Answer:
(a) [tex]I_{1}=3.2*10^{-3}W/m^{2}[/tex]
(b) [tex]\beta =95dB[/tex]
Explanation:
Given data
Distance r₁=50 m
Distance r₂=2 m
Intensity I₂=2.0 W/m²
To find
(a) The Sound Intensity I₁
(b) The Sound Intensity level β
Solution
For (a) the Sound Intensity I₁
[tex]\frac{I_{1} }{I_{2}}=\frac{(r_{2})^{2} }{(r_{1})^{2} }\\I_{1} =I_{2}(\frac{(r_{2})^{2} }{(r_{1})^{2} })\\I_{1}=(2.0W/m^{2} )(\frac{(2m)^{2} }{(50m)^{2} })\\I_{1}=3.2*10^{-3}W/m^{2}[/tex]
For (b) the Sound Intensity level β
The Sound Intensity level β is calculated as follow
[tex]\beta =(10dB)log_{10}(\frac{I}{I_{o} } )\\\beta =(10dB)log_{10}(\frac{3.2*10^{-3}W/m^{2} }{1.0*10^{-12} W/m^{2} } )\\\beta =95dB[/tex]
How do the magnitudes of the inertial (the density times acceleration term), pressure, and viscous terms in the Navier-Stokes equation compare?
Answer:
The general equation of movement in fluids is obtained from the application, at fluid volumes, of the principle of conservation of the amount of linear movement. This principle establishes that the variation over time of the amount of linear movement of a fluid volume is equal to that resulting from all forces (of volume and surface) acting on it. Expressed in This equation is called the Navier-Stokes equation.
The equation is shown in the attached file
Explanation:
The derivative of velocity with respect to time determines the change in the velocity of a particle of the fluid as it moves in space. It also includes convective acceleration, expressed by a nonlinear term that comes from convective inertia forces). With this equation, Stokes studied the motion of an infinite incompressible viscous fluid at rest at infinity, and in which a solid sphere of radius r makes a rectilinear and uniform translational motion of velocity v. It assumes that there are no external forces and that the movement of the fluid relative to a reference system on the sphere is stationary. Stokes' approach consists in neglecting the nonlinear term (associated with inertial forces due to convective acceleration).
The mass of the Sun is 2 × 1030 kg, the mass of the Earth is 6 × 1024 kg, and their center-to-center distance is 1.5 × 1011 m. Suppose that at some instant the Sun's momentum is zero (it's at rest). Ignoring all effects but that of the Earth, what will the Sun's speed be after 3 days? (Very small changes in the velocity of a star can be detected using the "Doppler" effect, a change in the frequency of the starlight, which has made it possible to identify the presence of planets in orbit around a star.)
Answer:
0.00461031264 m/s
Explanation:
G = Gravitational constant = 6.67 × 10⁻¹¹ m³/kgs²
M = Mass of the Earth = 6 × 10²⁴ kg
r = Distance between Earth and Sun = [tex]1.5\times 10^{11}\ m[/tex]
t = Time taken = 3 days
Acceleration is given by
[tex]a=\dfrac{GM}{r^2}\\\Rightarrow a=\dfrac{6.67\times 10^{-11}\times 6\times 10^{24}}{(1.5\times 10^{11})^2}\\\Rightarrow a=1.77867\times 10^{-8}\ m/s^2[/tex]
Velocity of the star
[tex]v=u+at\\\Rightarrow v=0+1.77867\times 10^{-8}\times 3\times 24\times 60\times 60\\\Rightarrow v=0.00461031264\ m/s[/tex]
The Sun's speed will be 0.00461031264 m/s
A pair of identical 10-cm-diameter circular rings face each other. The distance between the rings is 20.0 cm . The rings each have a charge of + 20.0 nC . What is the magnitude of the electric field at the center of either ring?
Answer:
The magnitude of electric field at the center of each ring is 129.96 N/C
Explanation:
As per the question:
The diameter of the ring , d = 10 cm = 0.1 m
Radius, [tex]r = \frac{d}{2} = \frac{0.1}{2} = 0.05\ m[/tex]
Separation between the rings, d = 20.0 cm = 0.20 m
Charge on a ring, q = +20 nC = [tex]20\times 10^{- 9}\ C[/tex]
Now,
The electric field at the center of either ring is given by:
[tex]E = \frac{1}{4\pi \epsilon_{o}}\frac{qd}{(d^{2} + r^{2})^{\frac{3}{2}}}[/tex]
where
[tex]\frac{1}{4\pi \epsilon_{o}} = 9\times 10^{9}[/tex]
Thus
[tex]E = 9\times 10^{9}\times \frac{20\times 10^{- 9}\times 0.20}{(0.20^{2} + 0.05^{2})^{\frac{3}{2}}}[/tex]
E = 129.96 N/C
Charge q is accelerated starting from rest up to speed v through the potential difference V. What speed will charge q have after accelerating through potential difference 4V?
Final answer:
When a charge is accelerated through a potential difference, its speed can be calculated using the equation v = √(2qV/m). In the given example, an electron is accelerated through a potential difference of 4V, resulting in a speed of approximately 290 mV.
Explanation:
When a charge is accelerated through a potential difference, it gains kinetic energy. The relationship between the potential difference and the speed of the charge can be calculated using the equation:
v = √(2qV/m)
Where v is the final speed of the charge, q is the charge of the particle, V is the potential difference, and m is the mass of the particle.
In the given example, an electron with a charge of -1.60 × 10-19 C and a mass of 9.11 × 10-31 kg is accelerated to a speed of 10 × 104 m/s through a potential difference. To calculate the potential difference, we can rearrange the equation to:
V = m(v²)/(2q)
Substituting the values:
V = (9.11 × 10-31 kg)(10 × 104 m/s)²/ (2)(-1.60 × 10-19 C)
V = 2.91 × 10-2 V
So, the potential difference is approximately 29 mV.
What is the magnitude of the net force ∑ F on a 1.9 kg bathroom scale when a 74 kg person stands on it?
Answer:
725.2 N
Explanation:
Since it is not stated the scale, the person or both accelerated or experience weightlessness, the net force acting on the bathroom scale is the weight of the person acting downward as the person stands on the scale .
