The time it takes to travel 2.5cm from its mean position is 1.048 secs.
Describe the mean position.When there is no net force exerted on the body, it is in the mean position, sometimes referred to as the equilibrium position. An oscillating particle's phase: This shows how the particle is vibrating right now.
Given,
case(1), V1=4ms−1,y1=3m,
case(II), V2=3ms−1,y2=4m.
We know that, V=ω√( a^2−y^2 )
Case (I) 4=ω√(a^2−3^2)..(i)
Case(II) 3=ω√(a^2−4^2) …(ii)
Dividing (i) by (ii) , we get
16a^2−256=9a^2−81
After solving we get,
a=√25 =5m
Substituting it in (i), we get
ω= 4 / 4 = 1 rads^−1
When the particle is 2.5 meters from the extreme location, its distance from the mean position is given by the equation x = 5−2.5 = 2.5m.
Given that SHM must note the time from an extreme point, we will apply the relation:
x=acosωt.
2.5= 5cos 1 × t = 5 cos t
=> cost = 2.5/5 = 1/2 = cos ( [tex]\pi[/tex]/3 )
=> t = [tex]\pi[/tex] / 3 = 22 /7 x 3 = 1.048 secs
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Which wavelength, of electromagnetic radiation has the highest energy?
5.9x10^-3 m
O2.45x10^8 m
4.29x10^3 m
8.1x10^-8 m
The characteristics of electromagnetic radiation include amplitude (brightness), wavelength, frequency, and period. We have shown that the frequency of a light wave is proportional to its energy by the equation E = h v or E=hnu
so
Radiation with a wavelength of 8.1 X 10^-8 m has the highest energy
Why is it called electromagnetic?When a charged particle, like an electron, changes its velocity—that is, when it is accelerated or decelerated—electromagnetic radiation is created. The charged particle is responsible for losing the energy of the electromagnetic radiation that is thus created.Since the electric and magnetic fields are oscillating, the waves of energy are known as electromagnetic (EM). They are categorized by scientists based on their frequency or wavelength, from high frequency to low frequency (short to long wavelength).The characteristics of electromagnetic radiation include amplitude (brightness), wavelength, frequency, and period. We have shown that the frequency of a light wave is proportional to its energy by the equation E = h v or E=hnuTo learn more about : Electromagnetic radiation
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The number of _____ in the atom is what determines whether the atom is a potassium atom, a hydrogen atom, or an oxygen atom.
a ball of mass 0.140 kg moving with speed of 1.72 m/s hits a wall and bounces back with the same speed in the opposite direction. what is the change in the ball's kinetic energy?
Answer:
[tex]0\; {\rm J}[/tex].
Explanation:
The speed of an object is a scalar quantity and is independent of the direction in which the object is moving.
The kinetic energy of an object depends only on the mass and speed of this object. If an object of mass [tex]m[/tex] is moving at a speed of [tex]v[/tex], the kinetic energy of this object will be [tex](1/2)\, m\, v^{2}[/tex].
As a result, as long as the speed of the object stays unchanged, changes in the direction of motion of the object will not affect the kinetic energy of the object.
In this question, the speed of this ball was initially [tex]1.72\; {\rm m\cdot s^{-1}}[/tex]. The kinetic energy of this object was initially [tex](1/2)\, (0.140\; {\rm kg})\, (1.72\; {\rm m\cdot s^{-1}})^{2} \approx 0.207\; {\rm J}[/tex].
The speed of this ball stays the same after the ball bounces back from the wall: [tex]1.72\; {\rm m\cdot s^{-1}}\![/tex]. As a result, the kinetic energy of this object would still be [tex](1/2)\, (0.140\; {\rm kg})\, (1.72\; {\rm m\cdot s^{-1}})^{2} \approx 0.207\; {\rm J}[/tex].
As a result, the change in the kinetic energy of this object would be [tex]0.207\; {\rm J} - 0.207\; {\rm J} = 0\; {\rm J}[/tex].
HELP PLEASE!!! PHYSICS!!!
The maximum horizontal range the value of θ be 45° then the total time of flight exists 3.7 s.
What is meant by kinematic equation?When an object has either a constant velocity or constant acceleration, kinematic equations can be used to help in problem-solving.
