Final answer:
When the charge moves 0.450 m to the right, the work done is zero. When the charge moves 0.670 m upward, the work done can be calculated as (28.0 nC * Electric Field) * 0.670 m. When the charge moves 2.60 m at an angle of 45.0° downward from the horizontal, the work done can be calculated as (28.0 nC * Electric Field * cos(45.0°)) * 2.60 m.
Explanation:
In order to calculate the work done by the electric force, we can use the equation:
Work = Force * Distance
For part (a) when the charge moves 0.450 m to the right, we need to calculate the force first using the equation:
Force = Charge * Electric Field
Given that the charge is 28.0 nC and the electric field is directed vertically upward, we should consider the vertical component of the electric field. Since the charge is moving horizontally to the right, it is perpendicular to the electric field and does not contribute to the work done by the electric force. Therefore, the work done is zero.
For part (b) when the charge moves 0.670 m upward, we can calculate the force using the same equation. Since the charge moves in the same direction as the electric field, the work done is positive. The work done can be calculated as:
Work = Force * Distance = (28.0 nC * Electric Field) * 0.670 m
For part (c) when the charge moves 2.60 m at an angle of 45.0° downward from the horizontal, we can break down the movement into horizontal and vertical components. The horizontal component does not contribute to the work done by the electric force since it is perpendicular to the electric field. The vertical component contributes to the work done. We can calculate the vertical component of the distance traveled using the angle and multiply it by the electric field to get the force. The work done can be calculated as:
Work = Force * Distance = (28.0 nC * Electric Field * cos(45.0°)) * 2.60 m
A 1 kg rock is suspended by a massless string from one end of a meter stick at the 0 cm mark. What is the mass m suspended from the meter stick at the 75 cm mark if the system is balanced?
Answer:
2 kg
Explanation:
Note: For the meter stick to be balanced,
Sum of clock wise moment must be equal to sum of anti clock wise moment
Wd = W'd' ................ Equation 1
Where W = weight of the rock, d = distance of the meter stick from the point of support, W' = weight of the that must be suspended for the meter stick to be balanced, d' = distance of the mass to the point of support.
make W' the subject of the equation
W' = Wd/d'............... Equation 2
Taking our moment about the support,
Given: W = mg = 1 ×9.8 = 9.8 N, d = 50 cm, d' = (75-50) = 25 cm
Substitute into equation 2
W' = 9.8(50)/25
W' = 19.6 N.
But,
m = W'/g
m = 19.6/9.8
m = 2 kg.
To find the mass M suspended from the meter stick, we can use the principle of rotational equilibrium. By setting the torques on either side of the fulcrum equal to each other, we can calculate the mass M at the 75 cm mark to be 3 kg.
Explanation:To determine the mass M suspended from the meter stick at the 75 cm mark, we can use the principle of rotational equilibrium. Since the system is balanced, the torques on both sides of the meter stick must be equal.
The torque of the rock can be calculated using its weight, which is equal to its mass multiplied by the acceleration due to gravity. The torque of the mass M can be calculated by multiplying its mass by the distance from the fulcrum (75 cm) to its center of mass. By setting the torques equal to each other, we can solve for M.
The torque of the rock: TR = (1 kg)(9.8 m/s²)(0.75 m).
The torque of the mass M: TM = M(9.8 m/s²)(0.25 m).
Setting TR equal to TM and solving for M, we get M = (1 kg)(0.75 m)/(0.25 m) = 3 kg.
Learn more about mass here:https://brainly.com/question/33738912
#SPJ11
The potential difference between a pair of oppositely charged parallel plates is 402 V. If the spacing between the plates is doubled without altering the charge on the plates, what is the new potential difference between the plates
Final answer:
Doubling the distance between a pair of oppositely charged parallel plates, without altering the charge on them, does not change the potential difference. The potential difference remains at 402 V because it is directly influenced by the electric field and the charge on the plates, both of which remain constant in this scenario.
Explanation:
The question involves understanding how the potential difference between a pair of oppositely charged parallel plates changes when the distance between them is altered, without changing the charge on the plates. The original potential difference is given as 402 V when the spacing between the plates is a certain value.
If the spacing between the plates is doubled, the new potential difference remains the same, 402 V, because the potential difference between two plates is determined by the equation V = Ed, where 'E' is the electric field strength and 'd' is the distance between the plates. Since the charge on the plates remains constant, and assuming the electric field remains uniform, the electric field (E) does not change.
Therefore, doubling the distance without altering the charge or the electric field does not affect the potential difference. This is a key concept in electrostatics, highlighting how changes in geometry and charge distribution affect electric fields and potential differences.
Johnnie's father worked his entire career in the automotive manufacturing industry in Michigan. When Johnnie entered the workforce, the auto industry was in decline, so he instead found a professional career in the booming information technology sector, an industry that did not exist when his father began his career. This is an example of
a. structural mobility.
b. horizontal mobility.
c. exchange mobility.
d. social reproduction.