Weight = mass of a body × acceleration due to gravity
= 74 kg × 9.8 m/s²
= 725.2 N
The total mass of all the planets is much less than the mass of the Sun. (T/F)
Answer:
True
Explanation:
The total mass of all the planets is much less than the mass of the Sun is a True statement.
Sun contributes to most of the mass of the solar system. Sun contributes to 99.8% mass of the solar system. Only 0.2% of the mass of the solar system is given by the planets. Hence, the above statement is absolutely correct.
Which of the following statements are true?
a. Electric field lines and equipotential surfaces are always mutually perpendicular.
b. When all charges are at rest, the surface of a conductor is always an equipotential surface.
c. An equipotential surface is a three-dimensional surface on which the electric potential is the same at every point.
d. The potential energy of a test charge increases as it moves along an equipotential surface.
e. The potential energy of a test charge decreases as it moves along an equipotential surface.
Answer:
a,b and c are true.
Explanation:
Following are true statements
a. Electric field lines and Equipotential surfaces are always mutually perpendicular is a true statement.
b. When all charges are at rest, the surface of a conductor is always an equipotential surface.
c. An equipotential surface is a three-dimensional surface on which the electric potential is the same at every point.
Following are False statements
d. The potential energy of a test charge increases as it moves along an equipotential surface.
e. The potential energy of a test charge decreases as it moves along an equipotential surface.
Reason: A t any point in an equipotential surface, the potential is same throughout. There is no increase or decrease in potential energy as the test charge moves in an equipotential environment.
Statements a, b, and c are correct: Electric field lines and equipotential surfaces are always mutually perpendicular; when all charges are at rest, the surface of a conductor is always an equipotential surface; and an equipotential surface is a three-dimensional surface on which the electric potential is the same at every point. Statements d and e are not correct because the potential energy of a test charge does not change as it moves along an equipotential surface.
Explanation:The following statements are true about electrical fields and potential:
a. Electric field lines and equipotential surfaces are always mutually perpendicular. This statement is correct. An electric field line shows the direction of the force a positive test charge would experience. An equipotential line or surface is one where the potential is the same at any point on the line or surface. As such, they will always be perpendicular to each other.b. When all charges are at rest, the surface of a conductor is always an equipotential surface. This statement is correct. In static conditions, the surface of a conductor is at a uniform potential because charges flow until they reach an equilibrium.c. An equipotential surface is a three-dimensional surface on which the electric potential is the same at every point. This statement is right. That's why we named it equipotential (equal potential).d. The potential energy of a test charge increases as it moves along an equipotential surface. This statement is not correct. Since it's an equipotential surface, the potential energy stays the same.e. The potential energy of a test charge decreases as it moves along an equipotential surface. This statement is also not correct for the same reason stated above.Learn more about Electric Field and Potential here:https://brainly.com/question/31256352
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A 900-kg car cruising at a constant speed of 60 km/h is to accelerate to 100 km/h in 4 s. The additional power needed to achieve this acceleration is (a) 56 kW (b) 222 kW (c) 2.5 kW (d) 62 kW (e) 90 kW
To solve this problem we will apply the concepts related to power as a function of the change of energy with respect to time. But we will consider the energy in the body equivalent to kinetic energy. The change in said energy will be the difference between the two velocity data given by half of the mass. We will first convert the given units into an international system like this
Initial Velocity,
[tex]V_i = 60km/h (\frac{1000m}{1km})(\frac{1h}{3600s})[/tex]
[tex]V_i = 16.6667m/s[/tex]
Final Velocity,
[tex]V_f = 100km/h (\frac{1000m}{1km})(\frac{1h}{3600s})[/tex]
[tex]V_f = 27.7778m/s[/tex]
Now Power is defined as the change of Energy over the time,
[tex]P = \frac{E}{t}[/tex]
But Energy is equal to Kinetic Energy,
[tex]P = \frac{\frac{1}{2} m\Delta v^2}{t}[/tex]
[tex]P = \frac{\frac{1}{2} m(v_f^2-v_i^2)}{t}[/tex]
Replacing,
[tex]P = \frac{\frac{1}{2} (900)(27.7778^2-16.6667^2)}{4}[/tex]
[tex]P = 56kW[/tex]
Therefore the correct answer is A.
Final answer:
The additional power needed to achieve the acceleration is 62 kW.So,option (d) 62 kW is correct.
Explanation:
To calculate the additional power needed to achieve acceleration, we can use the formula for power: Power = Force x Velocity. We know the mass of the car (900 kg), the initial velocity (60 km/h), and the final velocity (100 km/h). We can convert the velocities to m/s and calculate the force required to accelerate the car. Then, we can multiply the force by the change in velocity to find the additional power needed.
In this case, the additional power needed is approximately 62 kW. Therefore, option (d) 62 kW is the correct answer.
Charge of uniform surface density (0.20 nC/m2 ) is distributed over the entire xy plane. Determine the magnitude of the electric field at any point having z = 2.0 m
Answer:
E= 11.3 N/C.
Explanation:
The electric filed at any point on the z-axis is given by the formula
[tex]E= \frac{\sigma}{2\epsilon_0}[/tex]
here, sigma is the charge density and ε_o is the permitivity of free space.
therefore,
[tex]E= \frac{0.2\times10^{-9}}{2\times8.85\times10^{-12}}[/tex]
solving it we get
E= 11.3 N/C.
Hence, the required Electric field is E= 11.3 N/C.
