Answer:
[tex]5.8\cdot 10^{-5}T[/tex]
Explanation:
The magnetic field produced by a current-carrying wire is:
[tex]B=\frac{\mu_0 I}{2\pi r}[/tex]
where
[tex]\mu_0=4\pi \cdot 10^{-7} H/m[/tex] is the vacuum permeability
I is the current in the wire
r is the distance from the wire
The direction of the field is given by the right-hand rule: the thum is placed in the same direction of the current, and the other fingers "wrapped" around the thumb gives the direction of the field.
First of all, here we are finding the magnetic field strength at a point 12.0cm from one wire and 13.6cm from the other: since the two wires are 6.50 cm apart, this means that the point at which we are calculating the field is located either on the left or on the right of both wires. So, by using the right-hand rule for both, we see that both fields go into the same direction (because the currents in the two wires have same direction).
Therefore, the net magnetic field will be the sum of the two magnetic fields.
For wire 1, we have:
[tex]I_1=18.5 A\\r_1=12.0 cm =0.12 m[/tex]
So the field is
[tex]B_1=\frac{(4\pi \cdot 10^{-7})(18.5)}{2\pi(0.12)}=3.1\cdot 10^{-5} T[/tex]
For wire 2, we have:
[tex]I_2=18.5 A\\r_2=13.6 cm=0.136 m[/tex]
So the field is
[tex]B_2=\frac{(4\pi \cdot 10^{-7})(18.5)}{2\pi(0.136)}=2.7\cdot 10^{-5} T[/tex]
Therefore, the total magnetic field is
[tex]B=B_1+B_2=3.1\cdot 10^{-5}+2.7\cdot 10^{-5}=5.8\cdot 10^{-5}T[/tex]
The flywheel of a steam engine begins to rotate from rest with a constant angular acceleration of 1.35 rad/s2. It accelerates for 28.3 s, then maintains a constant angular velocity. Calculate the total angle through which the wheel has turned 58.9 s after it begins rotating.
Answer:
Total angle through which the wheel has turned 58.9s after it begins rotating is 1709.52 rad
Explanation:
The image attached would offer a better explanation
Answer:
The answer to the question is;
The total angle through which the wheel has turned 58.9 s after it begins rotating is approximately 1709.67 rad.
Explanation:
To solve the question we note the equation for the motion of the flywheel as
ω₂ = ω₁ + α·t
Where:
ω₁ = Initial angular velocity = 0 rad/s as the body is initially at rest
ω₂ = Final angular velocity
α = angular acceleration = 1.35 rad/s²
t = Time = 28.3 s
Plugging in the values, we find ω₂
ω₂ = 0 + 1.35 rad/s²× 28.3 s = 38.205 rad/s
Since the acceleration is constant, only the mean velocity is required to determine the angle traveled during the first 28.3 seconds thus
Average velocity
ω[tex]_{average}[/tex]= [tex]\frac{Final .Velocity +Initial . Velocity}{2} = \frac{\omega_2+\omega_1}{2} = \frac{38.205 rad/s+0 rad/s}{2}[/tex]
= 19.1025 rad/s
The total angle traveled in 28.3 s is ω[tex]_{average}[/tex] × time
= 19.1025 rad/s × 28.3 s = 540.60075 rad
After this the remaining time left is
58.9 s - 28.3 s = 30.6 s
Since the flywheel is moving at a constant velocity of 38.205 rad/s during the last 30.6 s we have
Angle traveled in 30.6 s at an angular velocity of 38.205 rad/s is given by
Angle traveled = Time × Angular velocity = 30.6 s × 38.205 rad/s
= 1169.073 rad
Therefore, the total angle traveled by the flywheel in 58.9 s is given by
540.60075 rad + 1169.073 rad = 1709.67375 rad ≈1709.67 rad.
the total angle traveled by the flywheel in 58.9 s ≈ 1709.67 rad.
When two tuning forks are stuck simultaneously, 6 beats per second are heard. The frequency of one fork is 560 Hz. A piece of wax is placed on the 560 Hz fork to lower its frequency slightly. If the beat frequency is increased, what is the correct frequency for the second fork
Answer:
The correct frequenvy of the second fork is; ν2 = 566Hz
Explanation:
First of all, when two wave sources with slightly differing frequencies ν1 and ν2 generate waves at the same time and are superposed, then an interference effect will occur in time.
The intensity will be found to oscillate with time with a frequency (ν) called the beat frequency. It is depicted by:
ν = ± (ν1 −ν2).
In this question, there are two tuning forks, one with a frequency of let's say ν1=560Hz
The beat frequency is ν=6Hz
Therefore,
ν2=560 - 6 or ν2=560 + 6
i.e ν2=554 or ν2=566
For us to know the correct frequency, if the 560 Hz fork is loaded with wax, the increased inertia will lower its frequency.
Then it is found that the beat frequency increases. This can only mean that the other fork has a higher frequency. Hence the unkown frequency of the second fork must be,
ν2 = 566Hz
A 9-year-old has just fallen off the monkey bars. She has obvious deformity to her mid forearm. How should the radiographer care for her when taking x-rays?
Answer:
He will need to support the joint above and below the deformity, this will allow the xray to be taken without generating more damage to the child.
I hope you find this information useful and interesting! Good luck!
A uniform rod rotates in a horizontal plane about a vertical axis through one end. The rod is 3.46 m long, weighs 12.8 N, and rotates at 226 rev/min. Calculate (a) its rotational inertia about the axis of rotation and (b) the magnitude of its angular momentum about that axis.