A branch of physics called kinematics, which originated in classical mechanics, defines how points, bodies, and systems of bodies move without taking into account the forces that are responsible for their motion.
Generally from the kinematic equation
v = u - g × t/2
So v exists the velocity at maximum height and the value is v = 0 m/s
substitute the values in the above equation, we get
0 = u - 9.8 × 3.7/2
simplifying the above equation, we get
⇒ u = 18.13 m/s
Here u exists the initial velocity of the dart as it leaves that gun.
Generally the horizontal range of the dart is mathematically represented as
[tex]$R=\frac{u^2 \sin 2 \theta}{g}$$[/tex]
For maximum horizontal range the value of θ = 45°.
So, R max = [tex]$\frac{18.13^2 \sin 2(45)}{9.8} \\[/tex]
⇒ R max =33.54 m
Therefore, the total time of flight is t = 3.7 s.
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a particle is moving along the curve . as the particle passes through the point , its -coordinate increases at a rate of units per second. find the rate of change of the distance from the particle to the origin at this instant.
When the coordinate increases at a rate of units per second, the rate of change of the distance from the particle to the origin at this instant would be 0.3 units per second.
What is a coordinate and how it increases at units per second?Coordinate is the system in Mathematics in which different points or position is connected or other geometric elements on the manifold.By using coordinate phenomena, we may also find points on Earth.When a particle moves along the curve its coordinate increases at a rate of units per second, its rate increases.The distance from the particle to the origin at this instant will increase at 0.3 units per second.We use coordinates in geography too to determine the location coordinates in specific regions.To know more about the coordinates visit:
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What occurs when the velocity of Earth is doubled?
a. The orbit of Earth around the Sun becomes smaller
c. The Earth escapes the Sun
b. The orbit of Earth does not change
d. The orbit becomes more elliptical
couldnt comment on anyone elses/add answers so to anyone looking for it, THE ANSWER IS C - THE EARTH ESCAPES THE SUN!!!!
When the velocity of Earth is doubled, the orbit of Earth around the Sun becomes smaller ( A ).
v = √ G M / r
v = Orbital velocity
G = Gravitational constant
M = Mass of the celestial body
r = Radius of the celestial body
Rearranging for r,
√ r = √ ( G M ) / v
Squaring on both sides,
r = G M / v²
If the velocity of Earth is doubled,
v' = 2v
r' = G M / v'²
r' = G M / ( 2 v )²
r' = G M / 4 v²
r' = r / 4
So the radius of orbit of Earth becomes one-fourth its initial radius.
Therefore, when the velocity of Earth is doubled, the orbit of Earth around the Sun becomes smaller ( A ).
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two oppositely charged but otherwise identical conducting plates of area 2.50 square centimeters are separated by a dielectric 1.80 millimeters thick, with a dielectric constant of k
A material's relative static permittivity (or static relative permittivity) under specific conditions is a measure of how well it focuses electrostatic lines of flux. It is the ratio of electrical energy stored when a potential is applied to the permittivity of a vacuum. The relative static permittivity equals the relative permittivity calculated at zero frequency. The dielectric constant, relative dielectric constant, and static dielectric constant are other synonyms for relative static permittivity. While these phrases are still widely used, they are unclear and have been rejected by certain standards groups. There are two reasons for the potential uncertainty. depending on the context, relative permittivity
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What is the major different between the particles in a liquid and a gas of the same substance at the same temperature?
The particles of liquid are closely packed together than the particles of gas.
What is a liquid?A liquid is a state of matter that contains particles that are loosely packed and that takes the shape of its container.
A gas is a state of matter that contains particles that are randomly placed and has no definite shape.
Temperature is the property of matter that defines how hot or cold a particular state of matter is.
When liquid and gas is being compared, the particles of the liquid is loosely packed together while the particles of gas are randomly placed and which collided freely with the walls of its container.
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What is a similar Mid-Ocean Ridge on dry land compared to?
Answer:
Mid-ocean ridges around the globe are linked by plate tectonic boundaries and the trace of the ridges across the ocean floor appears similar to the seam of a baseball.
Explanation:
Does the law of conservation of energy apply to open systems? Explain.
No, law of conservation of energy is not applicable to open systems.
Law of conservation of energy states that energy present anywhere can neither be created nor be destroyed by any means, it can only be converted from one form of energy to other form of energy. It means total energy of an isolated system remains same.
