil surface which is greater than that of water surface.
11. A tight guitar string has a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 70% of its original length
Answer:
The frequency is [tex]f_n = 257.1 \ Hz[/tex]
Explanation:
From the question we are told that
The third harmonic frequency of the tight guitar string is [tex]f_3 = 540 \ Hz[/tex]
Let the original length be L
Then the length at which it is fingered is 0.7 L
Generally the fundamental is mathematically represented as
[tex]f = \frac{v_s}{ 2L}[/tex]
Now when it finger at 70% it original length is
[tex]f_n = \frac{v}{2 * (0.7 L)}[/tex]
[tex]f_n = \frac{v}{1.4 L}[/tex]
Here v the velocity of sound
So
[tex]\frac{f_n}{f} = \frac{\frac{v}{1.4L} }{\frac{v}{2L} }[/tex]
Also the fundamental frequency for the original length can also be represented as
[tex]f = \frac{f_3}{3}[/tex]
substituting values
[tex]f = \frac{540}{3}[/tex]
[tex]f = 180 \ Hz[/tex]
So
[tex]\frac{f_n}{180} = \frac{\frac{v}{1.4L} }{\frac{v}{2L} }[/tex]
=> [tex]f_n =\frac{180}{0.7}[/tex]
=> [tex]f_n = 257.1 \ Hz[/tex]
The fundamental frequency, if it is fingered at a length of only 70% of its original length, will be 257.1 Hz.
What is the frequency?Frequency is defined as the number of repetitions of a wave occurring waves in 1 second.
f is the frequency of tight guitar string = 540 Hz
Let's call the original length L.
The amount of time it is fingered is then 0.7 L.
In general, the fundamental frequency is expressed mathematically as;
[tex]\rm f = \frac{v_0}{2L} \\\\[/tex]
For the given conditions;
[tex]\rm f_n=\frac{v}{2 \times 0.7L} \\\\ \rm f_n=\frac{v}{1.4L}[/tex]
The ratio of the frequency is;
[tex]\rm \frac{f_n}{f} =\frac{\frac{v}{1.4L} }{\frac{V}{2L} }[/tex]
Also, the fundamental frequency for the original length can also be represented as;
[tex]\rm f= \frac{f'}{3} \\\\ f=\frac{540}{3} \\\\ \rm f=180\ Hz[/tex]
On putting the given data;
[tex]\rm \frac{f_n}{180} =\frac{\frac{v}{1.4L} }{\frac{V}{2L} }\\\\ \rm f_n=\frac{180}{0.7}\\\\\ \rm f_n=257.1\ Hz[/tex]
Hence the fundamental frequency, if it is fingered at a length of only 70% of its original length, will be 257.1 Hz.
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A positively charged particle has a velocity in the negative z direction at a certain point P. The magnetic force on the particle at this point is in the negative y direction. Which one of the following statements about the magnetic field at point P can be determined from this data?
a. Bx is positive
b. Bz is positive
c. By is negative
d. By is positive
e. Bx is negative
Answer:
a. Bx is positive
Explanation:
See attached file
A positively charged particle has a velocity in the negative z direction at point P. The magnetic force on the particle at this point is in the negative y direction. Which one of the following statements about the magnetic field at point P can be determined from this data?
A. Bx is positive.
B. Bz is positive.
C. By is negative.
D. By is positive.
E. Bx is negative.
Answer:
When reviewing the correct answer is A
Explanation:
The magnetic force is given by the expression
F = qv xB
where the bold letters indicate vectors, from this expression the module can be calculated
F = = q v b sin θ
the direction of the force is given by the rule of the right hand, for a positive charge the speed held by the thumb, the extended fingers point in the direction of the magnetic field and the palm points the direction of the force
in this case
the speed is in the negative part of the z axis
the force is in the negative direction of the axis and
consequently the magnetizing field is in the positive direction of the x axis
When reviewing the correct answer is A
The intensity of sunlight at the Earth's distance from the Sun is 1370 W/m2. (a) Assume the Earth absorbs all the sunlight incident upon it. Find the total force the Sun exerts on the Earth due to radiation pressure. N (b) Explain how this force compares with the Sun's gravitational attraction.
