a. the force that the mountain climber must exert with her feet in N) on the vertical rock face to remain stationary is 273 N.
b. the minimum coefficient of friction between her shoes and the cliff is 0.268.
What is the term of friction?
The force that prohibits one solid object from traveling across another is known as friction. Static friction, sliding friction, rolling friction, and fluid friction are the four main categories of friction.
a).
Balancing the forces in x-direction,
F cos(15) = T sin(31)
F = T sin(31)/cos(15) ...... (1)
balancing the forces in y-direction,
T cos(31) + F sin(15) = 52 x 9.8 = 509.6
T cos(31) + (T sin(31)/cos(15)) sin(15) = 509.6
T = (509.6 cos(15))/(cos(31) cos(15) + sin(31) sin(15))
T = 512 N
Force, F = 512 sin(31)/cos(15)
= 273 N
b)
Coefficient of friction,
u = sin(15)/cos(15)
= 0.268
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a parallel-plate capacitor is made from two plates 12.0 cm on each side and 4.50 mm apart. half of the space between these plates contains only air, but the other half is filled with plexiglas of dielectric constant 3.40 (figure 1). an 18.0 v battery is connected across the plates.
An 18.0 v battery is connected across the plates is 4.58 * 10^-9 J.
Ceq = A*eo/2*d * (K1 + K2)
Ceq = (0.12*0.12*8.85*10^-12)/(2*4.5*10^-3) * (1 + 3.4)
Ceq = 6.23 * 10^-11 F
Energy Stored = 1.2*cv^2
U = 1/2 * 6.23 * 10^-11 * 18.0^2 J
U = 1.0 * 10^-8 J
If we remove plexiglas,
Energy Stored = 1/2* cv^2
U = 1/2 * 2.832 * 10^-11 * 18.0^2 J
U = 4.58 * 10^-9 J
One or more electrochemical cells with external connections for powering electrical equipment make up an electric battery, which is a source of electric power. A battery's positive terminal functions as the cathode and its negative terminal as the anode while it is delivering electricity.
A battery is a device that uses an electrochemical oxidation-reduction (redox) cycle to turn the chemical energy included in its active components directly into electric energy. An electric circuit is used in this kind of reaction to transmit electrons from one substance to another.
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A ball is tossed straight up from the surface of a small, spherical asteroid with no atmosphere. The ball rises to a height equal to the asteroids radius and then falls.
What forces if any act on the ball while it is traveling up?
A: Only a decreasing gravitational force that acts downward
B: Only a constant gravitational force that acts downward
C: Both a constant gravitational force that acts downward and a decreasing force that acts upward
D: No forces act at all
A: Only a decreasing gravitational force that acts downward
From Newton's gravitational law, the force between two objects (a planet) is directly proportional to the product of their masses and inversely proportional to the square of their distance apart.
What does gravity mean?The force of attraction between any two bodies is directly proportional to the product of their masses and is inversely proportional to the square of the distance between them, according to Newton's universal law of gravitation.
What is the name of Newton's law of gravity?Every particle in the cosmos attracts every other particle with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between their centers, according to Newton's law of universal gravitation.
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The figure below shows an overhead view of three particles on which external forces act. The magnitudes and directions of the forces on two of the particles are indicated.
The
figure below shows an overhead view of three p
(a) What are the magnitude and direction of the force acting on the third particle if the center of mass of the three-particle system is stationary?
8 N, rightward
8 N, leftward
2 N, rightward
2 N, leftward
(b) What are the magnitude and direction of the force acting on the third particle if the center of mass of the three-particle system is moving at a constant velocity rightward?
2 N, rightward
8 N, leftward
2 N, leftward
8 N, rightward
(c) What are the magnitude and direction of the force acting on the third particle if the center of mass of the three-particle system is accelerating rightward?
less than 2 N, rightward
greater than 2 N, rightward
greater than 2 N, leftward
less than 2 N, leftward
On two of the particles, the strengths and directions of the applied force are shown. 2 N to the right, 2 N to the right, and more than 2 N to the right
a) 2 N rightward
for the center of mass to be stationary,
Net force = 0
SO, 2N rightward
(b) 2N rightward
for the center of mass to move with constant velocity
Net force = 0
So, 2N rightward
(c) greater than 2N rightward
for the center of mass to accelerate in rightward
Net force should be in rightward
So, greater than 2N rightward
In mechanics, a force is any action that has the potential to change, maintain, or deform a body's motion. The three principles of motion outlined by Isaac Newton in his Principia Mathematica are frequently used to illustrate the concept of force (1687). Newton's first law states that a body at rest or moving uniformly in a straight line will stay in that state until a force is applied to it. According to the second law, a body will accelerate (change in velocity) in the direction of any external force acting on it. The strength of the external force directly correlates with the strength of the acceleration.