An open system is a system that can exchange energy and matter from the surroundings. The flow of energy takes places in an open system. Therefore, the law of conservation does not apply to an open system as it can lose or gain energy, hence its total energy will not be constant and will violate law of conservation of energy.
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A child sits on the floor and twirls a 0. 100 kg ball connected to a 1. 0 m string in a horizontal circle along the floor with a speed of 2. 0 m/s. What forces are acting on the ball?.
The correct response that shows the forces that act on the ball is "all of the above."
What force acts on the ball?Let us recall that a force is that which is able to impart acceleration to a body and also to change the direction of the object. We also have to know that from the Newton's law, force must always be able to produce an acceleration in an object.
As the child is sitting on the floor and is twirling the ball round the circle there are three forces that acts on the ball and all these force are given as;
1) Tension force
2) Gravitational force
3) Normal force
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A dropped object reaches 41.65m/s in its fall. How long did it take to reach this speed?
With the use of formulas, it will take time 4.25 seconds for the object to reach the speed 41.65 m/s when dropped.
What is Speed ?Speed is the distance travelled per time taken. It is a scalar quantity and it is measured in m/s
If an object is dropped and reached 41.65 m/s in its fall, Let us first know the height at which it was dropped by using the formula
v² = u² + 2as
Since the object was dropped, u = 0
41.65² = 0 + 2 × 9.8 × H
1734.72 = 19.6H
H = 1734.72/19.6
H = 88.51 m
To know how long it takes to reach this speed, let us use this formula
H = ut + 1/2gt²
where u = 0
88.51 = 1/2 × 9.8 × t²
88.51 = 4.9t²
t² = 88.51/4.9
t² = 18.06
t = √18.06
t = 4.25 s
Therefore, it takes 4.25 seconds of time to reach this speed.
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please help will give 5 points to the best brainlist 30 points
1. A plank balance with outside support has a 30 kg child 3 meters left of the fulcrum and a 45 kg child 2 meters RIGHt of the fulcrum what will happen when the outside support is removed?
A. The right side of the plank will sink
B. Range is not enough info
C.The left side of the plank will sink
D.The plank will be balanced
2. A simple plank balance has a 500 gram weight 50 cm right of the fulcrum where should you place a 200 gram weight to balance it
A. 250 cm left of the fulcrum
B. 100cm left of the fulcrum
C.125 cm left of the fulcrum
D. 20 cm left of the fulcrum
3. A simple plank balance is used to weigh a mystery box when the bod is placed 5 marks left of the fulcrum it is balanced by a 10 kg weight placed 4 marks right of the fulcrum
What is the mass of the mystery box?
A. 10 kg
B. 16 kg
C. 12.5 kg
D. 8 kg
Based on the principle of moments, the correct options are:
1. If the outside support is removed, the plank will be balanced; option D
2. To balance the simple plank balance, place the 200 gram weight 125 cm left of the fulcrum; option C
3. the mass of the mystery box is 8 kg; option D
What is the principle of moments?The principle of moments is the principle that describes the turning effect produced by forces.
The principle of moments states that for a system of balanced forces, the sum of the clockwise moment about a point equals the sum of the anticlockwise moment about the same point.
The formula for calculating moments about a poit is given below:
Moment = force x perpendicular distance from the fulcrumConsidering the given questions:
1. Assuming the fulcrum is the balance point of the plank balance.
Taking left as anticlockwise and right as clockwise motion
Anticlockwise moment = 30 * 3
Anticlockwise moment = 90
Clockwise moment = 45 * 2
Anticlockwise moment = 90
Therefore, the plank balance is balanced.
2. Assuming the fulcrum is the balance point of the plank balance.
Taking left as anticlockwise and right as clockwise motion
Clockwise moment = 500 * 50
Anticlockwise moment = 25000
Anticlockwise moment = 200 * d
Anticlockwise moment = 200d
200d = 25000
d = 125 cm to the left of the fulcrum
3. Assuming the fulcrum is the balance point of the plank balance.
Taking left as anticlockwise and right as clockwise motion
Clockwise moment = 10 * 4
Anticlockwise moment = 40
let the mass be m
Anticlockwise moment = m * 5
Anticlockwise moment = 5m
5m = 40
m = 8 kg
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If a box is being pushed 50-N to the left, what would the reaction force be
The reaction force of the box will be 50 N in opposite direction.