Final answer:
Johnnie's move from automotive manufacturing to the IT sector due to changes in the economy is an example of structural mobility, which reflects broad societal shifts affecting whole groups within the social class system. Option a
Explanation:
Johnnie's career change from the declining auto industry that his father was a part of, to the burgeoning information technology sector, is an example of structural mobility. This type of mobility occurs due to large-scale economic and societal shifts rather than individual actions. For instance, in the past, industrialization led to the general upliftment of the population, causing widespread upward structural mobility. In more recent times, factors such as recessions and outsourcing have resulted in many experiencing downward structural mobility, as traditional jobs have become obsolete or have moved overseas.
Moreover, technological advancements have altered the kinds of skills employers seek in their workforce, leading to a situation where some individuals may find themselves structurally unemployed if they lack the necessary analytical and communication skills, despite having traits like reliability and physical strength that were formerly highly valued.
Therefore, Johnnie's entrance into a different industry than his father's, brought upon by changes in the economic landscape, is a reflection of the broader trend where entire groups in society move up or down the social class ladder due to changes in the social structure itself.
Two metal balls are the same size but one weighs twice as much as the other. The balls are dropped from the roof of a single story building at the same instant of time. The time it takes the balls to reach the ground below will be:
a.about half as long for the heavier ball as for the lighter one.
b.about half as long for the lighter ball as for the heavier one.
c,about the same for both balls.
d.considerably less for the heavier ball, but not necessarily half as long.
e..considerably less for the lighter ball, but not necessarily half as long.
Answer:
c, About the same for both balls.
Explanation:
If no air resistance is present, the rate of descent depends only on how far the object has fallen, no matter how heavy the object is. This means that two objects will reach the ground at the same time if they are dropped simultaneously from the same height.
An ideal gas is kept at constant volume of 2.00 L as its temperature is increased, raising the pressure from 15.0 kPa to 30.0 kPa. What work is performed by or on the gas during this process?
30.0 J performed by the gas
4.00 J performed on the gas
0 J
30.0 J performed on the gas
Answer:
0 J
Explanation:
The work done by an ideal gas is given by the equation:
[tex]W=p\Delta V[/tex]
where
W is the work done by the gas
p is the pressure of the gas
[tex]\Delta V[/tex] is the change in volume of the gas
In this problem, we have a gas kept at a constant volume of
V = 2.00 L
This is an isochoric process (constant volume). Since the volume is constant, the change in volume is zero:
[tex]\Delta V=0[/tex]
And therefore, this means that the work done by the gas is zero:
W = 0
In a manufacturing process, a large, cylindrical roller is used to flatten material fed beneath it. The diameter of the roller is 1.00 m and while being driven into rotation around a fixed axis, its angular position is expressed as
θ = 2.50t2 - 0.600t3
where θ is in radians and t is in seconds.
a) Find the maximum angular speed of the roller
b) what is the maximum tangential speed of the point an the rim of the roller?
c) at what time t should the driven force be removed from the roller so that the roller does not reverse its direction of rotation?
d) Through how many rotations has the roller turned between t=0 and the time found in part c?
Explanation:
Below is an attachment containing the solution.
A soccer ball is rolling with a constant acceleration of -1.5 m/s2 . At ti = 0 s, the ball has an instantaneous velocity of 14 m/s. After 3s of rolling, what would be the velocity of the ball (in m/s)?
Answer:
[tex]v_{f} = 9.5\,\frac{m}{s}[/tex]
Explanation:
The final velocity is:
[tex]v_{f} = v_{o} + a \cdot t[/tex]
[tex]v_{f} = 14\,\frac{m}{s} + (-1.5\,\frac{m}{s^{2}} )\cdot (3\,s)[/tex]
[tex]v_{f} = 9.5\,\frac{m}{s}[/tex]
The velocity of the soccer ball after 3 s of rolling would be 9.5 m/s.
For a soccer ball rolling with a constant acceleration of -1.5 m/s², we can use the equation for velocity with constant acceleration: v = (initial velocity) + (acceleration)(time). At t = 3 s, the ball has an initial velocity of 14 m/s and has been rolling for 3 s, so we can plug these into the equation to find the velocity:
v = 14 m/s + (-1.5 m/s²)(3 s) = 14 m/s - 4.5 m/s = 9.5 m/s
Therefore, after 3 s of rolling, the velocity of the ball would be 9.5 m/s.
Learn more about velocity of rolling soccer ball here:https://brainly.com/question/29964512
#SPJ3
Torque, a car manufacturer, aims to make its slogan "Burn Rubber" known to every individual in a way that they immediately associate it with the firm. The company has created a social media page where almost a thousand fans have registered. However, there are two competitors who advertise the same features as those of Torque cars. The firm has a large number of customers who think it manufactures the best cars and there is no other manufacturer better than Torque.
Answer:
A customer is about to buy a limited edition sports car from Torque. It is most likely that the customer will have d. limited problem solving, in which consumers decision rules to purchase are simple, and are not motivated to search for information about other optons, deciding to buy the car.
Explanation:
a. advertising clutter is the big amount of ad-messages that the consumer is exposed to everyday.
b. high involvement product or purchases features many variables to be considered by the customer before getting to a decision.
c. cognitive dissonance or conflicting attitudes causing mental discomfort.
Two carts are involved in an elastic collision. Cart A with mass 0.550 kg is moving towards Cart B with mass 0.550 kg, which is initially at rest. Cart A stops after the collision and Cart B begins to move.A)If cart A has an initial velocity of 0.8 m/s , what is the velocity of Cart B after the collision?B)What is the initial kinetic energy of Cart A?C)What is the initial kinetic energy of Cart B?D)What is the final kinetic energy of Cart A?E)What is the final kinetic energy of Cart B?F)Is the kinetic energy conserved for elastic collisions?G)Is the momentum conserved for elastic collisions?
