The 27.9 kg mass experience a net force of zero. Gravitational equilibrium occurs when the gravitational force on an object is equal to zero.
How is equilibrium impacted by gravity?Tilting an object will increase the height of its center of gravity when it is in a stable balance. When tilted, an item in unstable equilibrium will have a lower center of gravity. Finally, for objects in neutral equilibrium, the center of gravity will stay at the same height when pushed.
How can we determined this?To find the distance at which the 27.9 kg mass experiences a net force of zero, we need to calculate the gravitational force acting on it due to the other two masses. The gravitational force between two masses m1 and m2 at distance r is given by F = Gm1m2/r^2, where G is the gravitational constant.
First, we know that the distance between the 99 kg and 404 kg masses is fixed. Let's call this distance d.
Now we can set the gravitational force acting on the 27.9 kg mass due to the 99 kg mass and the 404 kg mass equal to zero and solve for r:
0 = G*(27.9 kg)(99 kg)/r^2 + G(27.9 kg)*(404 kg)/(d-r)^2
Solving for r, we get:
r = d * sqrt(404/(404+99))
Substituting d value will give the distance at which the 27.9 kg mass experiences a net force of zero in units of m.
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A cannon ball is launched horizontally from a cannon. the cannon is on the edge of a 50 m tall cliff. what is the acceleration of the cannon ball horizontally?
a 0
b not enough information
c 50 m/s2
d 9.8 m/s2
Answer:
a
Explanation:
The acceleration of the cannon ball horizontally is 0 m/s2, since it is already traveling at a constant velocity.
How do I find work done by friction over the full length of a roller coaster?
The full length is 0.34 meters(it’s a paper roller coaster but that doesn’t matter) and the mass of the marble is 0.005kg(5g). I can’t seem to find an equation for it?
According to Newton's third rule of motion, whenever a first object applies a force to a second object, the first object feels a force that is both equal to and opposite from the force that it applies.
What is Force?
In physics, a force is an influence that can change the motion of an object. A force can cause a mass object's velocity or acceleration to change. Force can be described intuitively as a push or a pull. Because it has both magnitude and direction, a force is a vector quantity.
To find the work done by friction over the full length of the roller coaster, you will need to calculate the force of friction acting on the marble over the entire track. The force of friction can be calculated using the formula: F = μ * N, where μ is the coefficient of kinetic friction and N is the normal force. Once you have calculated the force of friction, you can then calculate the work done by multiplying the force of friction by the distance travelled. The formula for work is W = F * d, where F is the force of friction and d is the distance travelled.
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why does a canvas tent leak when touched when it's raining
Please help thank you so much!!
Answer: A
Explanation: This is a condition that makes it hard for the body to obsorve oxygen.
Answer:
it's A
Explanation:
i just did the same thing
One million electrons travel between two points in a circuit. The total energy gained by the electrons is 1.6 × 10−10 J. What is the potential difference between the two points?
A. 1.6 x 10^-16 V
B. 1.6 x 10^-4 V
C. 1.0 x 10^3 V
D. 1.0 x 10^9 V
The potential difference between the two points is B. 1.6 x 10⁻⁴
The potential difference, also known as voltage, is the energy per unit charge that is transferred between two points in a circuit. We can use the formula:
V = E / Q
where V is the potential difference, E is the energy, and Q is the charge.
In this problem, we are given that the total energy gained by the electrons is 1.6 x 1010 J and the charge is Q = 1 x 10⁶ electrons. So, we can plug in these values into the formula:
V = 1.6 x 10-10 J / (1 x 10⁶) = 1.6 x 10⁻⁴ V
Therefore, the potential difference between the two points is 1.6 x 10⁻⁴ V.
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) while driving down the road, a firefly strikes the windshield of a bus and makes a quite obvious mess in front of the face of the driver. this is a clear example of an action-reaction pair. the firefly hits the bus and the bus hits the firefly. which of the two forces is greater: the force on the firefly or the force on the bus? (be careful)
The force on the firefly is greater than the force on the bus.