What is Newton's third law of motion?
Newton's third law of motion states that for every action there is equal and opposite reaction.
According to this law, the force exerted on an object is equal to the reaction experienced by the object.
The applied force is equal in magnitude but opposite in direction to the reaction of the impact.
Mathematically, this law can be illustrated as follows;
Fa = -Fbb
where;
Fa is the applied forceFb is the reaction experiencedThus, we can conclude that if a box is pushed to the left by a certain force, the reaction force will be equal in magnitude to the applied force but opposite in direction.
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Please solve for the tension force {F=ma
The tension force of the system is 395 N.
The acceleration of the system is 3.95 m/s².
What is the net force on the system?
The net force on the system is obtained by applying Newton's second law of motion as follows;
Net vertical force on the masses;
Fu = m₁g cosθ + m₂g
where;
m₁ is first massm₂ is second massg is acceleration due to gravityFu = (100 kg x 9.8 m/s²) cos(25) + (100 kg x 9.8 m/s²)
Fu = 1,868.2 N
Apply the formula for Newton's second law of motion,
m₂a - Ff = -m₁a
where;
F is the tension forceFf is the frictional forcea is the acceleration of first massm is the mass of the systemm₂a + m₁a = Ff
a(m₂ + m₁) = Fu sinθ
a = Fu sinθ / (m₂ + m₁)
a = (1868.2 x sin25) / (100 + 100)
a = 3.95 m/s²
The tension force is calculated as follows;
F(tens) = m₂a
F(tens) = 100 kg x 3.95 m/s² = 395 N
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what can you say about the specific heats of a and b? what can you say about the specific heats of a and b? the specific heat of the object a is greater than the specific heat of the object b. the specific heat of the object b is greater than the specific heat of the object a. the specific heats of both the objects are approximately the same. the information given is insufficient to compare the specific heats of the objects.
The information given is insufficient to compare the specific heat of the objects.
The specific heat capacity, commonly known as the specific heat capacity or cp in thermodynamics, is the product of the heat capacity of a sample of a substance and its mass. Informally, it is the quantity of heat that has to be added to a substance's mass in order to raise its temperature by a given amount. J kg 1 K, or specific heat capacity, is the SI unit for temperature. The specific heat capacity of water, for instance, is 4184 J kg 1 K1, or the amount of energy needed to elevate 1 kilogram of water by 1 K in temperature.
For each state of matter, specific heat capacity differs and frequently fluctuates with temperature.
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the 0.5???????? collar c starts from rest at ???? and slides with negligible friction on the fixed rod in the vertical plane. determine the velocity ???? with which the collar strikes end ???? when acted upon by the 5 ???? force, which is constant in direction. neglect the small dimensions of the collar.
The velocity with which the collar strikes end B is 2.32 m/s.
How to calculate the work done by external forces on a body?
We conclude from the work energy theorem that any work performed on a body results in a change in total energy.
Given, mass of the collar = m = 0.5 kg
Therefore, effective weight of the collar = m*g = (0.5)*(9.81) = 4.905 N
Force acting on the collar = 5 N
We know, work done by external forces equates to the change in kinetic energy of the body.
Thus, ΔU = T ⇒ 0.5 * 0.5 * (v²-0) = 0.2[5 cos(30°) - 5 sin(30°) + 4.905)
⇒ v² = 5.39 m²/s² ⇒ v = 2.32 m/s.
Therefore, the velocity with which the collar strikes end B when acted upon by the 5N force is 2.32 m/s.
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A hockey puck slides across the ice at a constant velocity. Is it in equilibrium? Why or why not? Select ALL the answers that are true.
A hockey puck slides across the ice at a constant velocity. Is it in equilibrium? Why or why not? Select ALL the answers that are true.
Yes, it is in equilibrium.
There is no net force acting on it because there is no acceleration.
There is a net force acting on it because it's moving with a constant velocity.
No, it's not in equilibrium.
Answer:
The first two answers are true.
Since F = M a and there is no acceleration there is no net force acting on the puck.
a scale used to weigh fish consists of a spring hung from a support. the spring's equilibrium length is 10.0 cm. when a 4.0 kg fish is suspended from the end of the spring, it stretches to a length of 13.4 cm.