A solid nonconducting sphere of radiusRcarries a chargeQdistributed uniformly throughout itsvolume. At a certain distancer1(r1< R) from the center of the sphere, the electric field has magnitudeE.If the same chargeQwere distributed uniformly throughout a sphere of radius 2R, the magnitude of theelectric field at the same distancer1from the center would be equal to______
Answer:
[tex]E' = \frac{1}{8} E[/tex]
Explanation:
Given data:
first case
Distance of electric field from center of sphere is r_1 <R
Electric field at r_1< R
[tex]E = \frac{kQr_1}{R^3}[/tex]
second case
Distance of electric field from centre of sphere is r_1 < 2R
Electric field at r_1< 2R
[tex]E' = \frac{kQr_1}{8R^3}[/tex]
so, we have
[tex]E' = \frac{1}{8} E[/tex]
A firefighter who weighs 712 N slides down a vertical pole with an acceleration of 3.00 m/s 2 ,directed downward.What are the (a) magnitude and (b) direction (up or down) of the vertical force on the firefighter from the pole and the (c) magnitude and (d) di- rection of the vertical force on the pole from the firefighter
Answer:
494.262996942 N
Upward
494.262996942 N
Downward
Explanation:
W = Weight of the firefighter = 712 N
g = Acceleration due to gravity = 9.81 m/s²
Mass is given by
[tex]m=\dfrac{W}{g}\\\Rightarrow m=\dfrac{712}{9.81}\\\Rightarrow m=72.5790010194\ kg[/tex]
Force is given by
[tex]T-W=-ma\\\Rightarrow T=W-ma\\\Rightarrow T=712-72.5790010194\times 3\\\Rightarrow T=494.262996942\ N[/tex]
The force on the firefighter is 494.262996942 N
directed upward
On the pole the force will be the same 494.262996942 N
But the direction will be downward
Final answer:
The magnitude of the vertical force on the firefighter from the pole is determined by the net force required for the given downward acceleration. The direction of the force the firefighter applies to the pole is downward while the reaction force from the pole is upward, with the magnitude being the same for both forces.
Explanation:
The question relates to the physics concept called Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to the object's mass. The law is usually expressed by the equation F = ma, where F is the net force, m is the mass, and a is the acceleration.
To find the magnitude of the vertical force on the firefighter from the pole, we need to take into account both the downward force due to gravity (which is the firefighter's weight) and the additional force needed to produce the acceleration. If the firefighter weighs 712 N and has an acceleration of 3.00 m/s2 downward, we can calculate the force exerted on the pole using F = ma. The mass (m) of the firefighter can be obtained by dividing the weight (W) by the acceleration due to gravity (g), m = W/g. From F = ma, we get F = (W/g)a. Inserting the given values, we have F = (712 N/9.8 m/s2) × 3.00 m/s2. The resulting force is less than the weight of the firefighter because the net force is reduced by the downward acceleration. The direction of the force exerted by the firefighter on the pole is downward since the firefighter is sliding down.
The reaction force exerted on the firefighter by the pole, according to Newton's third law, is equal in magnitude but opposite in direction to the force exerted by the firefighter on the pole. So, the magnitude would be the same, and the direction would be upward.
A thin, square, conducting plate 40.0 cm on a side lies in the xy plane. A total charge of 4.70 10-8 C is placed on the plate. You may assume the charge density is uniform. (a) Find the charge density on each face of the plate. 1.47e-07 What is the definition of surface charge density? C/m2 (b) Find the electric field just above the plate. magnitude N/C direction (c) Find the electric field just below the plate. magnitude N/C direction
Answer:
(a) Surface charge density is the charge per unit area.
[tex]\sigma = 1.46 \times 10^{-7}~{\rm Q/m^2}[/tex]
(b) [tex]\vec{E} = (+\^z)~8.34\times 10^3~{\rm N/C}[/tex]
(c) [tex]\vec{E} = (-\^z)~8.34\times 10^3~{\rm N/C}[/tex]
Explanation:
(a) Surface charge density is the charge per unit area. The area of the square plate can be calculated by its side length.
[tex]A = l^2 = (0.4)^2 = 0.16 ~{\rm m^2}[/tex]
Half of the total charge is distributed on one side and the other is distributed on the other side.
Therefore, surface charge density on each face of the plate is
[tex]\sigma = Q/A = \frac{2.35 \times 10^{-8}}{0.16} = 1.46 \times 10^{-7}~{\rm Q/m^2}[/tex]
(b) To find the electric field just above the plate, Gauss' Law can be used. Normally, Gauss' Law can only be used in infinite sheet (considering the flat surfaces), but just above the surface can be considered that the distance from the surface is much much smaller than the length of the plate (x << l).
In order to apply Gauss' Law, we have to draw an imaginary cylinder with radius r. The cylinder has to stay perpendicular to the plane.
[tex]\int\vec{E}d\vec{a} = \frac{Q_{enc}}{\epsilon_0}\\E2\pi r^2 = \frac{\pi r^2 \sigma}{\epsilon_0}\\E = \frac{\sigma}{2\epsilon_0}\\E = \frac{1.46 \times 10^{-7}}{2\times 8.8\times 10^{-12}} = 8.34\times 10^3~{\rm N/C}[/tex]
The direction of the electric field is in the upwards direction.
(c) The magnitude of the electric field is the same as that of upper side. Only the direction is reversed, downward direction.
100 kg of R-134a at 280 kPa are contained in a piston-cylinder device whose volume is 8.672 m3. The piston is now moved until the volume is one-half its original size. This is done such that the pressure of the R-134a does not change. Determine the final temperature and the change in the total internal energy of the R-134a. (Round the final answers to two decimal places.)
Answer:
∆u =-111.8 kJ/kg
T_fin=-10.09℃
Explanation:
note:
solution is attached in word file due to some technical issue in mathematical equation. please find the attached documents.
Calculate the acceleration of a 1400-kg car that stops from 39 km/h "on a dime" (on a distance of 1.7 cm).
Answer:
[tex]a=-3449.67\frac{m}{s^2}[/tex]
Explanation:
The car is under an uniforly accelerated motion. So, we use the kinematic equations. We calculate the acceleration from the following equation:
[tex]v_f^2=v_0^2+2ax[/tex]
We convert the initial speed to [tex]\frac{m}{s}[/tex]
[tex]39\frac{km}{h}*\frac{1000m}{1km}*\frac{1h}{3600s}=10.83\frac{m}{s}[/tex]
The car stops, so its final speed is zero. Solving for a:
[tex]a=\frac{v_0^2}{2x}\\a=-\frac{(10.83\frac{m}{s})^2}{2(1.7*10^{-2}m)}\\a=-3449.67\frac{m}{s^2}[/tex]
To calculate the acceleration of the car, use the formula a = (vf - vi) / t. Convert the initial velocity and distance to the appropriate units before substituting them into the formula.
To calculate the acceleration of the car, we can use the formula:
a = (vf - vi) / t
Where a is the acceleration, vf is the final velocity, vi is the initial velocity, and t is the time taken. In this case, the initial velocity is 39 km/h, which is converted to m/s by vi = 39 km/h * (1000 m/1 km) * (1 h/3600 s). The final velocity is 0 m/s since the car stops. The time taken can be found by t = d / vi, where d is the distance and vi is the initial velocity. The distance is given as 1.7 cm, which is converted to m by d = 1.7 cm * (1 m/100 cm). Substituting these values into the formula, we get the acceleration of the car.