The concept of action-reaction pair is described by Newton's third law of motion, which states that for every action, there is an equal and opposite reaction. In this scenario, the force of the firefly striking the bus is the action and the force of the bus striking the firefly is the reaction.
However, the force on the firefly is greater than the force on the bus. This is because the firefly is much smaller and less massive than the bus, so the force required to stop the firefly is much greater than the force required to stop the bus. Additionally, the firefly's impact on the bus would be negligible, while the bus' impact on the firefly would be fatal.
The forces acting on two objects in an action-reaction pair are equal in magnitude but opposite in direction, but the effect of these forces on the objects can be different based on the mass and velocity of the objects.
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the goose has a mass of 21.3 lb (pounds) and is flying at 8.00 miles/h (miles per hour). what is the kinetic energy of the goose in joules?
The goose weighs 21.3 pounds and travels at an average speed of 8 miles per hour (miles per hour). The goose's kinetic energy in joules is 61.86 kg m2/sec2.
Given,
Kinetic energy (K.E)=1/2mv²
where m=mass in kg,velocity =v m/sec
From data m=21.3lb
but 21.3lb =454g; 1000g=1kg
21.3lb×454g/1lb×(kg/1000g)=9.6702 kg
velocity=8.00 miles/h
1mile=1.61km; 1hour=60min =60×60 sec
8.00miles/hour ×(1 hour/60×60sec)×(1.61 km/1mile)×1000m/1km
v=3.577 m/sec
Kinetic energy (K.E)=1/2mv²
=1/2(9.67)(3.577 m/sec)²
=61.86 kg m²/sec²
∴KE=61.86 Joule
kinetic energy of the goose=61.86J
Kinetic energy is the type of energy that an object or particle possesses as a result of its motion. When work is performed on an object by applying a net force, the object accelerates and gains kinetic energy. Kinetic energy is a property of a moving object or particle that is affected by both its motion and mass. Translation (or movement along a path from one location to another), rotation about an axis, vibration, or any combination of motions are all possible.
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Compound 1 has a composition of 46.7 mass% of element A and 53.3 mass% of element B. A and B also form a second binary compound 2 with 30.4mass% of A and 69.6 mass% of B. Show that the data are consistent with the law of multiple proportions.
The data are consistent with the law of multiple proportions, as the ratios of element A to element B in each compound can be reduced to small whole numbers.
The law of multiple proportions states that when two elements combine to form two or more compounds, the masses of one element that combine with a fixed mass of the other element are in a ratio of small whole numbers. For compound 1, the mass of element A is 46.7 mass%, and the mass of element B is 53.3 mass%. For compound 2, the mass of element A is 30.4 mass%, and the mass of element B is 69.6 mass%.
The ratio of element A in compound 1 to element A in compound 2 is 46.7/30.4 = 1.54. The ratio of element B in compound 1 to element B in compound 2 is 53.3/69.6 = 0.764. The ratio of element A in compound 1 to element B in compound 1 is 46.7/53.3 = 0.875. The ratio of element A in compound 2 to element B in compound 2 is 30.4/69.6 = 0.436. These ratios can be simplified to 3:2:2:1, which are small whole numbers and therefore consistent with the law of multiple proportions.
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identify the conditions necessary for an object to be in rotational equilibrium. i. angular acceleration is zero ii. net torque is zero iii. angular acceleration is a maximum iv. net force is zero group of answer choices ii and iv only iii and iv only i and ii only ii and iii only
Rotational equilibrium is the condition of motion where there is no angular acceleration. Since the torque is what causes the movement's acceleration, there is no total torque in the rotational equilibrium.
What prerequisites must exist for an item to be in rotational and linear equilibrium?An object must satisfy two requirements of equilibrium in order to maintain static equilibrium. First, there must be no net force acting on the item. Second, there must be no net torque pulling on the object.