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Name the type of spherical mirror which
1 . has positive focal length .
2. always forms a virtual image .
Answer:
convex mirror
Explanation:
(answer need to be atleast 20 character long)
How does the inertia of the model car compare with the inertia of a real car
The mass of a real car is greater than that of a model car, hence it will have higher inertia.
What is inertia and give its example?
The concept of inertia states that an object will maintain its current motion unless a force changes its speed or direction. The phrase should be taken as a shortened form of Newton's first law of motion's description of "the principle of inertia."
Case Studies of the Law of Inertia in Daily Life (Inertia of Motion) People slump forward when the bus abruptly stops. The top part of the body continues to move forward due to inertia of motion when the driver of a bus abruptly brakes, but the bottom section of the body comes to rest along with the bus.
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What does an oscilloscope measuring electric current display
A. How resistance changes over time
B. How power changes over time
C. How current changes over time
D. How voltage changes over time
A fisherman has caught a fish on his pole, and to keep the pole steady he has to apply an upward force of F2 = 240 N at an angle of 83.5° with respect to the pole (see figure). The length of his pole is 4.1 m, and he is holding it a distance 0.35 m from the end, where he is applying a downward force F1.
With how much force, F1, in newtons, does he have to push straight downward on the end of his pole to keep the pole from moving? You may assume the pole is massless. F1 = What is the mass of the fish on the end of the pole, in kilograms? m =
The mass of the fish on the end of the pole, in kilograms m =2.090Kg.
What is Force?
Force is an influence that can cause an object to change its motion, direction, shape, or other physical attributes. Forces can be applied to objects, creating a change in their acceleration, velocity, or momentum. Forces can be either contact forces, such as pushing or pulling on an object, or non-contact forces, such as gravity, magnetism, and electricity. Forces can be described in terms of magnitude, direction, and point of application. Magnitude is the strength of the force, direction is the path the force is applied, and point of application is the point on the object where the force is applied. Forces can also be classified as balanced or unbalanced. Balanced forces occur when two forces of equal magnitude and opposite direction act on an object, resulting in no net force. Unbalanced forces occur when two forces of unequal magnitude act on an object, resulting in a net force.
Given that,
F2 = 240N
Angle = 83.5 degree
Length = 4.1m
Distance = 0.35m
How much force, F1 in newtons ?
What kind of fish is that hanging off the end of the pole?
Thus,
Calculating Torque about ‘A’
For equillibrium ∑τa= 0
F1 * L + F2 * (L – d) = 0
F1 * L= - F2* (L – d)
F1L SinΘ= F2(L – d) SinΘ
F1 = F2 (L – d)/L
F1 = 240 (4.1 – 0.35)/4.1
F1 = 219.51N
For equillibrium ∑ Fnet = 0
F2 + F1 + mg = 0
mg = F2- F1
m = F2 - F1/ g
m = 2.090Kg
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8. The horizontal and vertical components of a velocity are 46.1 m/s and 62.5 m/s respectively. What is the magnitude and direction of the velocity? Answer: 77.7 m/s, 53.6°
Answer:
The magnitude of the velocity is 77.7 m/s, and the direction is 53.6°.
Explanation:
To find the magnitude and direction of the velocity, we need to use the Pythagorean theorem and trigonometry. The magnitude of the velocity is given by the square root of the sum of the squares of the horizontal and vertical components:
magnitude = sqrt(46.1^2 + 62.5^2)
magnitude = 77.7 m/s
The direction of the velocity is given by the arctangent of the vertical component divided by the horizontal component:
direction = atan(62.5 / 46.1)
direction = 53.6 degrees
Thus, the magnitude of the velocity is 77.7 m/s, and the direction is 53.6°.