Answer:
a. Rotational inertia: 5.21kgm²
b. Magnitude of it's angular momentum: 123.32kgm²/s
Explanation:
Length of the rod = 3.46m
Weight of the rod = 12.8 N
Angular velocity of the rod= 226 rev/min
a. Rotational Inertia (I) about its axis
The formula for rotational inertia =
I = (1/12×m×L²) + m × ( L ÷ 2)²
Where L = length of the rod
m = mass of the rod
Mass of the rod is calculated by dividing the weight of the rod with the acceleration due to gravity.
Acceleration due to gravity = 9.81m/s²
Mass of the rod = 12.8N/ 9.81m/s²
Mass of the rod = 1.305kg
Rotational Inertia =
(1/12× 1.305 × 3.46²)+ 1.305 ( 3.46÷2)²
Rotational Inertia = 1.3019115 + 3.9057345
Rotational Inertia = 5.207646kgm²
Approximately = 5.21kgm²
b. The magnitude of the rod's angular momentum about the rotational axis is calculated as
Rotational Inertia about its axis × angular speed of the rod.
Angular speed of the rod is calculated as= (Angular velocity of the rod × 2π)/60
= (226×2π) /60
= 23.67 rad/s
Rotational Inertia = 5.21kgm²
The magnitude of the rod's angular momentum about the rotational axis
= 5.21kgm²× 23.67 rad/s
= 123.3207kgm²/s
Approximately = 123.32kgm²/s
For a body falling freely from rest (disregarding air resistance), the distance the body falls varies directly as the square of the time. If an object is dropped from the top of a tower 490 ft high and hits the ground in 7 sec, how far did it fall in the first 5 sec?
Explanation:
Below is an attachment containing the solution.
The distance covered by a freely falling object in a certain time is calculated by the formula d = 1/2 * g * t^2 where d is the distance, g is acceleration due to gravity and t is time. When plugging in the values g = 32 ft/sec^2 and t = 5 sec, we find that the object would have fallen 400 ft in the first 5 seconds.
Explanation:In physics, the distance that a free-falling object covers is given by the formula d = 1/2 * g * t^2, where g is the acceleration due to gravity. In typical physics problems, g is approximated as 32 feet/second^2 on Earth. If we plug t = 5 sec into the equation, we get:
d = 1/2 * 32 ft/sec^2 * (5 sec)^2 = 400 ft.
Therefore, the object would have fallen 400 ft in the first 5 seconds of free fall.
Learn more about Free Fall here:https://brainly.com/question/35159043
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The energy expenditure value of traveling by car is 3.6 mj/passenger-kilometer. The value for traveling by train is 1.1 mj/passenger-kilometer. What would be the best way to increase the efficiency of traveling by car?
Answer:
Using lighter material in car construction, improving energy efficiency by enhancing engine design or replacing the engine with more efficient technologies.
Explanation:
Using lighter materials in the car construction, reducing the potential energy required to accelerate and to move the car, as well as energy losses due to rolling friction. There is evidence of such benefits by replacing steel and aluminium parts with components made of composite materials.
Improving the design of internal combustion engines to minimize energy losses and accordingly, improving energy efficiency. A more radical approach is replacing internal combustion engines with electric engines, which offer higher efficiencies. Such conclusions can be easily inferred from model based on Work-Energy Theorem and Principle of Energy Conservation:
[tex]\eta_{engine} \cdot U_{engine} = \frac{1}{2} \cdot m_{car} \cdot v^{2} + \mu_{r} \cdot m_{car} \cdot g \cdot \Delta s[/tex]
6. Two blocks are released from rest at the same height. Block A slides down a steeper ramp than Block B. Both ramps are frictionless. The blocks reach the same final height indicated by the lower dashed line. Block B weighs more than Block A.
a. Is the work done by the gravitational force on Block A (greater/less than/equal to) the work done by the gravitational force on Block B? Explain your reasoning.
b. Is the speed of Block A (greater/less than/equal to) the speed of Block B? Explain your reasoning.
c. Is the momentum of Block A (greater/less than/equal to) the momentum of Block B? Explain your reasoning.
Answer:
a. the work done by the gravitational force on Block A is less than the work done by the gravitational force on Block B.
b. the speed of Block A is equal to the speed of Block B.
c. the momentum of Block A is less than the momentum of Block B.
Explanation:
a. The work done by the gravitational force is equal to:
w = m*g*h
where m is mass, g is the standard gravitational acceleration and h is height. Given that both blocks are released from rest at the same height, then, the bigger the mass, the bigger the work done.
b. With ramps frictionless, the final speed of the blocs is:
v = √(2*g*h)
which is independent of the mass of the blocks.
c. The momentum is calculated as follows:
momentum = m*v
Given that both bocks has the same speed, then, the bigger the mass, the bigger the momentum.
The work done by gravitational force on blocks A and B is equal as the work is independent of the path. Both blocks have the same speed when they reach the final height due to the conversion of potential energy into kinetic energy. However, the momentum of Block B is greater due to its larger mass.
Explanation:This question is about the principles of work, energy and momentum in physics. Let's address each part of it:
Work done by gravitational force: The work done by the gravitational force on both blocks A and B is equal. This is because work done by gravity depends only on the change in height, which is the same for both blocks, and the weight of the block. So, even though Block B is heavier as it weighs more than Block A, the work done is the same because the force of gravity has to move the blocks the same vertical distance.Speed of the blocks: The speed of both blocks A and B will be equal when they reach the final height. This is because, in the absence of friction and air resistance, the blocks will convert all of their gravitational potential energy at the start into kinetic energy at the end, irrespective of their weights or the steepness of the ramps.Momentum of the blocks: The momentum of Block B is greater than Block A. This is because momentum depends on both the mass and the velocity of an object. Even though both blocks have the same speed at the bottom, Block B is heavier, therefore, it will have more momentum.Learn more about Physics principles here:https://brainly.com/question/15872863
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Ball bearings can be made by letting spherical drops of molten metal fall inside a tall tower - called a shot tower - and solidify as they fall. If a bearing needs 4.0 s to solidify enough for impact, how high must the tower be?