What is the prerequisite for rotational equilibrium, according to Chegg?If a body meets the requirements below, it is said to be in rotational equilibrium: The forces operate within the same plane, cross at a common element, and finally, act within the same plane.
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Squid rely on jet propulsion when a rapid escape is necessary. A 1.5 kg squid at rest pulls 0.10 kg of water into its mantle, then ejects this water at a remarkable 45 m/s. Right after this ejection, how fast is the squid moving?
After the water is ejected, the squid's final speed is 3 m/s in the opposite direction.
What is the straightforward meaning of velocity?The dislocation that such an object a particle experiences in respect to time is expressed vectorially as pace. The meter a second (m/s) is the accepted unit measure velocity profile (also known as speed). The unidirectional speed of an item in motion, as measured by a specific unit of time and observed from a certain point of reference, is what is referred to as velocity.
mass m₁ = 1.5 kg
initial velocity, u₁ = 0
mass of water, m₂ = 0.1 kg
initial velocity , u₂ = 0
final velocity , v₂ = 45 m/s
conservation of linear momentum;
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
1.5(0) + 0.1(0) = 1.5v₁ + 45(0.1)
0 = 1.5v₁ + 4.5
1.5v₁ = -4.5
v1 = (-4.5)/1.5
v1 = -3 m/s
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a 60.0 kg skier is at the top of a slope 10.0 m above the ground. what is her gravitational potential energy of the skier-earth system?
A 60.0 kg skier is at the top of a slope 10.0 m above the ground. The gravitational potential energy of the skier-earth system is 5880J.
Given,
m=60 kg
h=10m
g=9.8
P.E=mgh
=60*10*9.8
=5880J
William Rankine, a Scottish engineer, and physicist from the nineteenth century coined the term potential energy. Potential energy is classified into several types, each of which is associated with a specific type of force.
Because of its position, an object, as we know, can store energy. When a bow and arrow are drawn, some energy is stored in the bow, which is responsible for the kinetic energy gained when the bow is released.
Similarly, when a spring is displaced from its equilibrium position, it gains energy, which we see as stress in our hands when we stretch it. Potential energy is a type of energy that is created as a result of an alteration.
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You double the partial pressure of a gas over a liquid at constant temperature. Which of these statements is then true?.
"The correct statement is There are twice as many gas molecules in the liquid."
Henry's Law states that the partial pressure of a gas above a solution is precisely proportional to the mass of the gas that will dissolve into the solution.
Mathematically, C = kH × P
where, kH is Henry's constant
P = Partial pressure
Because the relationship between concentration and gas partial pressure is straightforward. Therefore, the number of molecules in the liquid will increase as partial pressure increases.
So, we can conclude that the statement there are twice as many gas molecules in the liquid, is true.
The given question is incomplete. The complete question contains options. They are 'a. The Henry’s Law constant is decreased by half. b. There are half as many gas molecules in the liquid. c. There is no change in the number of gas molecules in the liquid. d. The Henry’s Law constant is doubled. e. There are twice as many gas molecules in the liquid.'
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A student is twirling a rubber stopper in a vertical circle of radius 0.95 m. If the rubber stopper has a mass of 50 grams and the student is able to control the speed so that it is a constant 3.5 m/s at all points on the circle:
If the rubber stopper has a mass of 50 grams and the student is able to control the speed so that it is a constant 3.5 m/s at all points on the circle, then he will use the string half as the length of the original string.
A student is twirling a rubber stopper in a vertical circle of radius 0.95 m. If the rubber stopper has a mass of 50 grams and the student is able to control the speed so that it is a constant 3.5 m/s at all points on the circle. A physics student is performing a lab in which she twirls a rubber stopper at the end of a string around in a circle at nearly constant speed and tries to determine its acceleration. by the given primary information we can firmly conclude that if the rubber stopper has a mass of 50 grams and the student is able to control the speed so that it is a constant 3.5 m/s at all points on the circle, then he will use the string half as the length of the original string.