A water wave is called a deep-water wave if the water’s depth is more than one-quarter of the wavelength. Unlike the waves
we’ve considered in this chapter, the speed of a deep-water wave depends on its wavelength:
v = Bgl2p Longer wavelengths travel faster. Let’s apply this to standing waves. Consider a diving pool that is 5.0 m deep and 10.0 m wide. Standing water waves can set up across the width of the pool. Because water sloshes up and down at the sides of the pool, the boundary conditions require antinodes at x = 0 and x = L. Thus a standing water wave resembles a standing sound wave in an open-open tube.
a. What are the wavelengths of the first three standing-wave modes for water in the pool? Do they satisfy the condition for being deep-water waves?
b. What are the wave speeds for each of these waves?
c. Derive a general expression for the frequencies fm of the possible standing waves. Your expression should be in terms of m, g, and L.
d. What are the oscillation periods of the first three standing wave
The oscillation periods of the first three standing wave is 3.58 sec.
Deep-sea waves lie deeper than half a wavelength. A water wave is a shallow water wave if the depth is less than the wavelength divided by 20.
calculation:-
a. The wavelength of the first three standing waves are V = √g h m/2π
b. V1 = 5.59, V2 = 3.95, V3 = 3.22 m/s
C. A general expression for the frequencies fm of the possible standing waves. Your expression should be in terms of m, g, and L frequency = 1/lamda m × √g h m/2π.
d. The oscillation periods of the first three standing wave are T = 1/f
= √4πL/ng
putting the values t = 3.58
t2 = 2.52 sec and t3 = 1.25 sec.
Deep-sea waves do not interact with the seafloor on their way so their velocity is independent of water depth. However, when the wave enters shallow water, the interaction with the bottom changes the wave. The wave speed slows down the wavelength shortens and the wave height increases.
They bend in paths that are more perpendicular to the water surface propagate more slowly and decrease in wavelength as they enter shallow water. So when a wave of water travels from deep water to shallow water it slows down shortens its wavelength and changes direction.
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A 4.0 kg bucket of water is raised from a well by a rope.
The acceleration of gravity is 9.81 m/s2 .
If the upward acceleration of the bucket is 2.6 m/s2, find the force exerted by the rope on the bucket of water.
Answer in units of N
If the upward acceleration of the bucket is 2.6 m/s2, the force exerted by the rope on the bucket of water is 10.4 N.
The force exerted by the rope on the bucket of water, you can use Newton's second law of motion, which states that the force acting on an object is equal to the object's mass multiplied by its acceleration. In this case, the force acting on the bucket of water is the force exerted by the rope, and the object's mass is 4.0 kg and its acceleration is 2.6 m/s^2. Therefore, you can use the following equation to find the force:
= F = ma
Putting values from the problem gives:
= F = (4.0 kg) x (2.6 m/s^2)
= 10.4 N
So, the force exerted by the rope on the bucket of water is 10.4 N.
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if the breaking tension of the cord is 620 n, what is the maximum mass of the sign to put on without breaking the cord
The highest tensile stress that a material can sustain before failing, such as breaking or irreversible deformation, is known as the material's breaking strength. The point at which a material transitions from elastic to plastic deformation is defined by its tensile strength.
What is an example of breaking stress?
A metal has a breaking stress or strength of 1,000 pounds per square inch, for instance, if a metal rod with a one square inch cross section can take a pulling force of 1,000 pounds but breaks if additional force is applied.
How can I determine a string's breaking strength?
The breaking strength of the string in a basic pendulum is equal to twice the weight of the bob. When the string is horizontal, the bob is freed from its resting position. When the string forms an angle with the vertical, it snaps.