Answer:
A) [tex]v_b=0.8\ m.s^{-1}[/tex] is the final velocity of the cart B after collision.
B) [tex]KE_A=0.176\ J[/tex]
C) [tex]KE_B=0\ J[/tex]
D) [tex]ke_a=0\ J[/tex]
E) [tex]ke_B=0.176\ J[/tex]
F) Yes, here the kinetic energy is conserved because the mass of both the bodies involved in the collision is same.
G) Yes, momentum is always conserved for an elastic collision.
Explanation:
Given:
mass of car A, [tex]m_a=0.55\ kg[/tex]mass of car B, [tex]m_b=0.55\ kg[/tex]initial velocity of car A, [tex]u_a=0.8\ m.s^{-1}[/tex]final velocity of the car A, [tex]v_a=0\ m.s^{-1}[/tex]A)
As given in the question that the cars undergo an elastic collision:
According to the conservation of momentum:
[tex]m_a.u_a+m_b.u_b=m_a.v_a+m_b.v_b[/tex]
[tex]0.55\times 0.8+0.55\times 0=0.55\times 0+0.55\times v_b[/tex]
[tex]v_b=0.8\ m.s^{-1}[/tex] is the final velocity of the cart B after collision.
B)
Initial kinetic energy of cart A:
[tex]KE_A=\frac{1}{2} m_a.u_a^2[/tex]
[tex]KE_A=0.5\times 0.55\times 0.8^2[/tex]
[tex]KE_A=0.176\ J[/tex]
C)
Initial kinetic energy of cart A:
[tex]KE_B=\frac{1}{2} \times m_b.u_b^2[/tex]
[tex]KE_B=0.5\times 0.55\times 0^2[/tex]
[tex]KE_B=0\ J[/tex]
D)
The final kinetic energy of cart A:
[tex]ke_A=\frac{1}{2} m_a.v_a^2[/tex]
[tex]ke_a=0.5\times 0.55\times 0^2[/tex]
[tex]ke_a=0\ J[/tex]
E)
The final kinetic energy of cart B:
[tex]ke_B=\frac{1}{2} m_b.v_b^2[/tex]
[tex]ke_B=0.5\times 0.55\times 0.8^2[/tex]
[tex]ke_B=0.176\ J[/tex]
F)
Yes, here the kinetic energy is conserved because the mass of both the bodies involved in the collision is same.
G)
Yes, momentum is always conserved for an elastic collision.
(a) The velocity of cart B is [tex]0.8m/s[/tex]
(b) Initial kinetic energy of cart A is [tex]0.176J[/tex]
(c) Initial kinetic energy of cart B is 0
(d) The final kinetic energy of cart A is 0
(e) The final kinetic energy of cart B is [tex]0.176J[/tex]
(f) The kinetic energy is conserved
(g) The momentum is conserved
Elastic collision:(a) The momentum of the system must be conserved, which means momentum before the collision must be equal to momentum after the collision.
Momentum before collision = [tex]m_Au_A+m_bu_B=0.55\times0.8+0.55\times0=0.44kgm/s[/tex]
Momentum after collision:
[tex]m_A+m_A+m_Bv_B=0.55\times0+0.55v_B=0.44\\\\v_B=0.8m/s[/tex]
(b) Initial kinetic energy of cart A:
[tex]K_{iA}=\frac{1}{2}m_Au_A^2=0.5\times0.55\times0.64=0.176J[/tex]
(c) Initial kinetic energy of cart B:
[tex]K_{iB}=\frac{1}{2}m_Bu_B^2=0.5\times0.55\times0=0J[/tex]
(d) The final kinetic energy of cart A:
[tex]K_{fA}=\frac{1}{2}m_Av_A^2=0.5\times0.55\times0=0J[/tex]
(e) Initial kinetic energy of cart B:
[tex]K_{iB}=\frac{1}{2}m_B_v_B^2=0.5\times0.55\times0.64=0.176J[/tex]
(f) yes the kinetic energy of the system is conserved for elastic collision
(g) The momentum is conserved in any case including the elastic collision
Learn more about elastic collision:
https://brainly.com/question/2356330?referrer=searchResults
We have seen that the heart produces a magnetic field, and that this can be used to diagnose problems with the heart. The magnetic field of the heart is a dipole field that is produced by a loop current in the outer layers of the heart. Suppose the field at the center of the heart is 90 pT (a pT is 10−12T ) and that the heart has a diameter of approximately 12 cm. What current circulates around the heart to produce this field?