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a spider is crawling at 630 ft/hr. the room is 15 ft wide. How long does it take the spider to travel
The time taken for the spider crawling at 630 ft/hr to travel through the 15 ft wide room is 42 hours
How do I determine the time taken for the spider to travel?From the formula of speed, we can obtain a formula for calculating time as illustrated below:
Speed = Distance / time
Cross multiply
Speed × time = Distance
Divide both sides by speed
Time = Distance / speed
Using the above formula, we can obtain the time taken from the spider to travel through the room. Details as follow:
Speed of spider = 630 ft/hrDistance travel = 15 ftTime taken to travel =?Time = Distance / speed
Time = 630 / 15
Time = 42 hours
From the calculation made above, we can conclude that the time taken is 42 hours
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a bungee jumper of mass 60 kg steps off a 40-m high cliff. it takes approximately 40 n to stretch the cord 1 meter. how close does the jumper get to the ground?
Assuming the bungee cord is perfectly elastic, the jumper will reach a minimum distance of 14.7 meters from the ground after the cord has stretched.
What is distance?
Distance is the amount of space between two objects or points. It is typically measured in units such as meters, feet, or miles. Distance can also be measured in a more abstract sense, such as the amount of time it takes for something to happen or the amount of effort required to complete a task.
Distance can also refer to the difference between two things, such as the difference between two people’s opinions on a particular topic. Distance can also refer to physical separation, such as the distance between two people who are in different countries or cities. Distance can also be used to express the size of something, such as how far a car can travel on a single tank of gas.
Given: m = mass of jumper = 60kg
h = height of cliff = 40m
Also,
k = F/x = 40N/1m = 40N/m
Now, when jumper jumps,
F = m×g
= 60×9.8
= 588 N
Therefore,
x = (588N)/(40N/m) = 14.7m
Thus, jumper gets to a close of 14.7 meters to the ground.
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A sample of an unknown material weighs 290 N in air and 190N when immersed in alcohol of specific gravity 0.700.
(a) What is the volume of the material?
m3
(b) What is the density of the material?
kg/m3
The volume of the material is 27.14 m³ and the density of the material is 1.02 kg/m³.
The sample of the unknown material as a weight of 290 Newton in the air and when it is must in alcohol of specific gravity 0.70 it has a weight of 190 Newton.
We know,
B = VpG
B is buoyancy that will be 190N,
V is volume of material,
p is the density of alcohol,
G is the acceleration due to gravity,
Putting values,
190 = V(0.7)(10)
V = 27.14 m³
The volume of the material is 27.14 m³.
Now, we know,
Density = Mass/volume
Density = W/Vg
Putting values,
Density = 290/27.14×10
Density = 1.02 kg/m³.
So, the density of material is 1.02 kg/m³.
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The ball is round on a string at 35° with respect to the vertical. if the length of the string is 12cm. how fast must be the ball is spinning?
Given that T=ma and a= v^2/r, we can solve for the velocity, v = √(Tr/m)
how to solve this problem?To solve this problem, we need to use the concept of centripetal force, which is the force that keeps an object moving in a circular path. The centripetal force is given by the equation:
F = m * a
where F is the centripetal force, m is the mass of the object and a is the centripetal acceleration.
The centripetal acceleration is given by the equation:
a = v^2 / r
where v is the velocity of the object and r is the radius of the circular path.
The radius of the circular path in this case is the length of the string (12cm). The angle of 35° is not needed for solving the problem.
Now we can substitute the value of a into the equation for the centripetal force:
F = m * (v^2 / r)
We know the force is the tension of the string, T, and the mass of the object, m. So we can write
T = m * (v^2 / r)
Given that T=ma and a= v^2/r, we can solve for the velocity, v = √(Tr/m)
Without knowing the mass of the object and the tension of the string we can't find the velocity of the spinning ball.
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a 2 uc point charge and a 4 uc point charge are a distance l apart. where should a thurd point charge be placed so that the electrical force on that thurd charge is zero?