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The jumper has a mass of 55 kg, and the bridge's height above the river is 150 m. The rope has an unstretched length of 8 m and stretches a distance of 5 m before bringing the jumper to a stop. Determine the maximum speed of the jumper and the spring constant of the rope. In your calculation, use g 10 N/kg. m/s Vmax k = N/m E. Now suppose the jumper has a mass of 80 kg. Do you think the maximum speed of the jumper will increase, decrease, or stay the same?Will the rope need a larger, smaller, or the same spring constant to bring the jumper to a stop in the same distance as part D? (Your answers to these questions are not graded for correctness.)The maximum speed of the jumper will This answer has not been graded yet. The rope will need spring constant that is This answer has not been graded yet. Now calculate the maximum speed of this more massive jumper and the spring constant of the rope needed to bring the jumper to a stop after the = 10 N/kg for your calculations.) Were your predictions correct? rope stretches 5 m. (Again, use g m/s Vmax k = N/m
The speed of jumper is 54.22 m/s and the spring constant of the rope is 6468N/m.
Given data
Jumper weighs 55 kg, which is its mass.
The bridge is 150 meters tall above the river.
The stretched length of the rope is 8 meters (L).
The length after stretching is L' = 5m.
In this situation, the jumper's potential energy will be transferred into the spring potential energy of the rope when they jump. Potential energy of a jumper will then equal the potential energy of a spring in a rope.
The spring constant in this case is k.
Making the following calculation: mgh = 1/2 Kl2 55 90.8 150 = 1/2 k 5 5 k=6468 N/m
Applying the third kinematic equation of motion, find the jumper's final speed as v2 = U2 + 2as.
We discover U=54.22 m/s.
As a result, we can say that the speed of jumper is 54.22 m/s and the spring constant of the rope is 9187.5 N/m.
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Two round concentric metal wires lie on a tabletop, one inside the other. The inner wire has a diameter of 22.0 and carries a clockwise current of 15.0 , as viewed from above, and the outer wire has a diameter of 40.0. What must be the direction (as viewed from above) of the current in the outer wire so that the net magnetic field due to this combination of wires is zero at the common center of the wires? What must be the magnitude of the current in the outer wire so that the net magnetic field due to this combination of wires is zero at the common center of the wires?
The current in the outer wire is in the counterclockwise direction.
The concept of the right-hand thumb rule and magnetic field at the center of a current carrying loop is required to solve the problem.
First, determine the direction of the current in the outer wire by using the right-hand thumb rule. Then, calculate the magnitude of current in the outer wire by equating the sum of magnetic fields due to each wire to zero.
The magnetic field at the center of a current loop is, B = [tex]\mu[/tex]₀I/2R
Here, I is the current through the loop, R is the radius of the loop, and
[tex]\mu[/tex]₀ is the permeability of free space.
The right-hand thumb rule is used to find the direction of the magnetic field. Curl the fingers of the right hand into a half circle in such a way that the thumb points in the direction of the current, then the fingers will point in the direction of the magnetic field.
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you place a small air cart on a 3.00 m air track and set it into motion with a speed of 0.70 m/s. due to very good elastic bumpers at each end of the track, the cart oscillates back and forth between the two ends of the track with essentially no loss in energy. determine the period and the frequency for this motion. you may assume that the length of the cart is negligible compared to the length of the track.
The motion has an 8.57 second period, and its frequency is 0.11 Hz. You can suppose that the distance between the cart and the track is little.
Period= T = 2*3/0.7 = 8.57 sec
The period of the motion is 8.57seconds
freq = f = 1/T = 1 /8.57 = 0.11 Hz
The frequency of the motion is0.11Hz
The number of waves that pass a fixed point in a unit of time is known as frequency in physics. It is also the number of cycles or vibrations that a body in periodic motion experiences in a unit of time. When a body in periodic motion moves through a series of events or locations before returning to its initial state, it is said to have experienced one cycle or one vibration. A simple harmonic motion is also seen under angular velocity.
If one cycle or vibration takes half a second to complete, the frequency is two per second; if it takes a full hour, the frequency is one hundred per hour. Frequency is often equal to the reciprocal of the period, or time interval; for example, frequency = 1/period = 1. (time interval).
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A student calculates the time taken (in minutes) for the light from the sun to reach the Earth. The sun is 93 million miles away (1 mile 1.609 km) and the speed of light is 3.00 x 108 m/s. The calculation is set up as follows: 9.3 x 10^7 mi x 1609 km/1 mi x 10^3m/1 km x 1 s/3.00 x 10^8 m x 1 min/60s Select the correct answer, quoted to the correct number of significant figures. O 8.3 min, since 9.3 x 10 has 2 significant figures O 8.313, since 1.609 has 4 significant figures O 8 min, since there is only 1 significant figure in 60 s O 8.31 min, since 3.00 x 10° has 3 significant figurts
The time taken (in minutes) for the light from the sun to reach the Earth is 8.3 minutes.