Answer:
F= 3.56e22N
Explanation:
Using the force of radiation acting on the earth which is
force = radiation pressure x area = (intensity/c)xpi R^2
force = 1370W/m^2 x pi x( 6.37x10^6m)^2/3x10^8m/s
force = 5.82x10^8 N
But the sun's gravitational attraction means the magnitude of the solar gravitational force on earth: If that's the case, the answer is approx 10^22 N:
F=GMm/r^2
G=6.67x10^(-11)=6.67e-11
M=mass sun = 2x10^30kg=2e30
m=mass earth = 6x10^24kg
r=earth sun distance = 1.5x10^11m
F=(6.6e-11)(2e30)(6e24)/(1.5e11)^2 =
F= 3.56e22N
Si se deja caer una piedra desde un helicóptero en reposo, entonces al cabo de 20 s cual será la rapidez y la distancia recorrida por la piedra
Answer:
La piedra alcanza una rapidez de 196.14 metros por segundo y una distancia recorrida de 1961.4 metros en 20 segundos.
Explanation:
Si se excluye los efectos del arrastre por la viscosidad del aire, la piedra experimenta un movimiento de caída libre, es decir, que la piedra es acelerada por la gravedad terrestre. La distancia recorrida y la rapidez final de la piedra pueden obtenerse con la ayuda de las siguientes ecuaciones cinemáticas:
[tex]v = v_{o} + g\cdot t[/tex]
[tex]y - y_{o} = v_{o}\cdot t + \frac{1}{2}\cdot g \cdot t^{2}[/tex]
Donde:
[tex]v[/tex], [tex]v_{o}[/tex] - Rapideces final e inicial de la piedra, medidas en metros por segundo.
[tex]t[/tex] - Tiempo, medido en segundos.
[tex]g[/tex] - Aceleración gravitacional, medida en metros por segundo al cuadrado.
[tex]y[/tex]. [tex]y_{o}[/tex] - Posiciones final e inicial de la piedra, medidos en metros.
Si [tex]v_{o} = 0\,\frac{m}{s}[/tex], [tex]g = -9.807\,\frac{m}{s^{2}}[/tex], [tex]y_{o} = 0\,m[/tex], entonces:
[tex]v = 0\,\frac{m}{s} +\left(-9.807\,\frac{m}{s^{2}} \right) \cdot (20\,s)[/tex]
[tex]v = -196.14\,\frac{m}{s}[/tex]
[tex]y-y_{o} = \left(0\,\frac{m}{s} \right)\cdot (20\,s) + \frac{1}{2}\cdot \left(-9.807\,\frac{m}{s^{2}} \right) \cdot (20\,s)^{2}[/tex]
[tex]y-y_{o} = -1961.4\,m[/tex]
La piedra alcanza una rapidez de 196.14 metros por segundo y una distancia recorrida de 1961.4 metros en 20 segundos.
How do you stay hydrated during warm-up and scheduled activity?
Answer:
In order to stay hydrated during warm-up(s) drink 8oz of water 20-30 mintues before you start exercising or during your warm-up(s), make sure you drink 7 to 10 oz of water every 10 to 20 minutes during exercise, and drink 8oz of water no more than 30 minutes after you exercise.
In order to stay hydrated during scheduled activity(s) drink 17 to 20 oz of water 2 to 3 hours before you start to exercise, like said before drink 8 oz of water 20 to 30 minutes before you start exercising or during your warm-up(s), drink 7 to 10 oz of water every 10 to 20 minutes during exercise, also said before drink 8 ounces of water no more than 30 minutes after you exercise.
Answer: My scheduled activity was one hour of softball practice. I play catcher, so my thighs and knees take a lot of abuse from kneeling and standing. The lunges were excellent at preparing my thighs for softball. The high knees exercise and arm pumping didn’t feed into softball too well. I suppose that they might help me with base running.
Explanation: EDMENTUM
An automotive air conditioner produces a 1-kW cooling effect while consuming 0.75 kW of power. What is the rate at which heat is rejected from this air conditioner
Answer:
The rejected by the air conditioning system is 1.75 kilowatts.