Answer:
height of tower= 78.48 meters
Explanation:
So here are your givens:
time(t)= 4 s.
initial velocity(u) = 0 m/s
acceleration due to gravity (g)= 9.81 m/s^2
distance(s)=s meters
using one of Newton's equation of motion ;
[tex]s=ut+\frac{1}{2} gt^{2} \\s=0(4)+\frac{1}{2}(9.81)(4)^{2} \\s=\frac{1}{2} (9.81)(16)\\s=\frac{156.96}{2} \\s=78.48[/tex]
height of the tower from the ground=total distance covered by bearing
height of tower= 78.48 meters
Final answer:
The shot tower needs to be at least 78.4 meters tall for a ball bearing to solidify in 4.0 seconds given the acceleration due to gravity.
Explanation:
Calculating the Height of the Shot Tower
To determine how high the tower must be for a ball bearing to solidify in 4.0 seconds, we can use the kinematic equation for free-fall motion without initial velocity, which is h = 1/2gt², where h is the height, g is the acceleration due to gravity (9.8 m/s² on Earth), and t is the time in seconds. For t = 4.0 seconds, we get:
h = 1/2 * 9.8 m/s² * (4.0 s)²
h = 1/2 * 9.8 * 16
h = 4.9 * 16
h = 78.4 meters
Therefore, the shot tower must be at least 78.4 meters tall to allow a ball bearing to solidify in mid-air within 4.0 seconds before impact.
The quantity of heat Q that changes the temperature L1Tof a mass mof a substance isgiven by Q = cmt:T, where c is the specific heat capacity of the substance. Forexample,forH20,c=1caljg'C",Andfora change of phase, the quantity of heat Q that changes the phase of a mass m is Q = ml., where L is the heat of fusion or heat of vaporization of the substance. For example, for H20, the heat offusion is 80 cal/g (or 80 kcaljkg) and the heat of vaporization is 540 cal/g (or 540 kcaljkg). Use these relationships to determine the number of calories to change (a) 1 kg ofO°C ice to O°C ice water, (b) 1 kg ofO°C ice water to 1 kg of 100°C boiling water, (c) 1 kg of 100°C boiling water to 1 kg of 100°C steam, and (d) 1 kg ofO°C ice to 1 kg of 100°C steam.
Answer:
a) Q = 80,000 cal
b) Q = 100,000 cal
c) Q = 540,000 cal
d) Q = 720,000 cal
Explanation:
a)1 kg from 0⁰ Ice to 0⁰ water, the heat produced is latent heat of fusion
[tex]Q_{l} = ML_{f}[/tex] = 1 * 80
[tex]Q_{l}[/tex] = 80 kCal = 80,000 cal
b) 1 kg of O°C ice water to 1 kg of 100°C boiling water
Specific heat capacity, c = 1000cal/kg.C
[tex]Q_{c} = mc \delta T\\Q_{c} = 1 * 1000 * (100 - 0)\\Q_{c} =100000 cal[/tex]
c) 1 kg of 100°C boiling water to 1 kg of 100°C steam
Latent heat of vaporization is needed for this conversion
[tex]Q_{v} = ML_{v} \\L_{v} = 540 kCal/kg\\Q_{v} =1* 540 \\Q_{v} = 540 kCal = 540000 cal[/tex]
d) 1 kg of O°C ice to 1 kg of 100°C steam.
Q = [tex]Q_{L} + Q_{c} + Q_{v}[/tex]
Q = 80,000 + 100,000 + 540,000
Q = 720,000 cal
Final answer:
To change 1 kg of ice at 0°C to water at 0°C, 80 kcal of energy is required. To change 1 kg of water at 0°C to boiling water at 100°C, 100 cal of energy is required. To change 1 kg of boiling water at 100°C to steam, 540 kcal of energy is required.
Explanation:
The quantity of heat required to change the phase of a substance is given by the equation Q = mL, where m is the mass of the substance and L is the heat of fusion or heat of vaporization. For example, to change 1 kg of ice at 0°C to water at 0°C, the energy required is Q = (1 kg)(80 kcal/kg) = 80 kcal. To change 1 kg of water at 0°C to boiling water at 100°C, the energy required is Q = (1 kg)(1 cal/g °C)(100°C) = 100 cal. To change 1 kg of boiling water at 100°C to steam, the energy required is Q = (1 kg)(540 kcal/kg) = 540 kcal.
What is the minimum diameter mirror on a telescope that would allow you to see details as small as 5.20 km on the moon some 384000 km away? Assume an average wavelength of 550 nm for the light received.
cm
Answer:
= 4.96cm
Explanation:
distance between objects of moon = 5.20km = 5.2 × 10³ m
Wavelength of light, λ = 550nm = 5.50 × 10⁻⁷m
distance of moon, L = 384000 km = 3.84 × 10⁸m
formula for resolving power of two objects
d = (1.22 × λ ×L) / D
D = (1.22 × λ ×L) / d
D = (1.22 × 5.50 × 10⁻⁷ ×3.84 × 10⁸) / 5.2 × 10³
D = 4.96cm
A(n) ? is a premises wiring system whose power is derived from a source of electric energy or equipment other than a service. Such systems have no direct connection from circuit conductors of one system to circuit conductors of another system, other than those established through bonding or grounding connections.