So the acceleration of the car is approximately -8.45 m/s^2.
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A 1100 kgkg safe is 2.4 mm above a heavy-duty spring when the rope holding the safe breaks. The safe hits the spring and compresses it 52 cm . What is the spring constant of the spring?
To find the spring constant (k) of the spring, the potential energy of the falling safe is equated with the elastic potential energy of the spring at maximum compression. The calculated spring constant is approximately 20641 N/m.
To determine the spring constant of the spring, we can use the conservation of energy principle. Since the safe falls from a height onto the spring and compresses it, we can equate the potential energy of the safe at the height to the elastic potential energy stored in the spring at maximum compression.
The potential energy (PE) of the safe when it is above the spring is given by PE = mgh, where m is the mass (1100 kg), g is the acceleration due to gravity (9.81 m/s2), and h is the height (2.4 m). The elastic potential energy (EPE) stored in the spring when compressed is given by [tex]EPE = (1/2)kx^2[/tex], where k is the spring constant we need to find, and x is the compression distance (0.52 m).
Equating these two energies, [tex]mgh = (1/2)kx^2[/tex], we solve for the spring constant (k). Plugging in the values gives us:
[tex]1100 kg * 9.81 m/s^2 * 2.4 m = (1/2)k * (0.52 m)^2[/tex]
Solving for k, we get:
[tex]k = (1100 kg * 9.81 m/s^2 * 2.4 m) / (0.5 * (0.52 m)^2)[/tex]
After calculating, we find that the spring constant k is approximately 20641 N/m.
The spring constant k of the spring is 232614 N/m.
Use energy conservation: lost gravitational energy equals stored elastic potential energy in spring.
Gravitational Potential Energy (GPE) lost by the safe:
Height dropped by safe: [tex]\( h = 2.4 \, \text{m} + 0.52 \, \text{m} = 2.92 \, \text{m} \)[/tex]
Mass of safe (m): 1100 kg
Acceleration due to gravity [tex](\( g \)): \( 9.81 \, \text{m/s}^2 \)[/tex]
GPE lost = [tex]\( mgh = 1100 \times 9.81 \times 2.92 \)[/tex]
Elastic Potential Energy (EPE) stored in the spring:
Compression of spring [tex](\( x \)): 0.52 m (52 cm)[/tex]
EPE stored = [tex]\( \frac{1}{2} k x^2 \)[/tex]
Set lost gravitational potential energy equal to spring's stored elastic energy.
[tex]\[ mgh = \frac{1}{2} k x^2 \][/tex]
Rearrange the formula to solve for k:
[tex]\[ k = \frac{2mgh}{x^2} \][/tex]
Substitute the values:
[tex]\[ k = \frac{2 \times 1100 \times 9.81 \times 2.92}{(0.52)^2} \][/tex]
[tex]\[ k = \frac{2 \times 1100 \times 9.81 \times 2.92}{0.2704} \][/tex]
[tex]\[ k = \frac{62898.672}{0.2704} \][/tex]
[tex]\[ k \approx 232613.6 \, \text{N/m} \][/tex]
An electron is accelerated eastward at 1.06 109 m/s2 by an electric field. Determine the magnitude and direction of the electric field.
Answer:
Electric field, [tex]E=6.02\times 10^{-3}\ N/C[/tex] to the west direction.
Explanation:
Given that,
Acceleration of the electron, [tex]a=1.06\times 10^9\ m/s^2[/tex] (eastwards)
We need to find the magnitude and direction of the electric field. From Newton's law and electrostatic force,
ma = qE
[tex]E=\dfrac{ma}{q}[/tex]
[tex]E=\dfrac{9.1\times 10^{-31}\times 1.06\times 10^9}{1.6\times 10^{-19}}[/tex]
[tex]E=6.02\times 10^{-3}\ N/C[/tex]
The direction of electric field is in opposite direction of the acceleration of the electron. So, the electric field is acting in west direction.
The magnitude of the electric field accelerating an electron eastward is 6.04 × 10⁴ N/C, and its direction is westward since the electron has a negative charge.
Explanation:To determine the magnitude and direction of the electric field that accelerates an electron eastward, we can use the formula F = qE, where F is the force, q is the charge of the electron, and E is the electric field strength. The force exerted on the electron can be found using Newton's second law, F = ma, where m is the mass of the electron (9.11 × 10⁻³¹ kg) and a is the acceleration (1.06 × 10⁹ m/s²). Thus, F = (9.11 × 10⁻³¹ kg)(1.06 × 10⁹ m/s²) = 9.66 × 10⁻¹¹ N. We then solve for E by rearranging the formula to E = F/q, with q being the charge of an electron (-1.60 × 10⁻¹¹ C). Thus, E = (9.66 × 10⁻¹¹ N) / (-1.60 × 10⁻¹¹ C) = -6.04 × 10⁴ N/C. The negative sign indicates that the electric field points westward since it accelerates the electron eastward, and the electron has a negative charge.
An oscillator with angular frequency of 1.00 s-1has initial displacement of 1.00 m and initial velocity of 1.72 m/s. What is the amplitude of oscillation?
Final answer:
The amplitude of the oscillator is 1.989 m.
Explanation:
The amplitude of an oscillator can be determined using the initial displacement and initial velocity of the system. In this case, the initial displacement is given as 1.00 m and the initial velocity as 1.72 m/s. The amplitude, also known as the maximum displacement, is equal to the square root of the sum of the squares of the initial displacement and initial velocity.
Using the formula:
X = √(x₀² + v₀²)
Where X is the amplitude, x₀ is the initial displacement, and v₀ is the initial velocity.
Substituting the given values into the formula:
X = √(1.00² + 1.72²)
= √(1 + 2.9584)
= √3.9584
= 1.989 m
The amplitude of the oscillator is 1.989 m.
If the electron just misses the upper plate as it emerges from the field, find the magnitude of the electric field.
Answer:
The magnitude of the electric field be 171.76 N/C so that the electron misses the plate.