Answer:
Current circulating is 8.59×10^-6A
Explanation:
Magnetic field at the center of the loop is given by, B= μI/2R
I = 2RB/μ
given that B is 90x 10^-12 T
radius is 0.12 m /2 = 0.06m
we know that μ is 4π x 10^-7 T.A/m
Substituting the given values we get,
I= (((2(0.06m)(90x 10^-12 T))/(4π x 10^-7 T.A/m))
I is 8.59 x 10^-6 A
The current circulating around the heart is 8.59×10⁻⁶A
Calculating the current:The magnetic field B at the center of the loop of radius R with current I is given by,
B= μ₀I/2R
Rearranging the terms we get:
I = 2RB/μ₀
Given that B is 90×10⁻¹² T
radius is R = 0.12 m /2 = 0.06m
Substituting the given values we get,
I = 2×0.06×90×10⁻¹² / 4π×10⁻⁷
I = 8.59 x 10⁻⁶ A
Learn more about magnetic field:
https://brainly.com/question/19542022?referrer=searchResults
Two speakers, one directly behind the other, are each generating a 240-Hz sound wave. What is the smallest separation distance between the speakers that will produce destructive interference at a listener standing in front of them?
Answer:
The smallest separation distance between the speakers is 0.71 m.
Explanation:
Given that,
Two speakers, one directly behind the other, are each generating a 240-Hz sound wave, f = 240 Hz
Let the speed of sound is 343 m/s in air. The speed of sound is given by the formula as :
[tex]v=f\lambda\\\\\lambda=\dfrac{v}{f}\\\\\lambda=\dfrac{343\ m/s}{240\ Hz}\\\\\lambda=1.42\ m[/tex]
To produce destructive interference at a listener standing in front of them,
[tex]d=\dfrac{\lambda}{2}\\\\d=\dfrac{1.42}{2}\\\\d=0.71\ m[/tex]
So, the smallest separation distance between the speakers is 0.71 m. Hence, this is the required solution.
According to the question,
Frequency, f = 240 HzSpeed of sound, v = 343 m/sThe wavelength will be:
→ [tex]\lambda = \frac{v}{f}[/tex]
By substituting the values, we get
[tex]= \frac{343}{240}[/tex]
[tex]= 1.43 \ m[/tex]
hence,
The smallest separation distance will be:
= [tex]\frac{\lambda}{2}[/tex]
= [tex]\frac{1.43}{2}[/tex]
= [tex]0.715 \ m[/tex]
Thus the above solution is correct.
Learn more about distance here:
https://brainly.com/question/15409465
Estimate how long the sun would last if it were merely a huge fire that was releasing chemical energy. Assume that the sun begins with roughly 108 joules per kilogram
Answer:
≅ 17000 years or 1.7 x 10⁴ years
Explanation:
time= total energy/power
= (10⁸J/kg)(2x10³⁰ kg) / 3.8 x 10²⁶ J/s
= 526,315,789,473 s
= 16689 years
≅ 17000 years or 1.7 x 10⁴ years
Final answer:
If the Sun were simply a large fire releasing chemical energy, it would have a lifetime of approximately 16,438 years, considering a mass of 2.0 x 10³⁰ kilograms and an energy release of 10^8 joules per kilogram. This is significantly shorter than the Sun's actual lifespan, confirming that nuclear reactions, not chemical combustion, power the Sun.
Explanation:
If the Sun were simply a large fire releasing chemical energy, we can estimate its lifetime using certain assumptions. Firstly, if the Sun's mass is predominantly hydrogen and its energy output is due to combustion with oxygen, the amount of energy released per kilogram would be about 108 joules. With this in mind, we recall that the Sun's mass is approximately 2.0 × 1030 kilograms. The resource provided illustrates that combustion produces about 45,000,000 calories, or approx. 1.88 × 108 joules, per second for a combusting mass of one kilogram (previously cited as 1.6 × 10-19 joules for a typical energy in a chemical bond). With a simple energy balance calculation, we find that the theoretical Sun-as-a-fire would consume its mass in:
Total energy available = mass × energy per kilogram = 2.0 × 1030 kg × 108 joules/kg = 2.0 × 1038 joules.
If the Sun's luminosity is 3.8 × 1026 watts and 1 watt is equivalent to 1 joule per second, the time in seconds for the Sun to deplete this energy at its current luminosity is:
Lifetime in seconds = Total energy / Luminosity = 2.0 × 1038 joules / 3.8 × 1026 watts = 5.26 × 1011 seconds.
Since there are roughly 32 million seconds in a year, the lifetime of the Sun, if it were burning chemically, can be estimated as:
Lifetime in years = Lifetime in seconds / seconds per year = 5.26 × 1011 seconds / 3.2 × 107 seconds/year = approximately 16,438 years.
This is a very short lifetime compared to the Sun's actual age of approximately 4.6 billion years, indicating the real Sun is sustained by nuclear reactions and not chemical combustion.
In the absence of an electric field, a radioactive beam strikes a fluorescent screen at a single point. When an electric field is applied, the radioactive beam is separated into three different components. One of the components is deflected toward the positive electrode because it is negatively charged, one of the components is deflected toward the negative electrode because it is positively charged, and one component is not deflected in any direction; instead, it moves along a straight path. Identify the charges possessed by the different components of the radioactive beam by observing their behavior under the influence of an electric field.
Answer: Beta, alpha and gamma ray
Explanation: The component being deflected to the positive side is the beta radiation because it is negatively charged and thus is attracted by the positive terminal of the Electric Field.
The component being deflected to the negative side is the alpha radiation, it's is positively charged and thus being attracted by the negative part of the Electric Field.
The component that went straight down without deflection is the gamma radiation. It is neutral and possess no charge and thus is not deflected.