Answer: Separately derived system
Explanation: A separately derived system is used to describe a premise wiring system whose power is derived from a source of electrical energy such as transformer, solar photovoltaic cell or generator. A separately derived system has no direct connection to any conductor from another system or doesn't generate it's power from any direct connection to a conductor from another system or source except those from established from bonding or grounding connections. Separately derived systems usually generate it's power on it's own.
An isolated power system is isolated from other systems, using bonding or grounding for safety, and may include an isolation transformer. Electrical safety devices like circuit breakers or fuses prevent thermal hazards, and a three-wire system enhances both thermal and shock safety.
Explanation:The student's question refers to an "isolated power system" which is a type of electrical distribution system. An isolated power system is unique because it is separated from other power systems. It has no direct connection with the circuit conductors of another system, with the exception of connections through bonding or grounding. This premise of design is intended to enhance safety, and it usually involves the use of an isolation transformer to prevent shock. Moreover, it avoids a sudden increase in the voltage that could disrupt the power supply.
Electrical safety devices, such as circuit breakers and fuses, are critical in such systems to interrupt excessive currents and prevent thermal hazards. The three-wire system, which is essential for safety in modern household and industrial wiring, utilizes live/hot, neutral, and earth/ground wires. The neutral wire and the case of any connected appliance are both grounded, which means they are connected to the earth to ensure they exist at zero volts, providing an alternative return path for the current through the earth, thereby guarding against thermal and shock hazards.
A man on the 14 th floor of a building sees a bucket (dropped by a window washer) passing his window and notes that it hits the ground 1 second later. Assuming a floor is 4.9 meters high (and neglecting air friction), from what floor was the bucket dropped?
Answer:
The bucket was the dropped from 56 th floor.
Explanation:
Given that,
Height of floor = 4.9 m
Height of 14 floor = 68.6 m
Time taken = 1 sec
We need to calculate the speed of the bucket
Using equation of motion
[tex]s=ut+\dfrac{1}{2}gt^2[/tex]
Put the value into the formula
[tex]68.6=v\times1+\dfrac{1}{2}\times9.8\times(1)^2[/tex]
[tex]v=68.6-\dfrac{1}{2}\times9.8\times(1)^2[/tex]
[tex]v=63.7\ m/s[/tex]
We need to calculate the time
Using equation of motion
[tex]v=u+gt[/tex]
[tex]t=\dfrac{v}{g}[/tex]
Put the value into the formula
[tex]t=\dfrac{63.7}{9.8}[/tex]
[tex]t=6.5\ sec[/tex]
We need to calculate the distance
Using equation of motion
[tex]s=ut+\dfrac{1}{2}gt^2[/tex]
[tex]s=0+\dfrac{1}{2}gt^2[/tex]
Put the value into the formula
[tex]s=\dfrac{1}{2}\times9.8\times(6.5)^2[/tex]
[tex]s=207.025\ m[/tex]
We need to calculate the number of floor
[tex]n=\dfrac{s}{h_{f}}[/tex]
Put the value into the formula
[tex]n=\dfrac{207.025}{4.9}[/tex]
[tex]n=42.25\approx42[/tex]
The bucket was the dropped from
[tex]f=14+42= 56[/tex]
Hence, The bucket was the dropped from 56 th floor.
If you weigh 685 NN on the earth, what would be your weight on the surface of a neutron star that has the same mass as our sun and a diameter of 25.0 kmkm ? Take the mass of the sun to be msmsm_s = 1.99×1030 kgkg , the gravitational constant to be GGG = 6.67×10−11 N⋅m2/kg2N⋅m2/kg2 , and the free-fall acceleration at the earth's surface to be ggg = 9.8 m/s2m/s2 .
Answer:
[tex] W = 5.94 \cdot 10^{15} N [/tex]
Explanation:
To calculate the weight on the surface of a neutron star we can use the following equation:
[tex] W = m*g [/tex]
Where:
W: is the weight of the person
m: is the mass of the person
g: is the gravity of the neutron star
Hence, first we need to find m and g. The mass is equal to:
[tex]m = \frac{W}{g} = \frac{685 N}{9.81 m/s^{2}} = 69.83 kg[/tex]
Now, the gravity of the neutron star can be found using the followig equation:
[tex]F = \frac{G*m*M}{r^{2}} = m*g \rightarrow g = \frac{G*M}{r^{2}}[/tex]
Where:
G: is the gravitational constant = 6.67x10⁻¹¹ m³ kg⁻¹ s⁻²
M: is the mass of the neutron star = 1.99x10³⁰ kg
r : is the distance between the person and the surface of the neutron star = 25/2 = 12.5 km
[tex] g = \frac{6.67 \cdot 10^{-11} m^{3}kg^{-1}s^{-2}*1.99 \cdot 10^{30} kg}{(12.5 \cdot 10^{3} m)^{2}} = 8.50 \cdot 10^{13} m/s^{2} [/tex]
Now, we can find the weight on the surface of the neutron star:
[tex]W = m*g = 69.83 kg * 8.50 \cdot 10^{13} m/s^{2} = 5.94 \cdot 10^{15} N[/tex]
I hope it helps you!
Your weight on a neutron star with the same mass as the Sun and a diameter of 25.0 km would be approximately 5.95 × 10¹⁴ N. This is due to the extremely high gravitational acceleration on the neutron star's surface. Such high gravity results from the star's compactness and mass.