Explanation:
As data is incomplete here, so by seeing the complete question from the search the data is
vx_0=1.1 x 10^6
ax=0 As acceleration is zero in the horizontal axis so
Equation of motion in horizontal direction is given as
[tex]s_x=v_x_0 t[/tex]
[tex]t=\frac{s_x}{v_x}\\t=\frac{2 \times 10^{-2}}{1.1 \times 6}\\t=1.82 \times 10^{-8} s[/tex]
Now for the vertical distance
vy_o=0
than the equation of motion becomes
[tex]s_y=v_y_0 t+\frac{1}{2} at^2\\s_y=\frac{1}{2} at^2\\0.5 \times 10^{-2}=\frac{1}{2} a(1.82 \times 10^{-8})^2\\a=3.02 \times 10^{13} m/s^2[/tex]
Now using this acceleration the value of electric field is calculated as
[tex]E=\frac{F}{q}\\E=\frac{ma}{q}\\E=\frac{m_ea}{q_e}\\[/tex]
Here a is calculated above, m is the mass of electron while q is the charge of electron, substituting values in the equation
[tex]E=\frac{9.1\times 10^{-31} \times 3.02 \times 10^{13} }{1.6 \times 10^{-19}}\\E=171.76 N/C[/tex]
So the magnitude of the electric field be 171.76 N/C so that the electron misses the plate.
If the electron misses the upper plate, the magnitude of the electric field is equal to 171.88 Newton per coulomb.
Given the following data:
Distance = 2 cm to m = 0.02 meter.Vertical speed = [tex]1.6 \times 10^6[/tex] m/sVertical distance = 1 cm = [tex]\frac{0.01}{2} = 0.005\;m[/tex]Scientific data:
Mass of electron = [tex]9.1 \times 10^{-31}\;kg[/tex]Charge of electron = [tex]1.6 \times 10^{-19}\;C[/tex]To calculate the magnitude of the electric field:
First of all, we would determine the time taken by this electron to travel through the plates.
Time in the vertical direction.Mathematically, time is given by this formula:
[tex]Time = \frac{distance}{speed} \\ \\ Time = \frac{0.02}{1.10 \times 10^6} \\ \\ Time = 1.82 \times 10^{-8}\;m/s[/tex]
Next, we would find the acceleration of the electron in the vertical direction by using this formula:
[tex]a=\frac{2y}{t^2} \\ \\ a=\frac{2 \times 0.005}{(1.82 \times 10^{-8})^2}\\ \\ a=\frac{0.01}{3.31 \times 10^{-16}}\\ \\ a=3.02 \times 10^{13}\;m/s^2[/tex]
The formula for electric field.Mathematically, the electric field is given by this formula:
[tex]E=\frac{ma}{q}[/tex]
Where:
q is the charge.a is the acceleration.m is the mass.Substituting the given parameters into the formula, we have;
[tex]E=\frac{9.1 \times 10^{-31} \times 3.02 \times 10^{13}}{1.6 \times 10^{-19}}\\ \\ E=\frac{2.75 \times 10^{-17}}{1.6 \times 10^{-19}}[/tex]
Electric field, E = 171.88 N/C.
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Complete Question:
An electron is projected with an initial speed v0 = [tex]1.6 \times 10^6[/tex] m/s into the uniform field between the parallel plates. The distance between the plates is 1 cm and the length of the plates is 2 cm. Assume that the field between the plates is uniform and directed vertically downward, and that the field outside the plates is zero. The electron enters the field at a point midway between the plates. E = N/C
(a) If the electron just misses the upper plate as it emerges from the field, find the magnitude of the electric field.
The rocket-driven sled Sonic Wind No. 2, used for investigating the physiological effects of large accelerations, runs on a straight, level track 1070 m (3500 ft) long. Starting from rest, it can reach a speed of 224 m/s (500 mi/h) in 0.900 s. (a) Compute the acceleration in m/s2, assuming that it is constant. (b) What is the ratio of this acceleration to that of a freely falling body (g)? (c) What distance is covered in 0.900 s? (d) A magazine article states that at the end of a certain run, the speed of the sled de-creased from 283 m/s (632 mi/h) to zero in 1.40 s and that during this time the magnitude of the acceleration was greater than 40 g . Are these figures consistent?
Answer:
a) The acceleration of the rocket is 249 m/s².
b) The acceleration of the rocket is 25 times the acceleration of a free-falling body (25 g),
c) The distance traveled in 0.900 s was 101 m.
d) The figures are not consistent. The acceleration of the rocket was 20 g.
Explanation:
Hi there!
a) To calculate the acceleration of the rocket let's use the equation of velocity of the rocket:
v = v0 + a · t
Where:
v = velocity of the rocket.
v0 = initial velocity.
a = acceleration.
t = time.
We know that at t = 0.900 s, v = 224 m/s. The initial velocity, v0, is zero because the rocket starts from rest.
v = v0 + a · t
Solving for a:
(v - v0) / t = a
224 m/s / 0.900 s = a
a = 249 m/s²
The acceleration of the rocket is 249 m/s²
b) The acceleration of gravity is ≅ 10 m/s². The ratio of the acceleration of the rocket to the acceleration of gravity will be:
249 m/s² / 10 m/s² = 25
So, the acceleration of the rocket is 25 times the acceleration of gravity or 25 g.
c) The equation of traveled distance is the following:
x = x0 + v0 · t + 1/2 · a · t²
Where:
x = position of the rocket at time t.
x0 = initial position.
v0 = initial velocity.
t = time.
a = acceleration.
Since x0 and v0 are equal to zero, then, the equation of position gets reduced to:
x = 1/2 · a · t²
x = 1/2 · 249 m/s² · (0.900 s)²
x = 101 m
The distance traveled in 0.900 s was 101 m.
d) Now, using the equation of velocity, let's calculate the acceleration. We know that at 1.40 s the velocity of the rocket is zero and that the initial velocity is 283 m/s.
v = v0 + a · t
0 m/s = 283 m/s + a · 1.40 s
-283 m/s / 1.40 s = a
a = -202 m/s²
The figures are not consistent because 40 g is equal to an acceleration of 400 m/s² and the magnitude of the acceleration of the rocket was ≅20 g.
An air traffic controller notices two signals from two planes on the radar monitor. One plane is at altitude 1162 m and a 10.1-km horizontal distance to the tower in a direction 34.2° south of west. The second plane is at altitude of 4162 m and its horizontal distance is 9.5 km directed 21.5° south of west. What is the distance between these planes in kilometers?