The speed of sunlight is 300,000 kilometres per second. The basic equation "time= (distance/speed)" can be used to determine how long it takes for sunlight to reach Earth.
We are given that,
Speed of light = c = 3×10⁸ m/s
Distance from sun to earth = d = 93 million miles = 148.8× 10⁹m
Thus to calculate the time of sun light which is reached to earth by the equation,
t = d / c
t = (148.8 × 10⁹m)/( 3×10⁸ m/s)
t = 496 sec
t = 8 min 3 sec.
Therefore , the sunlight reached to earth in 8min 3sec.
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Three boxes are pushed on a floor with a constant force of magnitude F applied to box A. The boxes move to the right with an acceleration of 1.5 m/s2. The coefficient of kinetic friction between the bottom of a block and the floor is 0.4. 2.0 kg B 1.0 kg 3.0 kg What is the magnitude of the force that block B applies to block C? A) 1.5 N B) 4.5 N C) 7.3N D) 16.3 N E) There is not enough information to tell.
The magnitude of the force that block B applies to block C is 16.3 N .
Calculation :
Frictional force of this combination = 0.4*9.8(Ma + Mb)
= 0.4*9.8*3
F(ab)= 11.76 N
F(AB) = Net force of this combination = 3*1.5 = 4.5 N
since block ' c ' is also moving with the same acceleration ,
Net force on C by B = F - (F(ab) +F(AB) )
= 32.52 - (11.76 + 4.5)
= 32.52 - 16.26
= 16.3 N
The word "force" has a precise meaning. At this level it is appropriate to describe the force as pushing or pulling. A force does not contain or "have within" an object. A force is applied from one object to another. The idea of force is not limited to animate and inanimate objects.
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When does one's body start storing fat either by increasing the number of fat cells or by increasing the size of existing fat cells?
When one's body starts storing fat, both the number of fat cell and the size of existing fat cells increases.
What is the process of fat tissue growth and development in humans?Adipose tissue expands during infancy and adolescence as a result of an increase in fat cell quantity and, to a lesser extent, fat cell size. In spite of a significant turnover (about 10% of the fat cells every year) when body weight is stable, the number of fat cells in adults remains constant over time.
In adults, losing weight primarily affects fat cell size (making them smaller), whereas gaining weight results in an increase in fat cell size and quantity. The bone marrow is a significant source of fat cell regeneration during the course of a person's lifetime. This is most noticeable in obesity, when around 20% of all fat cells are produced from bone marrow.
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a plane electromagnetic wave is traveling in a vacuum. the magnetic field is directed along the z-axis and given by: B_z = 3.0 mu T sin(1.0 times 10^7 x - 3.0 times 10^15 t) True / False The wavelength lambda of the wave is 1.0 times 10^7 meters True / False The frequency f of the wave is 3.0 times 10^15 Hz. True / False The direction of the electric field is along the x-axis. True / False Doubling the magnetic field strength
In a vacuum, an electromagnetic wave is moving through the air. The wavelength is 1x10^7m and the frequency is 3x10^15Hz while the direction of the electric field is along the z-axis.
Given the magnetic field along z axis (B) = 3.0muTsin(1.0x10^7x - 3.0*10^15 t)
The formula for magnetic field is B = B0sin(wt+kx)
For direction of wave by comparing the equations we have
kx +(- 3.0 x 10^15 ) = 0
x = 3.0 x 10^15 /k in positive direction of x axis
The direction of propogation is along x axis and the magnetic field in y axis. The electric field is in both directions. So E along z axis
B0 = 3x10-7x4πT
ω = -3.0 x 10^15
∧ = 2π/k = 2x3.14/1.0x10^7 = 0.68/1.0x10^7 = 0.68x10-7
The wavelength ∧ of the wave is = 0.68x10-7m
frequency (f) = c/∧ = 3x10^8/0.68x10-7 = 4.41x10^15Hz
The frequency f of the wave is 4.41x10^15Hz
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A 12 kg runaway grocery cart runs into a spring with spring constant 220 N/m and compresses it by 80 cm .