To determine your weight on the surface of a neutron star, we need to calculate the gravitational acceleration on its surface and then use this to find the weight force.
Step-by-Step Solution:
Calculate the gravitational acceleration, gns, at the surface of the neutron star using the formula for gravitational acceleration: g = G * M / R², where:G is the gravitational constant, 6.67 × 10⁻¹¹N⋅m²/kg²M is the mass of the neutron star, which is equal to the mass of the Sun, 1.99 × 10³⁰ kgR is the radius of the neutron star, which is half of its diameter, so R = 25.0 km / 2 = 12.5 km = 1.25 × 10⁴ mSubstitute these values into the formula:gns = (6.67 × 10⁻¹¹N⋅m²/kg²) * (1.99 × 10³⁰ kg) / (1.25 × 10⁴ m)² = 8.51 × 10¹² m/s²To find your weight, use the weight formula: Weight = mass × gravitational acceleration.Your mass (m) can be found from your weight on Earth: WeightEarth = m × g, so:m = WeightEarth / g = 685 N / 9.8 m/s² = 69.9 kgNow, calculate your weight on the neutron star:Weightns = m × gns = 69.9 kg × 8.51 × 1012 m/s² ≈ 5.95 × 10¹⁴NSummary: Your weight on a neutron star with the same mass as the Sun and a diameter of 25.0 km would be approximately 5.95 × 10¹⁴N, which is significantly more than your weight on Earth.
Frequency of electromagnetic waves that a radio station is assigned
Answer:
Carrier Wave
Explanation:
A carrier wave is described or known as the continuous electromagnetic radiation, of constant amplitude and frequency, which is being given out or released by a transmitter. It is modulated in direct proportion to the signal,that is voice or music, which is meant to be transmitted or broadcasted.
It is mostly used for the transmission of information such as speech and music which can be seen in radio communication.
what will be the speed of a solid sphere of mass 2.0 kilograms and radius 15.0 centimeters when it reaches the bottom of a incline of length 5.0 meters. Assume the sphere starts from rest and rolls without slipping.
Explanation:
Below is an attachment containing the solution.
Help please!
Which setup could not be used to induce an electric current?
Spinning wire coils within an array of fixed permanent magnets
Spinning electromagnets within an array of fixed wire coils
Spinning permanent magnets within an array of fixed permanent magnets
Spinning wire coils within an array of fixed electromagnets
Answer:
Definitely Spinning permanent magnets within an array of fixed permanent magnets
Explanation:
Any relative motion between magnets (be they permanent or electromagnetic) and a coil of wire will induce an electric current in the coil.
What will not induce an electric current is the relative motion between the two coils of wire (because there is no change in magnetic field), or the relative motion between two magnets (there are no coils of wire to induce the current into).
Therefore, spinning permanent magnets within an array of fixed permanent magnets does not induce an electric current.
Answer:
Spinning permanent magnets within an array of fixed permanent magnets
Explanation:
Planetary orbits... are spaced more closely together as they get further from the Sun. are evenly spaced throughout the solar system. have the Sun at their exact center. are highly inclined to the ecliptic. are almost circular, with low eccentricities.
Answer:
E) are almost circular, with low eccentricities.
Explanation:
Kepler's laws establish that:
All the planets revolve around the Sun in an elliptic orbit, with the Sun in one of the focus (Kepler's first law).
A planet describes equal areas in equal times (Kepler's second law).
The square of the period of a planet will be proportional to the cube of the semi-major axis of its orbit (Kepler's third law).
[tex]T^{2} = a^{3}[/tex]
Where T is the period of revolution and a is the semi-major axis.
Planets orbit around the Sun in an ellipse with the Sun in one of the focus. Because of that, it is not possible to the Sun to be at the center of the orbit, as the statement on option "C" says.
However, those orbits have low eccentricities (remember that an eccentricity = 0 corresponds to a circle)
In some moments of their orbit, planets will be closer to the Sun (known as perihelion). According with Kepler's second law to complete the same area in the same time, they have to speed up at their perihelion and slow down at their aphelion (point farther from the Sun in their orbit).
Therefore, option A and B can not be true.
In the celestial sphere, the path that the Sun moves in a period of a year is called ecliptic, and planets pass very closely to that path.
Two charges A and B are fixed in place, at different distances from a certain spot. At this spot the potentials due to the two charges are equal. Charge A is 0.15 m from the spot, while charge B is 0.48 m from it. Find the ratio qB/qA of the charges.
Answer:
qa/qb = 0.3125
Explanation:
Let the distance of the point from first charge (qa) be ra.
Likewise, let the distance of the point from the second charge (qb) be ra
Now, from the question, ra=0.15m
While rb = 0.48m
Normally, we know that:
The electric potential due to a point charge, q, at a point located at a distance, r, away from it is given by the equation;
V = q/(4π(ϵo)r)
We know that 1/(4π(ϵo)) cam be said to ne K.
Therefore, V = Kq/r
Where K = 9 × 10^(9) V.m/C
Now, since from the question, the electric potential at the point is the same due to each of the charges, their electric potential will be the same, thus;
Va = Vb
So, (Kqa) / ra = (Kqb) / rb
This gives us; qa / ra = qb / rb
So rearranging, we get;
qa/qb = ra/rb = 0.15/0.48 = 0.3125
The ratio qB/qA of the charges is 3.2.
The electric potential owing to a point charge Q at a distance r from the charge is given as:
V = kQ / r
where k is the electrostatic constant.