Answer:
Beta rays (symbol β) are negatively charged because they are electrons.
Alpha rays (symbol α) are positively charged because they are helium nuclei.
Gamma rays (symbol γ or. ) are neutral, since they are photons only. Comprises of the shortest electromagnetic wavelength and thus provides the highest photon energy.
A man stands on a scale and holds a heavy object in his hands. What happens to the scale reading if the man quickly lifts the object upward and then stops lifting it?
Answer:
Explanation:
When he accelerates the heavy object up , the reading increases because an extra downward normal force acts on it, then scale reading returns to the same reading as when standing stationary, and then decreases as although he is lifting the heavy object , the acceleration is decreasing ,so the extra upward normal force acts.
Awning windows can be 100% openable and are best used where extreme weather conditions require a tight seal when the window is closed, although these windows are in common use everywhere.1. True2. False
Answer: True
Explanation: Awning windows
are Weather-tight, good choice in damp climates and can protect your home against moisture, even when they’re open during a rainstorm. Because of the way awning windows are constructed, they allow for nearly 100 percent of viable ventilation, without the threat of water seeping into the home. They also offer a superior seal against air pass through
These windows form a slant (of about 45 degree) after opening hence do not open 100%; this slant opening is advantageous in preventing rain from entering the building.
The windows can also be tightly sealed (from the inside) during extreme/cold weather conditions.
True, awning windows can be fully opened and are beneficial for creating a tight seal in extreme weather conditions. They also allow for maximum ventilation while preventing unwanted energy transfer, making them widely used regardless of climate. Design elements like overhangs and window orientation further enhance energy efficiency.
True, awning windows can be 100% openable and are indeed best used in areas that experience extreme weather conditions, thanks to their capability to form a tight seal when closed. The design of these windows allows them to prevent unwanted energy transfers by keeping the harsh weather out when they are closed, while still allowing for maximum ventilation when opened. This makes them highly versatile and thus they are in common use in various locations, not just those with extreme weather. Factors such as the orientation of the windows, the use of overhangs, and the placement of deciduous trees also play important roles in maximizing energy efficiency by modulating the amount of sunlight and heat entering a building.
For instance, overhangs above south-facing windows help keep a house cool in summer by casting a shadow over the window when the sun is high, and allowing sunlight to warm the rooms in winter when the sun stays closer to the horizon. Moreover, in climates where preventing heat gain is crucial, the largest windows may face north to avoid the sun, with south-facing windows being smaller and well insulated to allow for cross-ventilation without admitting much sunlight. Additionally, windows equipped with weatherstripping, and double-paned, low-emissivity glass can significantly reduce energy losses, contributing to a building's overall energy efficiency.
A 48.0-turn circular coil of radius 5.50 cm can be oriented in any direction in a uniform magnetic field having a magnitude of 0.480 T. If the coil carries a current of 23.3 mA, find the magnitude of the maximum possible torque exerted on the coil.
Answer:
Explanation:
Given that,
Number of turn is 48
N=48
Radius is 4.8cm
r=0.048m
Magnetic Field
B=0.48T
Current in coil
i=23.3mA
i=0.233A
Maximum Torque?
Maximum torque occur at angle 90°
Torque is given as
τ = N•I•A•B•sinθ
Where N is number of turn =48
I is current in coil =0.233A
A is area of circular coil form
Area of a circle is given as
A=πr²
A=π×0.048²
A=0.007238m²
B is magnetic field =0.48T
Maximum torque occurs at 90°
τ = N•I•A•B•sinθ
τ=48×0.233×0.007238×0.48×Sin90
τ = 0.0389Nm
This torque is large enough to exert the coil
Given Information:
Magnetic field = B = 0.480 T
Current = I = 23.3 mA = 0.0233 A
Number of turns = N = 48 turns
Radius = r = 5.50 cm = 0.055 m
Required Information:
Maximum possible torque = τ = ?
Answer:
Maximum possible torque = 0.0051 N.m
Explanation:
We know that toque τ is given by
τ = NIABsin(θ)
Where N is the number of turns of the circular coil, I is the current flowing through the circular coil, A is the area of circular coil, B is the magnetic field induced in the circular coil.
The area of the circular coil is
A = πr²
A = π(0.055)²
A = 0.009503 m²
The maximum torque is possible when θ = 90°
τ = 48*0.0233*0.009503*0.480*sin(90°)
τ = 0.0051 N.m
Consider the following tasks: A. Draw a closed curve around the system. B. Identify "the system" and "the environment." C. Draw a picture of the situation. Which of these are steps used to identify the forces acting on an object? 1. A only 2. B only 3. C only 4. A, B, and C 5. None of them
Answer:
Explanation:
To identify forces acting on an object
1. Draw a closed curve around the system.
2.Identify "the system" and "the environment."
3. Draw a picture of the situation. Which of these are steps used to identify the forces acting on an object?
All of these are correct.
A close loop doesn't allow external forces to act on the system and this only allows the the forces on the object to act alone.
Drawing the free body diagram will show the forces acting on the body.