Explanation:
A air conditioning system is a refrigeration cycle, whose receives heat from cold reservoir with the help of power input before releasing it to hot reservoir. The First Law of Thermodynamics describes the model:
[tex]\dot Q_{L} + \dot W - \dot Q_{H} = 0[/tex]
Where:
[tex]\dot Q_{L}[/tex] - Heat rate from cold reservoir, measured in kilowatts.
[tex]\dot Q_{H}[/tex] - Heat rate liberated to the hot reservoir, measured in kilowatts.
[tex]\dot W[/tex] - Power input, measured in kilowatts.
The heat rejected is now cleared:
[tex]\dot Q_{H} = \dot Q_{L} + \dot W[/tex]
If [tex]\dot Q_{L} = 1\,kW[/tex] and [tex]\dot W = 0.75\,kW[/tex], then:
[tex]\dot Q_{H} = 1\,kW + 0.75\,kW[/tex]
[tex]\dot Q_{H} = 1.75\,kW[/tex]
The rejected by the air conditioning system is 1.75 kilowatts.
Rays that pass through a lens very close to the principle axis are more sharply focused than those that are very far from the axis. This spherical aberration helps us understand why:_______
Answer: it is easier to read in bright light than dim light.
Explanation:
The ray of light is the direction that is used by light in travelling through a medium. Rays that pass through a lens very close to the principle axis are more sharply focused than those that are very far from the axis.
Because of the fact that the rays are close to the principle axis, the spherical aberration helps us to understand the reason why it is easier for people to read in bright light than readin iin dim light.
A 0.12-kg metal rod carrying a current of current 4.1 A glides on two horizontal rails separation 6.3 m apart. If the coefficient of kinetic friction between the rod and rails is 0.18 and the kinetic friction force is 0.212 N , what vertical magnetic field is required to keep the rod moving at a constant speed of 5.1 m/s
Answer:
The magnetic field is [tex]B = 8.20 *10^{-3} \ T[/tex]
Explanation:
From the question we are told that
The mass of the metal rod is [tex]m = 0.12 \ kg[/tex]
The current on the rod is [tex]I = 4.1 \ A[/tex]
The distance of separation(equivalent to length of the rod ) is [tex]L = 6.3 \ m[/tex]
The coefficient of kinetic friction is [tex]\mu_k = 0.18[/tex]
The kinetic frictional force is [tex]F_k = 0.212 \ N[/tex]
The constant speed is [tex]v = 5.1 \ m/s[/tex]
Generally the magnetic force on the rod is mathematically represented as
[tex]F = B * I * L[/tex]
For the rod to move with a constant velocity the magnetic force must be equal to the kinetic frictional force so
[tex]F_ k = B* I * L[/tex]
=> [tex]B = \frac{F_k}{L * I }[/tex]
=> [tex]B = \frac{0.212}{ 6.3 * 4.1 }[/tex]
=> [tex]B = 8.20 *10^{-3} \ T[/tex]
An electric field can be created by a single charge or a distribution of charges. The electric field a distance from a point charge has magnitude E = k|q'|/r^2.
The electric field points away from positive charges and toward negative charges. A distribution of charges creates an electric field that can be found by taking the vector sum of the fields created by individual point harges. Note that if a charge is placed in an electric field created by q', q will not significantly affect the electric field if it is small compared to q'. Imagine an isolated positive point charge with a charge Q (many times larger than the charge on a single electron).
1. There is a single electron at a distance from the point charge. On which of the following quantities does the force on the electron depend?
a. the distance between the positive charge and the electron
b. the charge on the electron
c. the mass of the electron
d. the charge of the positive charge
e. the mass of the positive charge
f. the radius of the positive charge
g. the radius of the electron
2. For the same situation as in Part A, on which of the following quantities does the electric field at the electron's position depend?
a. the distance between the positive charge and the electron
b. the charge on the electron
c. the mass of the electron
d. the charge of the positive charge
e. the mass of the positive charge
f. the radius of the positive charge
g. the radius of the electron
Answer:
a) true.
b) True
c) False. In the equation above the mass does not appear
d) True
e) False. Mass does not appear in the equation
f) False. The load even when distributed in the space can be considered concentrated in the center
Explanation:
1. The electric force is given by the relation
F = k Q e / r2
where k is the Coulomb constant, Q the charge used, e the charge of the electron and r the distance between the two.