This will create a system of three equal-sized point charges, and since the forces between point charges are equal and opposite, the forces on the third charge will cancel each other out and there will be no net force.
What is the charge ?
The charge is the amount of money that a person is asked to pay in exchange for goods or services. Charges can be in the form of a fixed price, a fee based on time spent or a percentage of the total cost. Charges may also be based on the complexity or difficulty of the job. Payment can be in the form of cash, check or credit card. Charges are typically due at the time of service, unless other arrangements have been made in advance.
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what is the velocity (in cm/s) of an object which moves 44 m in 2 s?
The velocity (in cm/s) of an object which moves 44 m in 2 s is 220 cm/s.
As per the given data:
Distance given as 44 m.
Time gives as 2s.
Velocity is to be calculated.
Conversion to distance from m to cm.
1m=100 cm
44m=4400 cm
The formula for velocity is:
Velocity = Distance / Time
Velocity = 4400 / 2
=220 cm/s
The velocity of the object is 220 cm/s.
Velocity is a vector expression of the displacement that an object or particle undergoes with respect to time . The standard unit of velocity magnitude (also known as speed ) is the meter per second (m/s). Alternatively, the centimeter per second (cm/s) can be used to express velocity magnitude.
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If a room has dimensions of 350m and width of 200m, calculate the number of square tiles of length 5m would be needed to tile the entire room
The number of the square tiles that would be needed to tile the entire room is 2,800 tiles.
What is the area of the room?
The area of the room is calculated by applying the following formula as shown below.
Mathematically, the formula for area of a rectangular room is given as;
A = L x B
where;
L is the length of the rectangular roomB is the breadth of the rectangular roomArea = 350 m x 200 m
Area = 70,000 m²
The area of the square tiles is calculated as follows;
A = L x L
where;
L is the length of the square tileA = 5 m x 5 m
A = 25 m²
The number of the square tiles that would be needed to tile the entire room is calculated as follows;
n = area of the entire room / area of each square tile
n = ( 70,000 m² ) / ( 25 m² )
n = 2,800
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rutherford created a planetary model for atoms after his experiments. imagine if rutherford's idea that electrons radiate energy while orbiting around a nucleus was true. which other model or scientific idea would have been strengthened by this?
Rutherford's idea that electrons radiate energy while orbiting around a nucleus would have strengthened the idea of quantum mechanics, which explains the behavior of particles at the subatomic level.
what is mechanics ?
Mechanics is a branch of science that studies the behavior of physical objects, their interactions, and the forces that act on them. It is sometimes referred to as the fundamental science, as it provides the underlying principles of many other sciences, such as engineering, aeronautical science, and medicine.
Mechanics is divided into two main branches: classical mechanics and quantum mechanics. Classical mechanics studies the motion of macroscopic objects, such as automobiles and aircraft, and is a cornerstone of engineering and the physical sciences. Quantum mechanics is the study of the behavior of microscopic objects, such as atoms and molecules, and is a cornerstone of modern chemistry and physics.
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A planet P revolves around the Sun in a circular orbit, with the Sun at the center, which is coplanar with and concentric to the circular orbit of Earth E around the Sun. P and E revolve in the same direction. The times required for the revolution of P and E around the Sun are TP and TE. Let Ts be the time required for P to make one revolution around the Sun relative to E: show that l/Ts = 1/TE - 1/Tp, Assume Tp; > TE.
When Ts is the time required for P to make one revolution around the Sun relative to E and Tp, Te are the times required for the revolution of P and E around the Sun, the relation between them is 1/Ts = 1/Te - 1/ Tp.
Substitute θe = ωe Ts and θp = ωp Ts in the equation θe = θp + 2 π
ωe Ts = 2 π + ωp Ts ---(1)
Substitute ωp = 2 π/ Tp and ωe = 2 π/Te
Placing above equations in (1), we have,
(2 π/Te) Ts = 2 π + (2 π/ Tp) Ts
On re-arranging, we have,
2 π/Te - 2 π/ Tp = 2 π/Ts
Eliminating 2 π in all the terms, we get,
1/Te - 1/ Tp = 1/Ts
Thus, the relation 1/Ts = 1/Te - 1/ Tp is proved.