Also, isolating the system from the environment so that it won't be affected by external forces or resistance
Sphere 1 with radius R_1 has positive charge q, Sphere 2 with radius 4.50 R_1 is far from sphere 1 and initially uncharged. The separated spheres are then connected with a wire then uncouth to retain only negligible charge. (a) What is the ratio V_1/V_2 of the final potentials of the spheres? (b) what fraction of q ends up on sphere? (c) What fraction of q ends up on sphere 2? (d) What is the ratio q_1/q_2 of the surface charge densities of the spheres?
Answer:
Explanation:
capacitance of sphere 2 will be 4.5 times sphere 1
a ) when spheres are in contact they will have same potential finally . So
V_1 / V_2 = 1
b )
Charge will be distributed in the ratio of their capacity
charge on sphere1 = q x 1 / ( 1 + 4.5 )
= q / 5.5
fraction = 1 / 5.5
c ) charge on sphere 2
= q x 4.5 / 5.5
fraction = 4.5 / 5.5
d ) surface charge density of sphere 1
= q /( 5.5 x A ) where A is surface area
surface charge density of sphere 2
= q x 4.5 /( 5.5 x 4.5² A ) where A is surface area
= q /( 5.5 x 4.5 A )
q_1/q_2 = 4.5
Determine the number of revolutions through which a typical automobile tire turns in 1 yr. Suppose the automobile travels 13500 miles each year on tires with radius 0.220 m.
Answer:
Number of revolution made by tire is 1.57 x 10⁷
Explanation:
Radius of tire, r = 0.220 m
Circumference of tire, C = 2πr
Substitute the value of r in the above equation.
C = 2 x π x 0.220 m = 1.38 m
Total distance covered by tire in a year, D = 13500 miles
But 1 mile = 1609.34 m
So, D = 13500 x 1609.34 m
Number of revolutions take by tire, N = [tex]\frac{D}{C}[/tex]
[tex]N=\frac{13500\times1609.34}{1.38}[/tex]
N = 15743543
9. Over a certain region of space, the electric potential is V = . (a) Find the expressions for the x, y, and z components of the electric field over this region. (b) What is the magnitude of the field at the point P that has coordinates (1.00, 0, 22.00) m?
Answer:
a)
The expression for the electric potential in this problem is:
[tex]V=5x-3x^2y+2yz[/tex]
where
x, y, z are the three spatial coordinates
The relationship between components of the electric field and electric potential is:
[tex]E_x=-\frac{dV}{dx}\\E_y=-\frac{dV}{dy}\\E_z=-\frac{dV}{dz}[/tex]
Therefore, we have to calculate the derivatives of the potential over the three variables.
Doing so, we find:
[tex]E_x=-\frac{d}{dx}(5x-3x^2y+2yz)=-(5-6xy)=6xy-5[/tex]
[tex]E_y=-\frac{d}{dy}(5x-3x^2y+2yz)=-(-3x^2+2z)=3x^2-2z[/tex]
[tex]E_z=-\frac{d}{dz}(5x-3x^2y+2yz)=-(2y)=-2y[/tex]
b)
Here we want to find the magnitude of the electric field at the point P that has coordinates
P (1.00, 0, 22.00) m
First of all, we find the components of the electric field at that point by substituting
x = 1.00
y = 0
z = 22.0
We find:
[tex]E_x=6xy-5=6(1)(0)-5=-5 N/C\\E_y=3x^2-2z=3(1)^2-2(22)=-41 N/C\\E_z=-2y=-2(0)=0[/tex]
Now, the magnitude of the electric field is given by
[tex]E=\sqrt{E_x^2+E_y^2+E_z^2}[/tex]
And by substituting,
[tex]E=\sqrt{(-5)^2+(-41)^2+0}=41.3 N/C[/tex]
Two masses exert a force of 1,161 N on each other when they are 20 km apart. How much force will these two masses exert on each other when they are 40 km apart?
Explanation:
Below is an attachment containing the solution.
(Atwood’s Machine): Two masses, 9 kg and 12 kg, are attached by a lightweight cord and suspended over a frictionless pulley. When released, find the acceleration of the system and the tension in the cord.
Answer:
Acceleration = 1.428m/s2
Tension = 102.85N
Explanation:
The detailed solution is attached
Answer:
The acceleration of the system is 1.401 m/s² and
The tension in the cord is 100.902 N
Explanation:
Let the 9 kg mass be m
Let the 12 kg mass be M
By Newton's second law of motion we have
For the 9 kg mass, T - mg = ma and for the 12 kg mass we have T - Mg = -Ma
Here we took the upward acceleration as positive a of the 9 kg mass and the downward acceleration of the 12 kg mass as -a
Solving for T for the 9 kg mass we have
T = mg + ma
Substituting the value of T in to the 12 kg mass equation, we have
mg + ma - Mg = -Ma or a = [tex](\frac{M-m}{M+m} )g[/tex] therefore the acceleration is
1.401 m/s²
and the tension is T = mg + ma = 9×(9.81+1.401) = 100.902 N
A box contains 9 new light bulbs and 6 used light bulbs. Each light bulb is the same size and shape. Meredith will randomly select 2 light bulbs from the box without replacement. What is the probability Meredith will select a new light bulb and then a used light bulb
Answer:
(9/35) = 0.257
Explanation:
Box contains 9 new light bulbs and 6 used light bulbs, total number of bulbs = 15.