The strength depends on:
a) true.
b) True
c) False. In the equation above the mass does not appear
d) True
e) False. Mass does not appear in the equation
f) False. The load even when distributed in the space can be considered concentrated in the center
two.
a) True
b) Treu
c) Fail
f) false
For a single electron located at a distance from a positive charge, we have:
1. The force on the electron depends on the distance between it and the positive charge (option a) and the charge of both particles (option b and d).
2. The electric field at the electron's position depends on the distance between the positive charge and it (option a) and the charge of the positive particle (option d).
Part 1
The force on a single electron at a distance from the point charge is given by Coulomb's law:
[tex] F = \frac{Kq_{1}q_{2}}{r^{2}} [/tex] (1)
Where:
K: is the Coulomb's constant q₁: is the charge of the positive chargeq₂: is the charge of the electrond: is the distance between the positive charge and the electronAs we can see in equation (1), the force on the electron by the positive charge depends on both charges q₁ and q₂, and the distance, so the correct options are:
a. The distance between the positive charge and the electron
b. The charge on the electron
d. The charge of the positive charge
The other options (c, e, f, and g) are incorrect because the electric force does not depend on the particles' masses or their radii.
Part 2The electric field (E) at a distance "r" from a point charge is given by:
[tex] E = \frac{Kq_{1}}{r^{2}} [/tex] (2)
From equation (2), we can see that the electric field is directly proportional to the charge and inversely proportional to the distance of interest (r).
The electric field at the electron's position is given by the one produced by the positive charge, so the correct options are:
a. The distance between the positive charge and the electron
d. The charge of the positive charge
The other options (b, c, e, f, and g) are incorrect because the electric field is independent of the mass of the charges involved and their radii.
Therefore, the correct options for part 1 are a, b, and d and for part 2 are a and d.
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Consider the following three objects, each of the same mass and radius:
(1) a solid sphere
(2) a solid disk
(3) a hoop
All three are released from rest at the top of an inclined plane. The three objects proceed down the incline undergoing rolling motion without slipping. Use work-kinetic energy theorem to determine which object will reach the bottom of the incline first.
a) 1, 2, 3
b) 2, 3, 1
c) 3, 1, 2
d) 3, 2, 1
e) All three reach the bottom at the same time.
Answer:
Explanation:a 1
A block with a mass of 0.28 kg is attached to a horizontal spring. The block is pulled back from its equilibrium position until the spring exerts a force of 1.0 N on the block. When the block is released, it oscillates with a frequency of 1.2 Hz. How far was the block pulled back before being released?
Answer:
Explanation:
For spring
[tex]n=\sqrt{\frac{k}{m} }[/tex]
where n is frequency of oscillation and k is force constant and m is mass
Putting the values
[tex]1.2=\sqrt{\frac{k}{.28} }[/tex]
k = .4032 N/m
F= k x
where F is force , k is force constant and x is extension
Putting the given values
1 = .4032 x
x = 2.48 m
At a certain instant the current flowing through a 5.0-H inductor is 3.0 A. If the energy in the inductor at this instant is increasing at a rate of 3.0 J/s, how fast is the current changing
Answer:
The current is changing at the rate of 0.20 A/s
Explanation:
Given;
inductance of the inductor, L = 5.0-H
current in the inductor, I = 3.0 A
Energy stored in the inductor at the given instant, E = 3.0 J/s
The energy stored in inductor is given as;
E = ¹/₂LI²
E = ¹/₂(5)(3)²
E = 22.5 J/s
This energy is increased by 3.0 J/s
E = 22.5 J/s + 3.0 J/s = 25.5 J/s
Determine the new current at this given energy;
25.5 = ¹/₂LI²
25.5 = ¹/₂(5)(I²)
25.5 = 2.5I²
I² = 25.5 / 2.5
I² = 10.2
I = √10.2
I = 3.194 A/s
The rate at which the current is changing is the difference between the final current and the initial current in the inductor.
= 3.194 A/s - 3.0 A/s
= 0.194 A/s
≅0.20 A/s
Therefore, the current is changing at the rate of 0.20 A/s.