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a 0.5 kg block has an acceleration of 0.2 m/s^2 when a force is exerted on it. a second block has an acceleration of 0.1 m/s^2 when given the same force. what is the mass of the second block?
The second block weighs one kilogram.
What is mass?A mass measurement reveals how much matter is there in an object.
Usually, the metric systems of grams, kilograms, and tonnes are used to compute it.
How do you determine it?As we know that F = ma.
Considering that the force applied to the first block and the second block are equal.
The acceleration of the first block is 0.2 m/s^2 and the acceleration of the second block is 0.1 m/s^2, we can set up the following equation:
F = ma
where F is the force exerted on both blocks, m1 is the mass of the first block (0.5 kg), a1 is the acceleration of the first block (0.2 m/s^2), m2 is the mass of the second block, and a2 is the acceleration of the second block (0.1 m/s^2).
So substituting,
F = m1 * a1 = m2 * a2
Rearranging for m2
m2 = F / a2
m2 = (F / 0.1 m/s^2)
m2 = (F/0.1) = m1 * (a1/a2)
m2 = (0.5kg * (0.2/0.1)) = 1kg
So, the mass of the second block is 1 kg.
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A car starts moving from a full stop at a traffic light. The car covers a distance of 75 meters at an acceleration of 012 meters per second squared. What is the magnitude of the final velocity of the car?
Answer:
The final velocity of the car can be calculated using the equation:
v = u + at
where:
v = final velocity
u = initial velocity (since the car starts from a full stop, the initial velocity is 0)
a = acceleration (0.12 m/s^2)
t = time (unknown, but can be calculated using the distance and velocity)
To find the time, we can use the distance and velocity formula:
d = ut + (1/2)at^2
75 = 0 + (1/2)(0.12)(t^2)
t = sqrt(75/(1/2)(0.12))
t = sqrt(625/0.06)
t = sqrt(10416.67)
t = 102.41 seconds
Now we can substitute the values for u, a and t into the first equation to find the final velocity:
v = u + at
v = 0 + (0.12)(102.41)
v = 12.29 m/s
The magnitude of the final velocity of the car is 12.29 m/s.
he centers of a 12 kg lead ball and a 70 g lead ball are separated by 14 cm. part a part complete what gravitational force does each exert on the other? express your answer using two significant figures. f
5.6 * 10⁻⁷N gravitational force will exert on both lead balls.
Given information:
mass of 1st ball(m₁) = 12kg
mass of 2nd ball (m₂) = 70g
distance between both balls (r)= 14cm
To find gravitational force
F = Gm₁m₂/r²
= 5.6 N
The force of attraction between any two bodies is directly proportional to the product of their millions and is equally proportional to the forecourt of the distance between them.
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a car speedometer has a 8% uncertainty. what is the range of possible speeds (in km/h) when it reads 25 km/h? (there are two answers. enter the lowest value first and the highest value second. for each answer, enter a number.)
The range of possible speeds (in km/h) at the given uncertainty is 23 km/h to 27 km/h.
What is uncertainty in measurement?
Uncertainty is defined as the range of possible values within which the true value of the measurement lies.
The range of possible speeds (in km/h) when it reads 25 km/h is calculated as follows;
the uncertainty of the speed = ± 8%
The lowest speed reading = ( 100% - 8%) x 25 km/h
= ( 92 % ) x 25 km/h
= 0.92 x 25 km/h = 23 km/h
The highest speed reading = ( 100% + 8%) x 25 km/h
= ( 108 % ) x 25 km/h
= 1.08 x 25 km/h = 27 km/h
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a load of 60 j 80 has a current of 4.80 a with a phase angle of 30o, the total power absorbed/supplied by the load is:
P is power, V is voltage, I is current, and θ is the phase angle between the current and voltage. In this case, the voltage across the load is 60V, the current is 4.8A, and the phase angle is 30 degrees.