Answer:
[tex]|R|=4.373km[/tex]
Explanation:
Given data
For first plate let it be p₁
[tex]p_{z1}=1162 m\\ p_{x1}=10.1km\\\alpha _{1}=34.2^{o}[/tex]
For second plate let it be p₂
[tex]p_{z2}=4162 m\\p_{x2}=9.5km\\\alpha _{2}=21.5^{o}[/tex]
To find
Distance R between them
Solution
To find distance between two plates first we need to find p₁ and p₂
Finding p₁
According to vector algebra
[tex]p_{1}=p_{x1}i+p_{y1}j+p_{z1}k\\ as\\tan\alpha =tan(34.2^{o} )=(p_{y1}/p_{x1})\\p_{y1}=10.1tan(34.2^{o} )\\p_{y1}=6.864km[/tex]
So we get
[tex]p_{1}=-10.1i-6.864j+1.162k[/tex]
Now to find p₂
[tex]p_{2}=p_{x2}i+p_{y2}j+p_{z2}k\\ as\\tan\alpha =tan(21.5^{o} )=(p_{y2}/p_{x2})\\p_{y2}=9.5tan(21.5^{o} )\\p_{y2}=3.74km[/tex]
So we get
[tex]p_{2}=-9.5i-3.74j+4.162k[/tex]
Now for distance R
According to vector algebra the position vector R between p₁ and p₂
[tex]R=p_{1}-p_{2}\\ R=(p_{x1}-p_{x2})i+(p_{y1}-p_{y2})j+(p_{z1}-p_{z2})k\\R=(-10.1-(-9.5))i+(-6.864-(-3.74))j+(1.162-4.162)k\\R=-0.6i-3.124j-3k\\|R|=\sqrt{(0.6)^{2}+(3.124)^{2}+(3)^{2} }\\ |R|=4.373km[/tex]
To find the distance between two planes, calculate the horizontal distances using the given angles and distances. Use the Pythagorean theorem to find the distance by applying the formula. The distance between the two planes is approximately 14.1 km.
Explanation:To find the distance between the two planes, we can use the Pythagorean theorem. First, we calculate the horizontal distances using the given angles and distances. For the first plane, the horizontal distance is 10.1 km * cos(34.2°), and for the second plane, it is 9.5 km * cos(21.5°). Next, we use the Pythagorean theorem to find the distance between the two planes: d = √((9.5 km * cos(21.5°))^2 + (10.1 km * cos(34.2°))^2).
Calculating the values, we get d ≈ 14.1 km.
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A moving electron passes near the nucleus of a gold atom, which contains 79 protons and 118 neutrons. At a particular moment the electron is a distance of 7.5 × 10−9 m from the gold nucleus. (a) What is the magnitude of the electric force exerted by the gold nucleus on the electron?
Answer:
[tex]F=3.2345*10^{-10}N[/tex]
Explanation:
Given data
Distance r=7.5×10⁻⁹m
Charge of electron -e= -1.6×10⁻¹⁹C
Charge of proton e=1.6×10⁻¹⁹C
To find
Electric force F
Solution
From Coulombs law we know that:
[tex]F=K\frac{q_{1}q_{2} }{r^{2} }[/tex]
q₁ is charge of electron
q₂ is the charge of gold nucleus which contains 79 positively charge protons and 118 neutral neutrons.
The Charge of single proton e=1.6×10⁻¹⁹C
79 proton charge q₂=79×1.6×10⁻¹⁹=1.264×10⁻¹⁷C
So
[tex]F=\frac{1}{4\pi *8.85*10^{-12} } \frac{-1.6*10^{-19}*1.264*10^{-17}}{(7.5*10^{-9})^{2} }\\ F=3.2345*10^{-10}N[/tex]
The magnitude of the electric force exerted by the gold nucleus on the electron [tex]3.235\times10^{-10}\rm N[/tex].
What is electric force?Electric force is the force of attraction or repulsion between two charged particles. It can be given as,
[tex]F=K\dfrac{q_1\times q_2}{r^2}[/tex]
Here [tex]k[/tex] is coulomb's constant, [tex]q[/tex] is charge on the objects and [tex]r[/tex] is the distance between two objects.
Given information-
The number of proton in gold atom is 79.
The number of neutrons in gold atom is 118.
The distance of the electron from the nucleus is [tex]7.5 \times 10^{-9} \rm m[/tex].[tex]r[/tex]
a) The magnitude of the electric force exerted by the gold nucleus on the electron-The charge on electron is [tex]-1.6\times 10^{-19} C[/tex] and the charge on the proton is [tex]1.6\times 10^{-19} C[/tex].
Put the values in the above equation as,
[tex]F=8.98\times10^9\times\dfrac{(79\times1.6\times10^{-19})\times1.6\times10^{-19}}{(7.5\times10^{-19})^2}\\F=3.235\times10^{-10}\rm N[/tex]
Hence the magnitude of the electric force exerted by the gold nucleus on the electron [tex]3.235\times10^{-10}\rm N[/tex].
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Two college students are sliding down a hill on excellent sleds so you can ignore friction. One has a mass of 85 kg and one has a mass of 75 kg. Which will reach the bottom of the hill first? a. they will both reach at the same time. b. 85 kg person c. 75 kg person
Answer:
a. They both reach at the same time.
Explanation:
On a frictionless incline, the only force that moves the person downwards is the x-component of the persons weight. (x-direction is the direction along the incline.)
[tex]F = mg\sin(\theta)[/tex]
Here, θ is the angle of the incline above horizontal.
This force is equal to 'ma' according to Newton's Second Law.
Comparing the weights of the two persons gives
[tex]F_1 = 85g\sin(\theta) = 85a_1\\F_2 = 75g\sin(\theta) = 75a_1\\a_1 = g\sin(\theta)\\a_2 = g\sin(\theta)[/tex]
Since the accelerations of both persons are the same, they reach the bottom at the same time.
The crucial point here is that the acceleration on a frictionless incline is independent from the mass of the object. If there were friction on the surface, then the person with smaller mass would reach the bottom first.