Since the potentials due to charges A and B are equal at the given spot, we can write:
VA = VB
Substituting the values:
kQA / 0.15 = kBQB / 0.48
Simplifying:
qB/qA = 0.48 / 0.15 = 3.2
How much energy does it take to melt a 16.87 g ice cube? ΔHfus = 6.02 kJ/mol How much energy does it take to melt a 16.87 g ice cube? = 6.02 kJ/mol 108 kJ 102 kJ 5.64 kJ 936 J none of the above
Answer:
How much energy does it take to melt a 16.87 g ice cube? ΔHfus = 6.02 kJ/mol How much energy does it take to melt a 16.87 g ice cube? = 6.02 kJ/mol
A. 108 kJ
B. 102 kJ
C. 5.64 kJ
D. 936 kJ
E. none of the above
5.64 kJ
Explanation:
The Heat of fusion is the heat energy required to dissolve a given mass of ice at melting point.
Step by Step CalculationThe heat energy required to dissolve ice can be calculated using the expression below;
Q = ΔH[tex]_{f}[/tex] x m ...............................................1
where Q is the heat energy required;
ΔH[tex]_{f}[/tex] is the heat of fusion for ice;
m is the mole
All the parameters above are provided in the question except m, so to get m we use the molar mass of water (also for ice) which is 18.01528 g/mol .
This means that 18.01528 g of ice is contained in one mole, therefore the mole for 16.87 g of ice is given as;
[tex]m = \frac{16.87g}{18.015g/mol}[/tex]
m = 0.9364 mole of ices
Now the parameters are complete, we are given;
ΔH[tex]_{f}[/tex] = 6.02 kJ/mol
m = 0.9364 mol
Q =?
Substituting into equation 1, we have
Q = 6.02 kJ/mol x 0.9364 mol
Q = 5.64 kJ
Therefore, the energy required to melt 16.87 g of ice is 5.64 kJ
The energy required to melt a 16.87 g ice cube can be calculated by first converting the mass to moles and then multiplying by the enthalpy of fusion. The calculated energy is 5.64 kJ.
Explanation:The amount of energy required to melt an ice cube can be calculated using the enthalpy of fusion, which is given as 6.02 kJ/mol for ice. In order to make the conversion, we need to convert the mass of the ice cube from grams to moles. Since the molecular weight of water is approximately 18.015 g/mol, the 16.87 g ice cube amounts to 0.937 mol of ice. We then multiply this amount by the enthalpy of fusion to obtain the required energy. Thus, Energy = (0.937 mol) * (6.02 kJ/mol) = 5.64 kJ. Therefore, it would take about 5.64 kJ of energy to melt the 16.87 g ice cube.
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A 0.153 kg glider is moving to the right on a frictionless, horizontal air track with a speed of 0.700 m/s. It has a head-on collision with a 0.308 kg glider that is moving to the left with a speed of 2.16 m/s. Suppose the collision is elastic.
Answer:
3.1216 m/s.
Explanation:
Given:
M1 = 0.153 kg
v1 = 0.7 m/s
M2 = 0.308 kg
v2 = -2.16 m/s
M1v1 + M2v2 = M1V1 + M2V2
0.153 × 0.7 + 0.308 × -2.16 = 0.153 × V1 + 0.308 × V2
= 0.1071 - 0.66528 = 0.153 × V1 + 0.308 × V2
0.153V1 + 0.308V2 = -0.55818. i
For the velocities,
v1 - v2 = -(V1 - V2)
0.7 - (-2.16) = -(V1 - V2)
-(V1 - V2) = 2.86
V2 - V1 = 2.86. ii
Solving equation i and ii simultaneously,
V1 = 3.1216 m/s
V2 = 0.2616 m/s
In a particular television picture tube, the measured beam current is 23.3 µA . How many electrons strike the tube screen every 28 s ? The fundamental charge is 1.602 × 10−19 C. Answer in units of electrons.
Answer:
Explanation:
Given that
Beam current (i)=23.3µA
And the time to strike(t)=28s
Also, a fundamental charge e=1.602×10^-19C
Then, the charge quantity is given as,
q=it
Then, q=23.3×10^-6×28
q=6.524×10^-4C
Also, the number of electron N is given as
q=Ne
Therefore, N=q/e
So, N=6.524×10-4/1.602×10^-19
N=4.072×10^15
There are 4.072×10^15 electrons strike the tube screen every 28 s.
When The fundamental charge is 1.602 × 10−19 C So, There are [tex]4.072\times 10\wedge 15[/tex] electrons that strike the tube screen every 28 s.
Calculate of Units of Electrons
Given that information as per the question
Beam current (i) is =23.3µA
And also the time to strike(t)=28s
Also, a fundamental charge e=[tex]1.602\times10\wedge -19C[/tex]
Then, the charge quantity is given as,
q is =it
Then, q=[tex]23.3\times 10\wedge-6×28[/tex]
q is =[tex]6.524\times10\wedge -4C[/tex]
Also, When the number of electron N is given as
Now, q=Ne
Therefore, N is =q/e
So, N is = [tex]6.524\times10-4/1.602\times10\wedge-19[/tex]
N is = [tex]4.072\times 10\wedge 15[/tex]
Therefore, There are [tex]4.072\times 10\wedge 15[/tex] electrons that strike the tube screen every 28 s.