Calculation-Z= 60+j80
Z = R+ jx
So X = 80
Current I = 4.8 A
Reactive power =(i)2 X
= 4.8x4.8x80= 1843 vars absorbed by load.
What is 3-phase voltage?The three independent wires required for a three-phase connection, on the other hand, are used to transmit electricity. The voltage of a single-phase power supply system can go as high as 230 Volts. However, it can transmit a voltage of up to 415 Volts on a three-phase connection.
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A metal bar is in the xy-plane with one end of the bar at the origin. A force F = (7.25 N)i + (-3.03 N)j is applied to the bar at the point x = 2.76 m, y = 3.05 m.
a. What is the position vector r for the point where the force is applied?
b. What are the magnitude of the torque with respect to the origin produced by F?
c. What is the direction of the torque with respect to the origin produced by F?
The position vector is 2.76i+3.05j, the magnitude of the torque is 20.0055 N*m, and the direction of the torque is perpendicular to the plane.
What is force?A force is an influence that has the power to alter an object's motion. An object with mass can change its velocity, or accelerate, as a result of a force.
a. The position vector for the point where the force is applied is given by the coordinates of the point in the xy-plane. In this case, the point is at (2.76 m, 3.05 m), so the position vector is:
r = 2.76i + 3.05j
b. The torque with respect to the origin produced by F is given by the cross product of the position vector and the force vector. The magnitude of the torque is given by the formula:
τ = r x F
τ = (2.76i + 3.05j) x (7.25i - 3.03j)
τ = ((3.05)(-3.03) - (2.76)(7.25))i + ((2.76)(-3.03) - (3.05)(7.25))j
τ =20.0055 N*m
c. The direction of the torque with respect to the origin is given by the cross product of the position vector and the force vector, the direction is perpendicular to the plane formed by the position vector and the force vector. The direction of the torque is out of the plane in a direction perpendicular to the plane.
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A spring has a length of 0.180 m when a 0.300 kg mass hangs from it, and a length of 0.750 m when a 2.10 kg mass hangs from it. (a) What is the force constant (in N/m) of the spring? N/m (b) What is the unloaded length (in m) of the spring?
The force constant of the spring is 30.6N and the unloaded length of the spring is 0.57m.
The force constant (k) of the spring is calculated by the equation
k = (mass× gravity) / (change in length).
In this question, the mass is the difference between the two masses (2.10 kg - 0.300 kg = 1.800 kg),
And the change in length is the difference between the two lengths (0.750 m - 0.180 m = 0.570 m).
Therefore, the force constant of the spring is
(1.800 kg × 9.8 m/s²) / (0.570 m) = 30.6 N/m.
The unloaded length of the spring is determined by subtracting the length of the spring when the 0.300 kg mass hangs from it (0.180 m) from the length of the spring when the 2.10 kg mass hangs from it (0.750 m). Therefore, the unloaded length of the spring is
0.750 m - 0.180 m = 0.570 m.
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A cell membrane has a resistance and a capacitance and thus a characteristic time constant.
What is the time constant of a 9.0-nm-thick membrane surrounding a 0.040-mm-diameter spherical cell? Assume the resistivity of the cell membrane as 3.6×107 ??m and the dielectric constant is approximately 9.0.
The membrane's time constant is 2.87 ms. The resistance and capacitance of RC circuits are used to calculate the time constant. The time constant's value is determined in milliseconds.
How can the time constant be determined?The time constant is calculated using the equation,
T = R*C in seconds.
Describe the time constant.In physics and engineering, the parameter that specifies how a first-order, linear time-invariant (LTI) system reacts to a step input is known as the time constant, which is typically symbolized by the Greek letter tau. The time constant is the main property of a first-order LTI system.
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