The rate at which the current is changing is;
di/dt = 0.2 A/s
We are given;
Inductance; L = 5 H
Current; I = 3 A
Rate of Increase of energy; dE/dt = 3 J/s
Now, the formula for energy stored in inductor is given as;
E = ¹/₂LI²
Since we are looking for rate at which current is changing, then we differentiate both sides of the energy equation to get;
dE/dt = LI (di/dt)
Plugging in the relevant values gives;
3 = (5 × 3)(di/dt)
di/dt = 3/(5 × 3)
di/dt = 0.2 A/s
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A child pulls on a wagon with a force of 75 N. If the wagon moves a total of 42 m in 3.1 min, what is the average power delivered by the child
Answer:
16.96 W
Explanation:
Power: This can be defined as the rate at which work is done by an object. The S.I unit of power is Watt(W).
From the question,
P = (F×d)/t....................... Equation 1
Where P = power, F = force, d = distance, t = time.
Given: F = 75 N, d = 42 m, t = 3.1 min = 3.1×60 = 186 s
Substitute these values into equation 1
P = (75×42)/186
P = 16.94 W
Hence the average power delivered by the child = 16.96 W
The average power delivered by the child is 16.96 W.
What is Power?Power can be defined as the rate at which work is done by an object. The S.I unit of power is Watt(W).
Work done is the product of force and displacement caused.
Then the formula of power will be
P = (F×d)/t
Substitute F = 75 N, d = 42 m, t = 3.1 min = 3.1×60 = 186 s, we get the power as
P = (75×42)/186
P = 16.94 W
Hence, the average power delivered by the child is 16.96 W.
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Suppose you are looking into the end of a long cylindrical tube in which there is a uniform magnetic field pointing away from you. If the magnitude of the field is decreasing with time the direction of the induced magnetic field is
Answer:
If the magnitude of the field is decreasing with time the direction of the induced magnetic field is CLOCKWISE
Explanation
This is because If the magnetic field decreases with time, the electric field will be produced in order to oppose the change in line with lenz law. Thus The right hand rule can be applied to find that the direction of electric field is in the clockwise direction.
The resistance of a 0.29 m long piece of wire is measured to be 0.31 Ohms. The wire has a cross-sectional area of 0.003 m2. What is the resistivity of the wire?
Answer:
3.21×10⁻³ Ωm
Explanation:
Applying,
R = Lρ/A................... Equation 1
Where R = Resistance of the wire, L = Length of the wire, ρ = Resistivity of the wire, A = cross sectional area of the wire.
Make ρ the subject of the equation
ρ = RA/L................... Equation 2
Given: R = 0.31 Ohms, A = 0.003 m², L = 0.29 m
Substitute into equation 2.
ρ = 0.31(0.003)/0.29
ρ = 3.21×10⁻³ Ωm
In your own words, discuss how energy conservation applies to a pendulum. Where is the potential energy the most? Where is the potential energy the least? Where is kinetic energy the most? Where is kinetic energy the least?
Answer:
Explanation:
Energy conservation applies to the swinging of pendulum . When the bob is at one extreme , it is at some height from its lowest point . So it has some gravitational potential energy . At that time since it remains at rest its kinetic energy is zero or the least . As it goes down while swinging , its potential energy decreases and kinetic energy increases following conservation of mechanical energy . At the At the lowest point , its potential energy is least and kinetic energy is maximum .
In this way , there is conservation of mechanical energy .
Asteroid A has 3.5 times the mass and 2.0 times the velocity of Asteroid B. If
Asteroid B has a kinetic energy of 2,300,000 J then what is the kinetic energy of
Asteroid A?
Answer:
K_A = 32.2 10⁶ J
Explanation:
In this exercise we must relate the quantities given to find the kinetic energy
Asteroid A data
m_A = 3.5 m_B
v_A = 2.0 v
they also give the value of the kinetic energy of asteroid A
K_B = 2.3 10⁶ J
the expression for scientific energy is
K = ½ m v²
let's replace
K_A = ½ m_a V_a2
K_A = ½ 3.5 m_B (2.0 v_B)^2
K_A = 3.5 2² (½ m_B v_B²)
K_A = 14 K_B
K_A = 32.2 10⁶ J
if the current in the circuit decreases, what does that mean about the rate at which the charge(and voltage) change in a capacitor?