What was the speed of the cart just before it hit the spring?
The speed of the cart just before it hit the spring is 3.42 m/s.
Elastic potential energy is the energy that is stored when a force is applied to deform an elastic object.
Given the mass of the cart is 12 kg, the spring constant is 220 N/m, and the compressed length is 80 cm.
Given that the runaway grocery cart compresses the string. When this cart stops, the kinetic energy (KE) of this cart becomes zero because of maximum compression. This KE will be converted to the elastic potential energy of the spring. Then,
[tex]\begin{aligned}U&=\frac{1}{2}kx^2\\&=\frac{1}{2}\times220\times0.80^2\\&=\mathrm{70.4\;J}\end{aligned}[/tex]
This elastic potential energy is equal to the initial KE.
[tex]\begin{aligned}70.4&=\frac{1}{2}\times 12\times v^2\\140.8&=12v^2\\v^2&=11.73\\v&=\mathrm{3.42\;m/s}\end{aligned}[/tex]
The answer is 3.42 m/s
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The 2.7-cm-diameter solenoid in (Figure 1) passes through the center of a 6.0-cm-diameter loop. The magnetic field inside the solenoid is 0.30 T .
A. What is the magnetic flux through the loop when it is perpendicular to the solenoid?
B. What is the magnetic flux through the loop when it is tilted at a 60 angle?
A. The magnetic flux through the loop, when it is perpendicular to the solenoid, is approximately 8.49 Weber (Wb).
B. The magnetic flux through the loop, when it is tilted at a 60-degree angle, is approximately 4.24 Weber (Wb).
A:
To find the magnetic flux through the loop when it is perpendicular to the solenoid, we can use the formula for magnetic flux:
[tex]\phi=BAcos(\theta)[/tex]
The area of the loop is given by:
[tex]A=\pi(d/2)^2[/tex]
B = 0.30 T and d = 6.0 cm
The magnetic flux is given as:
[tex]\phi= 0.30T\times (\pi \times (6/2)^2\\\phi=8.49\ Wb[/tex]
B:
To find the magnetic flux through the loop when it is tilted at a 60-degree angle, we need to consider the new angle (θ = 60 degrees) between the magnetic field and the loop's normal vector.
The magnetic flux:
[tex]\phi=0.30*(\pi*(6/2)^2)cos(60^o)\\\phi=4.24\ Wb[/tex]
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A 25 cm rod moves at 6.8 m/s in a plane perpendicular to a magnetic field of strength 0.12 T. The rod, velocity vector, and magnetic field vector are mutually perpendicular, as indicated in the accompanying figure.(a) Calculate the magnetic force on an electron in the rod (In N). (Enter the magnitude.) N (b) Calculate the electric field in the rod (in V/m). (Enter the magnitude.) V/m (c) Calculate the potential difference between the ends of the rod (in V). (d) What is the speed of the rod (in m/s) if the potential difference is 1.0 V? m/s
Option B is correct. The cross product of velocity and magnetic field, q [v B], determines the strength of the force.
The magnetic field's direction is anticipated by the right-hand thumb rule, and as a result, the resultant force is perpendicular to both the velocity and magnetic field directions.
Using the known currents in the wires, the force per unit length can then be computed as follows: Fl=(4107Tm/A)(5103A)2(2)(5102m)=11010N/m.
Given, \sV=200V\sv=100m/s
e=1.6×10 \s−19 \s C
m=9.1×10 −31 \s Kg \sm \se \s \s = \s9.1×10 \s−31
1.6×10 \s−19
m \se \s \s =1.75×10 \s11
The best choice is B.
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consider a diffuser operating in an adiabatic process. the device decelerates the flow, causing a decrease in the kinetic energy of the fluid. noting from the first law that energy cannot be destroyed, describe physically what happens to the lost kinetic energy.
A diffuser is an adiabatic device that slows down a fluid to reduce its kinetic energy.
The transfer of heat from one system to another is caused by heat, temperature, and external variables. When heat is transferred, things do change. A process is referred to as adiabatic if there is no heat transfer.