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You're having a hard time pushing a refrigerator across the kitchen floor. The force of your own push is 993 N. The force of friction opposing your own push is 973 N. If the refrigerator has a mass of 355 kg, what is the refrigerator's acceleration
Answer:
The acceleration of the refrigerator is [tex]a= 0.056 ms^{-2}[/tex]
Explanation:
The expression of the equation of the net force acting on the refrigerator is as follows;
F-f= ma
Here, F is the applied force, f is the force of friction, m is the mass and a is the acceleration.
It is given in the problem that you're having a hard time pushing a refrigerator having mass 355 kg across the kitchen floor. The force of your own push is 993 N. The force of friction opposing your own push is 973 N.
Put F= 993, f= 973 N and m = 355 kg in the above expression of the equation to calculate the acceleration of the refrigerator.
993 - 973 = (355)a
20 = 355 a
[tex]a= 0.056 ms^{-2}[/tex]
Therefore, the acceleration of the refrigerator is [tex]a= 0.056 ms^{-2}[/tex].
The refrigerator's acceleration is 0.0563 m/s², calculated by subtracting the force of friction from the pushing force and then dividing by the refrigerator's mass.
Explanation:To find the acceleration of the refrigerator, we first need to calculate the net force acting on it. The net force is the difference between the force of the push and the force of friction.
Step 1: Calculate the Net Force
Net Force = Force of the push - Force of friction
Net Force = 993 N - 973 N
Net Force = 20 N
Step 2: Apply Newton's Second Law of Motion
According to Newton's Second Law of Motion, the acceleration (a) can be calculated using the formula:
a = Net Force / Mass
Substituting the known values:
a = 20 N / 355 kg
a ≈ 0.0563 m/s²
The refrigerator's acceleration when being pushed across the kitchen floor is approximately 0.0563 meters per second squared.
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during a crash, an airbag inflates to stop a dummys forward motion. the dummy mass is 75 kg. if the net force is on the dummy is 825 N toward the rear of the car, what is the dumys deceleration
Answer:
11 m/s²
Explanation:
Deceleration: This can be defined as the rate of decrease of velocity. The S.I unit of deceleration is m/s².
From the question,
F = md ..................... Equation 1
Where F = Force acting on the dummy towards the rear of the car, m = mass of the dummy, d = deceleration of the dummy.
make d the subject of the equation
d = F/m............... Equation 2
Given: F = 825 N, m = 75 kg.
substitute into equation 2
d = 825/75
d = 11 m/s²
Answer:
11 m/s^2.
Explanation:
Given:
Mass = 75 kg
Force = 825 N
F = m × a
a = 825 ÷ 75
= 11 m/s^2.
energy conservation-problems 1. A slingshot fires a pebble from the top of a building at a speed of 14.0m/is. The building is 31.0m tall. Ignoring all frictional effects, find the speed with which the pebble strikes the ground
Answer:
Horizontal velocity is 14 m/s
Vertical velocity is 28.3 m/s
Explanation:
Hello dear friend, you have not mentioned the type of speed that you require for this problem.
In this case, there are three possibilities with which the slingshot can be fired i.e. Horizontally, Vertically straight up and vertically straight down. Below is the explanation / answer to all three possibilities
Fired horizontally:
initial conditions:
Vertical Velocity = 0 ; Horizontal Velocity = 14m/s
final conditions:
Vertical Velocity (v² = u² + 2gs) but initial vertical velocity is zero
v² = 2gs so v² = 2(9.8)(31) = 607
v = 24.6m/s
but Horizontal Velocity is still = 14m/s
Resultant velocity from these two velocity components (Pythagoras theorem)
V² = (v horizontal)² + (v vertical)² = 14² + 24.6²
V = 28.3m/s
angle = tan ⁻¹(24.3/14) = 60.1⁰
V = 28.3m/s at angle of 60.1⁰ to the horizontal
Fired Vertically Straight Up
distance before the pebble reaches maximum height from top of building
v² = u² + 2gs
where, v is zero at maximum height
g is minus for upward motion.
v² = u² + 2gs
0 = 14² - 2(9.8)s
s = 196/19.6 = 10.0m
totals distance from maximum height to the ground = 10.0 m + 31.0 m = 41.0m
v² = u² + 2gs
now u from maximum height is 0 and g is positive for downward motion
v² = 2gs
v² = 2(9.8)(41.0)
v = 28.3m/s
v = 28.3m/s vertically straight up
Fired Vertically Straight Down
v² = u² + 2gs
u = 14m/s, g = 9.8m/s², s = 31.0m
v² = 14² + 2(9.8)(31.0)
v = 28.3m/s
v = 28.3m/s vertically straight down
A 2.0 m length of wire is made by welding the end of a 120 cm long silver wire to the end of an 80 cm long copper wire. Each piece of wire is 0.60 mm in diameter. The wire is at room temperature, so the resistivities are as given in Table 27.2. A potential difference of 5.0 V is maintained between the ends of the 2.0 m composite wire.
a.) What is the current in the copper section? b.) What is the current in the silver section?
b.) What is the magnitude of E in the copper section?
c.) What is the magnitude of E in the silver section?
d.) What is the potential difference between the ends of the silver section of the wire?
Using physics concepts of Ohm's law, resistance calculation, and electric field magnitude calculation, we can find the current in copper and silver sections, the electric field magnitudes, and the potential difference in silver section. The potential difference across the silver section will be the same as that applied across the entire wire due to copper's negligible resistance.
Explanation:The student's question is related to electricity and magnetism, a branch of physics. In the scenario described, the resistance (R) of each wire section can be found using the formula R = ρL/A, where ρ is resistivity, L is length, and A is cross-sectional area. Here, resistivity needs to be known from Table 27.2.