Probability of selecting two bulbs; a new light bulb and then, a used light bulb in that order = [(probability of selecting a new bulb) × (probability of selecting a used bulb from the rest)] = [(9/15) × (6/14)] = (9/35) = 0.257
The probability that Meredith will select a new bulb and then a used bulb in sequential order without replacement is around 26%.
Explanation:The question asks about the probability of selecting a new light bulb and then a used light bulb from a box containing 9 new light bulbs and 6 used light bulbs. Probability events like these are solved using multiplication rules of probability that each event is independent.
First, the probability of picking a new bulb is 9/15 (total bulbs are 15). If you pick one out, you don't replace it, so there are only 14 bulbs left. Thus, the probability of picking a used bulb now is 6/14. Hence the probability of both events happening in order is the multiplication of both, i.e., (9/15)*(6/14) = 54/210 = 0.257 or around 26%.
Learn more about Probability here:https://brainly.com/question/32117953
#SPJ12
A woman fires a rifle with barrel length of 0.5400 m. Let (0, 0) be where the 125 g bullet begins to move, and the bullet travels in the +x-direction. The force exerted by the expanding gas on the bullet is (16,000 + 10,000x − 26,000x2) N, where x is in meters. A) Determine the work done by the gas on the bullet as the bullet travels the length of the barrel.
B) If the barrel is 1.05 m long, how much work is done?
Answer:
Explanation:
Given that,
Length of barrel =0.54m
Mass of bullet=125g=0.125kg
Force extend
F=16,000+10,000x-26,000x²
a. Work done is given as
W= ∫Fdx
W= ∫(16,000+10,000x-26,000x² dx from x=0 to x=0.54m
W=16,000x+10,000x²/2 -26,000x³/3 from x=0 to x=0.54m
W=16,000x+5,000x²- 8666.667x³ from x=0 to x=0.54m
W= 16,000(0.54) + 5000(0.54²) - 8666.667(0.54³) +0+0-0
W=8640+1458-1364.69
W=8733.31J
The workdone by the gas on the bullet is 8733.31J
b. Work done is given as
Work done when the length=1.05m
W= ∫Fdx
W= ∫(16,000+10,000x-26,000x² dx from x=0 to x=1.05m
W=16,000x+10,000x²/2 -26,000x³/3 from x=0 to x=1.05m
W=16,000x+5,000x²- 8666.667x³ from x=0 to x=1.05mm
W= 16,000(1.05) + 5000(1.05²) - 8666.667(1.05³) +0+0-0
W=16800+5512.5-10032.75
W=12,279.75J
The workdone by the gas on the bullet is 12,279.75J
Chromatic aberration in lenses is a result of which wave property of light?
Answer:
Dispersion
Explanation:
Chromatic aberration refers to the failure of a lenses to focus all the wavelengths or colours in white light at the same point. This is due to dispersion of light in glass. The refractive index of the lenses elements varies with different wavelengths of light. The different colours of white light will travel at different speeds through the lens hence they cannot all be focused at the same point. Dispersion results from the refraction of the various wavelengths of light to varying degrees.
Chromatic aberration in lenses is a result of the property of light, wavelength. It leads to dispersion of different colors of light due to the dependence of lens's refractive index on color or wavelength, causing different colors to have different focal points. This can be partially corrected in optical systems using multiple lenses of different materials.
Explanation:Chromatic aberration in lenses is caused by the property of light known as wavelength. This concept is related to the wave nature of light, where the wavelength is the distance between successive peaks or troughs of a light wave. Chromatic aberration occurs because the index of refraction in a lens is dependent on the light's wavelength, which is related to its color. Because the index of refraction varies with wavelength, different colors (wavelengths) of light are bent by different amounts when they pass through a lens and hence have different focal points.
For example, in a single convex lens, violet light, which has a shorter wavelength, is bent more than red light, which has a longer wavelength. Therefore, violet light converges to a focal point closer to the lens compared to red light, which results in the dispersion of colors, as depicted in Figure 26.28. However, this chromatic aberration can be partially corrected by employing a two-lens system, often consisting of a converging and a diverging lens made of different materials with different dispersions, referred to as an achromatic doublet. However, completely rectifying chromatic aberration is typically not possible, which is why systems such as telescopes often prefer mirrors as they do not depend on wavelength for reflection.
Learn more about Chromatic Aberration here:https://brainly.com/question/32631338
#SPJ11
1) Calculate the torque required to accelerate the Earth in 5 days from rest to its present angular speed about its axis. 2) Calculate the energy required. 3) Calculate the average power required.
Final answer:
To find the torque to accelerate Earth in 5 days to its angular speed, calculate the moment of inertia and use τ = Iα. The energy required is given by E_k = (1/2)Iω^2, and average power is P = E_k / t.
Explanation:
To calculate the torque required to accelerate the Earth from rest to its present angular speed about its axis in 5 days, we first need to determine the Earth's moment of inertia (I) and its angular acceleration (α). The Earth's moment of inertia can be estimated using the formula I = (2/5)MR^2, where M is the mass of the Earth and R is its radius. The angular speed (ω) is 2π rad/day since there are 2π radians in a full rotation and the Earth completes one rotation per day. The angular acceleration, α, is then ω divided by the time in seconds to accelerate, which is 5 days or 5 x 24 x 3600 seconds. The formula τ = Iα is used to calculate torque.