Consider the internal combustion engine (ICE) found in classic automobiles. The ICE won't be able to function without the air pressure generated in the combustion chamber to move the piston inside a cylinder. Similar to this, the steam engine, which was widely employed throughout the early stages of the Industrial Revolution, functions according to the same theory. Heat is delivered to a small space, which causes the wet air to expand and force cylinders to rise and fall.
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An airliner arrives at the terminal, and the engines are shut off. The rotor of one of the engines has an initial clockwise angular speed of 1940 rad/s. The engine's rotation slows with an angular acceleration of magnitude 79.3 rad/s2. (a) Determine the angular speed after 10.0 s. (b) How long does it take the rotor to come to rest?
The angular speed after 10.0 seconds is approximately 2733 rad/s. it takes approximately 24.5 seconds for the rotor to come to rest.
In this problem, we are given the initial angular velocity of a rotor (1940 rad/s) and its angular acceleration (79.3 rad/s^2). We are asked to find the angular velocity after 10.0 seconds and the time it takes for the rotor to come to rest. To find the angular velocity after 10.0 seconds, we can use the formula omega_f = omega_i + alpha*t, where omega_f is the final angular velocity, omega_i is the initial angular velocity, alpha is the angular acceleration, and t is the time elapsed.
Plugging in the given values, we find that the final angular velocity is approximately 2733 rad/s. To find the time it takes for the rotor to come to rest, we set the final angular velocity to 0 and solve for t. We can use the same formula as before: omega_f = omega_i + alpha*t. Plugging in the values for omega_i and alpha, we find that it takes approximately 24.5 seconds for the rotor to come to rest.
In summary, the angular velocity of the rotor after 10.0 seconds is approximately 2733 rad/s, and it takes approximately 24.5 seconds for the rotor to come to rest.
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A car travels 10 miles east in 30 minutes. What is the car's velocity in miles per hour
Answer:
20 mph
Explanation:
10 miles per 30 minutes is the same as 10 miles per 0.5 hours
Constant Velocity [tex]= \frac{distance}{time} = \frac{10 miles}{0.5 hours}[/tex] = 20 miles per hour = 20 mph
a current - carrying wire is pulled away from a conducting loop in the direction shown. As the wire is moving, is there a cw current around the loop, a ccw current or no current? Show the induced field and give clear explanation to your answer.
If the current increases continuously, then the direction of the induced current in the loop is clockwise.
A compass needle put above a straight wire carrying current points north (the magnetic south pole), hence the magnetic field at that location is towards geometric south, and using the right hand thumb rule, we can determine that the direction of the current is east. A counterclockwise current will be produced (ccw). The size of the loop shrinks as the bar ascends through the zone of constant magnetic field, and as a result, the flux through the loop also shrinks.
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most of the new star formation in the galaxy is found in the most of the new star formation in the galaxy is found in the bulge. halo. galactic center. spiral arms. globular clusters.
"Most of the new star formation in the galaxy is found in the spiral arms."
Spiral arms are the regions of strong star formation and are more prominent in blue light. From the centre of spiral and barred spiral galaxies, these regions extend.
Transient weaknesses in the gases that encourage star formation and produce turbulence lead to spiral arms. In other words, spiral arms contain a lot of gases, which are the primary building blocks needed for the development of new stars.
They are not hard or permanent structures, as evidenced by the presence of spiral arms. A density wave is currently thought to circle a spiral galaxy, creating spiral arms.
The thin disk of the galaxy contains all of the spiral arms.
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a ball is thron upward witha an intial velocity of 61 feet per second from an initial height of 12 feet express the heigs in feet of the ball as a function of the time t (insecond ) how long will the ball be in the air
The time at which the ball remains in the air after it is thrown vertically upward with an initial velocity of 61 feet per second from an initial height of 12 feet is 4 seconds.
Motion that is normal to a defined horizontal surface is often referred to as vertical motion. The height of a ball launched from a certain height while maintaining a constant speed is modeled as h(t) = at²+bt+c where h(t) is the height of the ball, t is time, and a, b, and c are constants.