Once the resistance of each wire section is known, Ohm's law (V = IR) can be used to find the current (I) in each section. The same current will flow in both sections of the wire since it is a series circuit. The potential difference across each section can then be calculated using Ohm's law.
The magnitude of the electric field E in each section can be calculated from E = V/d, where V is the potential difference across the section and d is its length.
The potential difference across the silver section is the same as the potential difference applied across the entire wire because the copper wire has negligible resistance compared to silver.
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A heavy turntable, used for rotating large objects, is a solid cylindrical wheel that can rotate about its central axle with negligible friction. The radius of the wheel is 0.330 m. A constant tangential force of 300 N applied to its edge causes the wheel to have an angular acceleration of 0.876 rad/s2.
(a)
What is the moment of inertia of the wheel (in kg · m2)?
_____ kg · m2
(b)What is the mass (in kg) of the wheel?
_________ kg
(c)The wheel starts from rest and the tangential force remains constant over a time period of 6.00 s. What is the angular speed (in rad/s) of the wheel at the end of this time period?
________ rad/s
Answer:
a) [tex]I = 113.014\,kg\cdot m^{2}[/tex], b) [tex]m = 2075.556\,kg[/tex]
Explanation:
a) The turntable has the following physical model by using Newton's laws:
[tex]F \cdot R = I \cdot \alpha[/tex]
The moment of inertia is:
[tex]I = \frac{F\cdot R}{\alpha}[/tex]
[tex]I = \frac{(300\,N)\cdot(0.33\,m)}{0.876\,\frac{rad}{s^{2}} }[/tex]
[tex]I = 113.014\,kg\cdot m^{2}[/tex]
b) The moment of inertia for a solid cylinder:
[tex]I = \frac{1}{2}\cdot m \cdot R^{2}[/tex]
The mass of the turntable is:
[tex]m = \frac{2 \cdot I}{R^{2}}[/tex]
[tex]m = \frac{(2)\cdot (113.014\,kg\cdot m^{2})}{(0.33\,m)^{2}}[/tex]
[tex]m = 2075.556\,kg[/tex]
_____ has the potential to superimpose digital data over real photos so that GPS maps can be combined with real pictures of stores and streets to help people locate their position.
Augmented reality has the potential to superimpose digital data over real photos so that GPS maps can be combined with real pictures of stores and streets to help people locate their position.
Explanation:
An engaging perception of an original globe atmosphere, where by computer-generated perceptual knowledge the transformation of real-world entities take place and also by multiple sensory modalities, involving somatosensory, visual, auditory, haptic and olfactory forms, thus known as augmented reality.
AR app uses GPS and camera from a smartphone to deploy an augmented reality-enabled GPS navigation system. As in the web, AR tool termed as Real View Navigation is accessible to all Android and iOS clients. Google is brought its first virtual reality walking directions, now recognized as Live Experience on Google Maps.
An air compressor takes normal air and pushes more and more of it in a rigid steel tank. The number of gas particles in the tank is increased. What happens to the temperature as more and more air is pushed into a tank which does not change size?
A. It increases
B. It stays the same
C. It decreases
Answer:
C. It decreases
Explanation:
The pressure law states that for a constant volume of gas in a sealed container the temperature of the gas is directly proportional to its pressure. This can be easily understood by visualizing the particles of gas in the container moving with a greater energy when the temperature is increased.
A common example is cooking gas when refilled, there is a perceptible change in the temperature of the cylinder.
Which of the following represents energy in its most disordered form? Group of answer choices Chemical-bond energy Electromagnetic (light) energy Heat energy Potential energy The kinetic energy of a moving object
Answer: Heat Energy
Explanation:
Heat is energy in its most disordered form. heat energy is the random jostling of molecules and is therefore not organized. As cells perform the chemical reactions that generate order within, some energy is inevitably lost in the form of heat. Because the cell is not an isolated system, the heat energy produced by the cell is quickly dispersed into the cell's surroundings where it increases the intensity of the thermal motions of nearby molecules. This increases the entropy of the cell's environment and keeps the cell from violating the second law of thermodynamics.
A plastic pipe carries deionized water in a microelectronics clean room, and one end of it is capped. the water pressure is p0 = 60 psi, and the cap is attached to the end of the pipe by an adhesive. calculate the shear stress present in the adhesive.
Answer:
Where the height of the cap is less than or equal to the radius of the bore of the plastic pipe then the ⇵⇵shear stress is less than o equal to 60 psi.
Explanation:
Shear stress = F/A
where F = Applied force
A = Cross sectional area of the member experiencing the force
If the cap covers a section of the pipe of height, h then the area = 2πrh
Where the 60 psi pressure is acting on the pipe bore, we have P₀ = 60 psi = F₀/A₀ where A₀ = area of pipe bore ≈ πr². Therefore if F₀ = F then we have
F₀/A₀ = F₀/πr² and F/A = F₀/2πrh = where h greater than or equal to 0.5×r then the shear stress is less than or equal to 60 psi
To calculate the shear stress in the adhesive, use the formula for shear stress and the given pressure and area.
Explanation:To calculate the shear stress present in the adhesive, we can use the formula for shear stress:
Shear stress = Force / Area
In this case, the force exerted by the water pressure on the capped end of the pipe is equal to the pressure multiplied by the area of the capped end. Since the water pressure is given as 60 psi, we need to convert it to a consistent unit, such as Pascals. 1 psi is equal to approximately 6895 Pascals. The area of the capped end can be calculated using the formula for the area of a circle: Area = pi * radius^2.
Once we have the force and area, we can substitute them into the formula for shear stress to find the value.
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