A wave on a string has a wavelength of 0.90 m at a frequency of 600 Hz. If a new wave at a frequency of 300 Hz is established in this same string under the same tension, what is the new wavelength? Group of answer choices
Answer:
λ₂ = 1.8 m
Explanation:
given,
wavelength of the string 1 = 0.90 m
frequency of the string 1 = 600 Hz
wavelength of string 2 = ?
frequency of the string 2 = 300 Hz
we now,
[tex]f\ \alpha\ \dfrac{1}{\lambda}[/tex]
now,
[tex]\dfrac{f_1}{f_2}=\dfrac{\lambda_2}{\lambda_1}[/tex]
[tex]\dfrac{600}{300}=\dfrac{\lambda_2}{0.9}[/tex]
λ₂ = 2 x 0.9
λ₂ = 1.8 m
Hence, the wavelength of the second string is equal to λ₂ = 1.8 m
A businesswoman is rushing out of a hotel through a revolving door with a force of 80 N applied at the edge of the 3 m wide door. Where is the pivot point and what is the maximum torque?
Answer:
Explanation:
Given
Force applied [tex]F=80\ N[/tex]
Door is [tex]d=3\ m[/tex] wide
for gate to revolve Properly Pivot Point must be at center i.e. 1.5 from either end
Torque applied is [tex]T=force\times distance[/tex]
Maximum torque
[tex]T_{max}=F\times \frac{d}{2}[/tex]
[tex]T_{max}=80\times \frac{3}{2}[/tex]
[tex]T_{max}=120\ N-m[/tex]
Final answer:
The pivot point of a revolving door is at its central axis, and the maximum torque exerted by the businesswoman on the revolving door is 120 Nm, calculated by multiplying the force (80 N) by the perpendicular distance from the pivot point to the point of application (1.5 m).
Explanation:
The question is asking about the concept of torque, which is a measure of the turning force on an object. In the scenario described, a businesswoman is applying a force of 80 N to a revolving door. The maximum torque can be calculated by multiplying the force applied by the perpendicular distance from the pivot point to the point of application. The pivot point of a revolving door is its central axis, which is the center of the door.
To calculate the maximum torque, we use the formula:
Torque = Force * Distance.
Here, Torque = 80 N * 1.5 m (since the force is applied at the edge of the 3 m wide door, the distance from the pivot point is half the width).
Thus, Torque = 120 Nm
This is the maximum torque exerted by the woman on the door relative to its central.
Under what conditions does the magnitude of the average velocity equal the average speed?
Final answer:
The magnitude of the average velocity equals the average speed when the direction of motion doesn't change and the speed is constant. These conditions are met in straightforward travel without directional change or speed variations. For round trips or trips involving direction changes, the average speed may differ from the magnitude of the average velocity.
Explanation:
The conditions under which the magnitude of the average velocity equals the average speed occur when the motion does not involve a change in direction. The average speed is calculated by dividing the total distance traveled by the elapsed time, while the magnitude of the average velocity is the total displacement divided by the elapsed time. For these two quantities to be the same, the direction of travel must remain constant, meaning there is no reversal or change in direction.
When you take a road trip and do not change direction, and your speed is consistent, then your average speed is equal to the magnitude of the average velocity. However, if you ended up back at your starting point, despite having moved, your displacement would be zero, and hence so would your average velocity, even though your average speed is greater than zero.
If you're calculating the ratio of the total distance as shown on the car's odometer to the time of the trip, you're calculating average speed. The speedometer of a car measures instantaneous speed, not velocity, because it does not provide information about direction.
You are designing an elevator for a hospital. The force exerted on a passenger by the floor of the elevator is not to exceed 1.46 times the passenger's weight. The elevator accelerates upward with constant acceleration for a distance of 2.2 m and then starts to slow down.What is the maximum speed of the elevator?
Answer:
Final velocity of the elevator will be 4.453 m/sec
Explanation:
Let mass is m
Acceleration due to gravity is g m/sec^2
Distance s = 2.2 m
As the elevator is moving upward so net force on elevator
[tex]F=mg+ma[/tex]
So according to question
[tex]1.46mg=mg+ma[/tex]
0.46 mg = ma
a = 0.46 g
a = 0.46×9.8 = 4.508 [tex]m/sec^2[/tex]
Initial velocity of elevator is 0 m/sec
From third equation of motion
[tex]v_f^2=v_i^2+2as[/tex]
[tex]v_f^2=0^2+2\times 4.508\times 2.2[/tex]
[tex]v_f=4.453m/sec[/tex]
So final velocity of the elevator will be 4.453 m/sec
If a guitar string has a fundamental frequency of 500 Hz, what is the frequency of its second overtone?
Does the speedometer of a car measure speed or velocity? Explain.
The speedometer of a car measures speed, which is a scalar quantity indicating how fast the car is moving without regard to direction. Velocity, on the other hand, includes both speed and direction, which the speedometer does not display. The odometer measures total distance traveled, not displacement, and dividing distance by time gives average speed, not velocity.
Explanation:The speedometer of a car measures speed, not velocity. Speed is a scalar quantity, which means it only describes how fast an object is moving regardless of its direction. On the other hand, velocity is a vector quantity that describes both the speed and the direction of an object's movement. For example, if a car is moving at 60 miles per hour (mph), the speedometer shows this speed, but it does not indicate whether the car is traveling north, south, east, or west – that would be necessary information to determine the car's velocity.
A car's odometer, in contrast, measures the total distance traveled by the car. This distance is a scalar quantity as well, which means it does not account for the direction of travel, only the cumulative distance covered. When you divide the total distance traveled, as shown on the odometer, by the total time taken for the trip, you are calculating the average speed of the car, not the magnitude of average velocity. These two quantities – average speed and the magnitude of average velocity – are the same when the car moves in a straight line without changing its direction.
Assume it takes 8.00 min to fill a 50.0-gal gasoline tank. (1 U.S. gal = 231 in.3) (a) Calculate the rate at which the tank is filled in gallons per second. .104 Correct: Your answer is correct. gal/s (b) Calculate the rate at which the tank is filled in cubic meters per second.