2. the exponent of the exponential function contains RC for the given circuit. who's is a constant. use units R and C to find units of RC. write ohms in terms of volts and amps and write farads in terms of volts and coulombs. Simplify
units of RC are__________
Answer:
`1. charge Q, on the capacitor increases, while the current will decrease
2. τ = t = secs
Explanation:
1. consider RC of a circuit to be am external source
voltage across the circuit is given as
v =v₀(1 - [tex]e^{\frac{t}{τ} }[/tex])
where v = voltage
v₀ = peak voltage
t = time taken
τ= time constant
as the charge across the capacitor increases, current decreases
the charge across the circuit is given as
Q= Q₀(1 - [tex]e^{\frac{t}{τ} }[/tex])
charge Q is inversely proportional to the current I
hence the charge across the circuit increases
2. τ = RC
unit of time constant, τ,
= Ω × F
=[tex]\frac{V}{I}[/tex] ˣ [tex]\frac{C}{V}[/tex]
=[tex]\frac{C}{A}[/tex]
=[tex]\frac{C}{C/t}[/tex]
τ = t = secs
which of the following is a physical change?
A. a newspaper burns when placed in a fire.
B.an iron chair rusts when left outside
C.a sample of water boils and releases gas.
D.a plant changes carbon dioxide and water into sugar
Kevin is a black high school senior. While walking home from a sporting event at school, he sees a police car and decides to take another street to avoid it. He worries that the police will stop and question him even though he has not done anything wrong. Which theory explains this thought process? Dramaturgy Social construction of reality Social exchange theory Ethnomethodology
Answer:
Ethnomethodology theory
Explanation:
Take note of the fact that we are told Kevin worries that the police will stop and question him even though he has not done anything wrong.
This statement shows us that Kevin already understood his society from past experiences, and thus he tries to avoid social interactions with particular member of his society (the police) who may be show discrimination towards him.
Comparing helium atoms with nitrogen molecules at the same temperature, the helium atoms on average are moving _______ and have _______ kinetic energy.
Answer:
Helium atoms compared to nitrogen atoms are moving faster and have a greater kinetic energy.
Explanation:
The molecular velocity of a gas at room temperature is inverse proportional to the square root of its molecular mass.
The greater the molecular mass of the gas the lesser the average speed of its molecules. Comparing the molecular masses of nitrogen and helium, helium is found to have a lower molecular mass and a corresponding greater velocity.
Hence helium moves faster than nitrogen and has a higher kinetic energy than nitrogen
A scientist is testing the seismometer in his lab and has created an apparatus that mimics the motion of the earthquake felt in part (a) by attaching the test mass to a spring. If the test mass weighs 13 N, what should be the spring constant of the spring the scientist use to simulate the relative motion of the test mass and the ground from part (a)?
Complete Question
The complete question is shown on the first uploaded image
Answer:
a
[tex]a_{max} = 0.00246 \ m/s^2[/tex]
b
[tex]k =722.2 \ N/m[/tex]
Explanation:
From the question we are told that
The amplitude is [tex]A = 1.8 \ cm = 0.018 \ m[/tex]
The period is [tex]T = 17 \ s[/tex]
The test weight is [tex]W = 13 \ N[/tex]
Generally the radial acceleration is mathematically represented as
[tex]a = w^2 r[/tex]
at maximum angular acceleration
[tex]r = A[/tex]
So
[tex]a_{max} = w^2 A[/tex]
Now [tex]w[/tex] is the angular velocity which is mathematically represented as
[tex]w = \frac{2 * \pi }{T}[/tex]
Therefore
[tex]a_{max} = [\frac{2 * \pi}{T} ]^2 * A[/tex]
substituting values
[tex]a_{max} = [\frac{2 * 3.142}{17} ]^2 * 0.018[/tex]
[tex]a_{max} = 0.00246 \ m/s^2[/tex]
Generally this test weight is mathematically represented as
[tex]W = k * A[/tex]
Where k is the spring constant
Therefore
[tex]k = \frac{W}{A}[/tex]
substituting values
[tex]k = \frac{13}{0.018}[/tex]
[tex]k =722.2 \ N/m[/tex]