To find the energy required, we can use the rotational kinetic energy formula E_k = (1/2)Iω^2, where ω is the final angular velocity. Subsequently, the average power required is the energy divided by the time over which it is expended, P = E_k / t, where t is the time in seconds.
A block in the shape of a rectangular solid has a crosssectional area of 3.50 cm2 across its width, a front-to-rear length of 15.8 cm, and a resistance of 935 0. The block’s material contains 5.33 $ 1022 conduction electrons/m3. A potential difference of 35.8 V is maintained between its front and rear faces. (a) What is the current in the block? (b) If the current density is uniform, what is its magnitude? What are (c) the drift velocity of the conduction electrons and (d) the magnitude of the electric field in the block?
Answer:
a) 38.3mA
b) 109.396A/m^2
c) 1.283cm/s
d) 226.582V/m
Explanation:
The equation for current is given by:
I = V/R = 35.6/ 935 = 0.03829 A Approximately 38.3mA
b) The equation to find the magnitude is given by:
J = I/A = 0.03829/ 0.000350m^2
J = 109.396A/m^2
c) The equation to calculate drift velocity of the electron is given by: Vd = J/ ne = 109.396/( 5.33×10^23 )(1.60×10^-19)
Vd = 0.01283 approximately 1.283cm/s
d) The magnitude of electric field in the block, E = V/L = 35.8/ 0.158m = 226.582V/m
The velocity of the transverse waves produced by an earthquake is 8.9 km/s, and that of the longitudinal waves is 5.1 km/s. A seismograph records the arrival of the transverse waves 68 s before the arrival of the longitudinal waves. How far away is the earthquake?
Answer: The distance is 723.4km
Explanation:
The velocity of the transverse waves is 8.9km/s
The velocity of the longitudinal wave is 5.1 km/s
The transverse one reaches 68 seconds before the longitudinal.
if the distance is X, we know that:
X/(9.8km/s) = T1
X/(5.1km/s) = T2
T2 = T1 + 68s
Where T1 and T2 are the time that each wave needs to reach the sesmograph.
We replace the third equation into the second and get:
X/(9.8km/s) = T1
X/(5.1km/s) = T1 + 68s
Now, we can replace T1 from the first equation into the second one:
X/(5.1km/s) = X/(9.8km/s) + 68s
Now we can solve it for X and find the distance.
X/(5.1km/s) - X/(9.8km/s) = 68s
X(1/(5.1km/s) - 1/(9.8km/s)) = X*0.094s/km= 68s
X = 68s/0.094s/km = 723.4 km
The speed of a moving sidewalk at an airport is 7 ft/sec. A person can walk 74 ft forward on the moving sidewalk in the same time it takes to walk 15 ft on a non moving sidewalk in the opposite direction. At what rate would a person walk on a non moving sidewalk
Answer:
10.56 ft/s.
Explanation:
given,
Speed of side walk = 7 ft/s
time taken to travel 74 ft on the moving sidewalk = time taken to walk 15 ft on non moving side walk.
We know,
[tex]time = \dfrac{distance}{speed}[/tex]
[tex]\dfrac{74}{w+7}=\dfrac{15}{w-7}[/tex]
[tex]59 w = 7\times 74 + 15\times 7[/tex]
[tex] 59 w = 623[/tex]
[tex]w = 10.56\ ft/s[/tex]
Rate at which person walk on non moving side walk is equal to 10.56 ft/s.
The person's walking speed on a non-moving sidewalk is approximately 1.78 ft/sec, determined by setting up and solving the equation based on equal times on the moving and non-moving sidewalks.
To find the rate at which a person would walk on a non-moving sidewalk, we need to set up an equation based on the given information.
We know the speed of the moving sidewalk is 7 ft/sec. Let's denote the walking speed of the person (on a non-moving sidewalk) as v ft/sec.
From the problem, the time taken by the person to walk 74 ft on the moving sidewalk should be equal to the time taken to walk 15 ft on a non-moving sidewalk in the opposite direction:
Time on the moving sidewalk:[tex]\frac{74}{7 + v} = \frac{15}{v}[/tex]
To solve for v, cross-multiply to get: 74v = 15(v+7)
74v = 15v + 105
74v − 15v = 105
59v = 105
[tex]v = \frac{105}{59}[/tex]
v ≈ 1.78 ft/sec
Therefore, the person's walking speed on a non-moving sidewalk is approximately 1.78 ft/sec.
You have a fixed length of wire and need to design a generator that will produce the greatest peak emf for a given frequency and magnetic field strength. You should use (a) a one-turn square coil, (b) a two-turn square coil, (c) either a one- or a two-turn square coil because both give the same peak emf for a given frequency and magnetic field strength.
Final answer:
The peak emf from a generator can be maximized by increasing the number of turns, increasing the area of the wired loop, and increasing the frequency. Both the one-turn and two-turn square coils can produce the same peak emf for a given frequency and magnetic field strength.
Explanation:
The peak emf from a generator can be maximized by maximizing the number of turns, maximizing the area of the wired loop, or maximizing the frequency. The one-turn and two-turn square coils are both options that can be used, as they both give the same peak emf for a given frequency and magnetic field strength. However, the other factors, such as the number of turns and area of the loop, may differ between the two options and can affect the overall performance of the generator.