The volumetric rate or flow rate of a fluid is defined as the amount of the volume of a fluid circulating on a surface per unit of time. In this case we have units given initially: Gallons and minutes. For the first part we will convert the minutes to seconds, and we will obtain the flow rate under that measure. For the second case we will convert the gallons to cubic meters and obtain the desired value. Recall the following conversion rates,
[tex]1 min = 60s[/tex]
[tex]1 U.S Gal = 0.00378541178 m^3[/tex]
If the flow rate is defined as the volume by time, the flow rate with the given values is
[tex]Q = \frac{V}{t}[/tex]
[tex]Q = \frac{50Gal}{8min}[/tex]
[tex]Q = 6.25 Gal/min[/tex]
PART A ) Converting to Gal/seconds, we have,
[tex]Q = 6.25 \frac{Gal}{min}(\frac{1min}{60s})[/tex]
[tex]Q = 0.10416Gal/s[/tex]
PART B) Converting Gal/seconds to [tex]m^3/s[/tex]
[tex]Q = 0.104116\frac{Gal}{s} (\frac{0.00378541178 m^3}{1 Gal})[/tex]
[tex]Q = 3.941*10^{-4}m^3/s[/tex]
The rate of filling the gasoline tank is 0.104 gallons per second or approximately 0.000383 cubic meters per second.
Explanation:To calculate the rate at which the gasoline tank is being filled, we need to first convert the given quantities into the relevant units. Given that the gasoline tank is 50.0 gallons and it takes 8.00 minutes to fill it, the flow rate is 50/480 (since 8 min = 480 s) = 0.104 gallons/second. Since 1 US gallon = 231 cubic inches, this gives us a flow rate of 0.104 x 231 = 23.5 cubic inches per second.
To convert this to the rate in cubic meters per second, we use the fact that 1 inch = 0.254 cm and 1 cubic meter = 1,000,000 cubic cm. Therefore, 23.5 cubic inches = 23.5 x 0.254^3 cubic meters = approximately 0.000383 cubic meters per second (m^3/s).
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A particle moving along the x axis in simple harmonic motion starts from its equilibrium position, the origin, at t = 0 and moves to the right. The amplitude of its motion is 2.00 cm, and the frequency is 1.50 Hz(a) show that the position of the particle is given by x = (2.00 cm) sin(3.00πt) (b) the maximum speed and the earliest time (t > 0) at which the particle has this speed, (c) the maximum
acceleration and the earliest time (t > 0) at which the particle has this acceleration, and (d) the total distance traveled between t = 0 and t = 1.00 s.
Answer:
(a). [tex]x=2.00\sin(3.00\pi t)[/tex], hence proved
(b). The maximum speed is 18.8 cm/s.
(c). The maximum acceleration is 177.65 cm/s².
(d). The total distance is 12 cm.
Explanation:
Given that,
Amplitude = 2.00 cm
Frequency = 1.50 Hz
Given equation of position of the particle is
[tex]x=2.00\ sin(3.00\pit)[/tex]
(a). show that the position of the particle is given by
[tex]x=2.00\sin(3.00\pi t)[/tex]
We know the general equation of S.H.M
[tex]x=A\sin(\omega t[/tex]...(I)
At t =0, x = 0
On differentiating equation (I)
[tex]v=\dfrac{dx}{dt}[/tex]
[tex]v=A\omega\cos(\omega t)[/tex]
At t = 0, the particle moving to the right
[tex]V=A\omega[/tex] > 0
Given statement is true.
The equation of position is
[tex]x=A\sin(\omega t)[/tex]
here, [tex]\Omega= 2\pi f[/tex]
Put the value in the equation
[tex]x=2.00\sin(2\times1.50\pi t)[/tex]
[tex]x=2.00\sin(3.00\pi t)[/tex]
Hence proved.
(b). We need to calculate the maximum speed
[tex]V=A\omega\cos(\omega t)[/tex]....(II)
At t = 0,
[tex]V_{max}=A\omega[/tex]
Put the value into the formula
[tex]V_{max}=2.00\times2\pi\times1.50[/tex]
[tex]V_{max}=6\pi[/tex]
[tex]V_{max}=18.8\ cm/s[/tex]
(c). We need to calculate the maximum acceleration
Using equation (II)
[tex]V=A\omega\cos(\omega t)[/tex]
On differentiating
[tex]a=\dfrac{dV}{dt}[/tex]
[tex]a=-A\omega^2\sin(\omega t)[/tex]
[tex]a_{max}\ when\ \sin(\omega t)\ is\ -1[/tex]
[tex]a_{max}=-A\omega^2\times-1[/tex]
[tex]a=A\omega^2[/tex]
[tex]a_{max}=2\times(3\pi)^2\approx 177.65 cm/s^2[/tex]
(d). We need to calculate the total distance traveled between t = 0 and t = 1.00 s
Using equation (II)
[tex]V=A\omega\cos(\omega t)[/tex]
On integration
[tex]\int{V}=\int_{t}^{t'}{A\omega\cos(\omega t)}[/tex]
Put the vale into the formula
[tex]\int{V}=\int_{0}^{1}{A\omega\cos(\omega t)}[/tex]
[tex]D=\int_{0}^{1}|6\pi\cos\left(3\pi t\right)|dt[/tex]
[tex]D=12\ cm[/tex]
Hence, (b). The maximum speed is 18.8 cm/s.
(c). The maximum acceleration is 177.65 cm/s².
(d). The total distance is 12 cm.
A particle in simple harmonic motion can be described by the equation x = (2.00 cm)sin(3.00πt). The maximum speed and maximum acceleration occur when the particle is at its maximum displacement from the equilibrium position. The total distance traveled between t = 0 and t = 1.00 s is 4.00 cm.
Explanation:The position of the particle in simple harmonic motion is given by the equation x = (2.00 cm)sin(3.00πt), where x represents the displacement from the equilibrium position and t represents time in seconds.
(b) The maximum speed of the particle is equal to the amplitude of the motion multiplied by the angular frequency, vmax = (2.00 cm)(2π)(1.50 Hz). The earliest time at which the particle reaches this maximum speed is when it passes through its equilibrium position, t = 0.
(c) The maximum acceleration of the particle is equal to the amplitude of the motion multiplied by the angular frequency squared, amax = (2.00 cm)(2π)(1.50 Hz)2. The earliest time at which the particle reaches this maximum acceleration is when it is at its maximum displacement from the equilibrium position, which occurs at t = 0.
(d) To find the total distance traveled between t = 0 and t = 1.00 s, we calculate the area under the velocity versus time graph. Since the particle is in simple harmonic motion, the velocity varies sinusoidally, and the total distance traveled is equal to two times the amplitude of the motion, dtotal = 2(2.00 cm) = 4.00 cm.
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