At the initial height h = 12 feet and t = 0,
12 = a(0)²+b(0)+c
c = 12
Differentiating equation h(t) = at²+bt+c concerning t, we get, [tex]\frac{dh(t)}{dt}&=2at+b[/tex]
Substituting t = 0 and dh(t)/dt = 61, we get,
[tex]\begin{aligned}61&=2a(0)+b\\b&=61\end{aligned}[/tex]
Again differentiating [tex]\frac{dh(t)}{dt}&=2at+b[/tex] concerning t, we get, [tex]\frac{d^2h(t)}{dt^2}=2a[/tex]
The acceleration caused by gravity on Earth is 32 feet per second. Since the ball travels downward, the value becomes negative. Substituting this in the above equation.
[tex]\begin{aligned}-32&=2a\\a&=-16\end{aligned}[/tex]
Substituting values of a, b, and c in h(t) = at²+bt+c, we get,
h(t) = -16t²+61t+12
Substituting h = 0 in the above equation, the time the ball remains in the air will be,
0 = -16t²+61t+12
0 = 16t²-61t-12
Using the quadratic formula,
[tex]\begin{aligned}t&=\frac{-(-61)\pm\sqrt{(-61)^2-4\times16(-12)}}{2\times16}\\t&=\frac{61\pm67}{32}\\t&=\frac{61+67}{32}\;\text{or}\;\frac{61-67}{32}\\t&=4\;\text{or}\;-\frac{3}{16}\end{aligned}[/tex]
Time cannot be negative, therefore, t = 4 seconds is the answer.
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white light falls on two narrow slits separated by 0.50 mm. the interference pattern is observed on a screen 5.5 m away.
The separation between the first maxima for red light (λ = 700nm) and violet light (λ = 400nm) = 80 x 10⁻⁵ cm
Light interferenceLight interference is a condition when two or more light waves combine to form a combined light wave. The condition for this light interference is that the light waves come from a coherent source, so that the amplitude, wavelength, and frequency are the same, and the phase difference is always fixed.
The question is incomplete, it should be:
What is the separation between the first maxima for red light (λ = 700nm) and violet light (λ = 400nm)?
We have,
Distance between slits = 0,5 mm = 5 x 10⁻⁴ m
Distance between the slit and the screen = 5.5 m
λ red = 700 nm =
λ violet = 400 nm
So, The separation between the first maxima:
Sin ∅m = mλ/d
= (1 x 400 x 10⁻⁹)/5 x 10⁻⁴
= 80 x 10⁻⁵ cm
The question is incomplete, it should be:
White light falls on two narrow slits separated by 0.50 mm. The interference pattern is observed on a screen 5.5 m away. (a) What is the separation between the first maxima for red light (λ = 700 nm) and violet light (λ = 400 nm)?
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compared with the usual classical measurement of momentum for a high-speed object, momentum measured relativistically
Momentum measured relativistically is greater than momentum measured classically for an object travelling at a high speed.
When there is no net external force acting on a system, momentum is preserved according to classical mechanics. As a result, momentum conservation can be used as a fundamental technique to study collisions. Since relativistic momentum is conserved, a lot of what we know about subatomic structure comes from studying the collisions of relativistic particles created by accelerators. The perceptual sense of classical momentum and relativistic momentum are identical. Large masses moving at high speeds are best for it. The conservation of momentum is guaranteed in all inertial frames by the definition of relativistic momentum. Relativistic momentum is conserved whenever a system has zero net external force, just like it is for classical momentum.
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a student spins a cup that is in contact with a platform in a horizontal circular path at a constant speed, as shown in figure 1. the platform is connected to two strings that are held by the student as the platform-cup system experiences uniform circular motion. a free-body diagram of the cup is shown in figure 2. which statement of reasoning best supports and correctly identifies the magnitude of the force the cup exerts on the platform?
√F1²+F2², because this force reflects the overall force the cup has applied to the platform.
What factors contribute to circular motion?The change in direction and centripetal force. A centripetal force is applied to any item travelling in a circle (or along a spherical route). Towards other words, the item is being physically pushed or pulled in the direction of the circle's center. This is the necessary centripetal force.
What exactly is the force pulling on a particle traveling in a circle?Centripetal force is the name of the force exerted on a particle that is rotating in a circle. It is this centripetal force that is focused inward that prevents the particle from deviating from or losing its circular course.
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