The spring constant approximately is 1153 N/m.
When an 8 kg fish is suspended in the spring, its new length is 16.8 cm.
How to find the spring constant?
The details provided are
The spring's length is 10.0 cm (L1).
Fish mass, m = 4 kg
L2, the spring's final length, is 13.4 cm
The spring's extension is determined by the formula:
x = L2 - L1 x = 13.4 cm - 10.0 cm x = 3.4 cm
The following formula is used to get the spring's spring constant;
F = kx
mg = kx
k = mg/x = 4 * 9.8/0.034 = 1,152.94M/m
The new spring extension when an 8 kg fish is hung on it;
x = mg/k = 8 * 9.8/1152.94 = 0.068m = 6.8cm
6.8 cm + 10 cm = 16.8 cm is the spring's new length.
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kami is walking through the airport with her two-wheeled suitcase. the suitcase handle is tilted 42 ∘∘ from vertical, and kami pulls parallel to the handle with a force of 120 nn. (force is measured in newtons, abbreviated nn.)
Vertical part of The F Sign theater will be equal to F. Our result is 76.4 degrees. I apologize, 76.4 Newton. This completes the vertical element of the solution.
In this issue, a luggage handle is pushed while inclined 46 degrees from vertical. 110 Newtons of force, parallel to the handle, are applied. Additionally, we must determine the magnitudes of the horizontal and vertical components of the applied force. so make a vertical angle. 46 degree force is additional.
As a result, the angle with the horizontal will be equal to 44 3 degrees, or roughly 93 - 46 degrees. Therefore, the title to 40 40 is the angle with the positive x-axis of the force. Therefore, fx's horizontal component is F.
Cost information 110 Newton times 44 degrees of force. This results in F. X. about 79.1 Newtons. We must determine the vertical component in section B. Because of this, the vertical component F. I will equal the F Sign theater. Our result is 76.4 degrees. I apologize, 76.4 Newton. This completes the vertical element of the solution.
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if the astronaut throws the tool with a force of 16.0 n , what is the magnitude of the acceleration a of the astronaut during the throw? assume that the total mass of the astronaut after she throws the tool is 80.0 kg .
The magnitude of the acceleration a of the astronaut during the throw is 0.2 m/s².
What is astronaut?
An astronaut is a person who has been prepared, outfitted, and sent into space as part of a human spaceflight program to serve as a commander or crew member. The phrase is occasionally used to refer to anyone who travels into space, including scientists, politicians, journalists, and tourists, despite the fact that it is typically designated for professional space travelers.
According to Newton's second law, an object's acceleration is inversely proportional to its mass and proportional to both the resulting force and the resultant force.
∑F = m. a
where, F = force, m = mass, a = acceleration of astronaut.
As per the information given in the question,
F = 16 N
M = 80 kg
putting these value in the equation,
16 = 80a
a = 16/80
a = 0.2 m/s²
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which of the following is a derived Unit (A) kg (B) meter (c) kelvin (D) Newton.
Answer:
D,Newton
Explanation:
b/c it is derived unit
Answer:
The newton
Explanation:
is drived because of its definition consist of multiplication of three defined base unit and nothing else it's not independently defined
A toy car with a mass of 2 kg is at rest. a horizontal force is applied to the trolley and it starts to move in the direction of the applied force at 4m * s ^ - 1 calculate the kinetic energy of the toy car after it has experienced this force
The kinetic energy of the toy car after it has experienced the force is: 16 Joules
The kinetic energy formula and the procedure we will use is:
K.E. = 1/2 * m * v²
Where:
v = speedm = massJoules = Kg m²*s²Information of the problem:
v = 4 m/sm = 2 kgApplying kinetic energy formula we get:
K.E. = 1/2 * m * v²
K.E. = 1/2 * 2 kg (4 m/s)²
K.E. = 1/2 * 2 kg * 16 m²/s²
K.E. = 1/2 * 32 kg *m²/s²
K.E. = 16 kg*m²/s²
K.E. = 16 Joules
What is kinetic energy?It is the energy possessed by a body due to its relative motion. It is usually expressed in Joules (J).
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A car with a mass of 1260 kg is travelling at 38.0 m/s when the driver sees a traffic jam ahead. If the average braking force in modern vehicles is 2010 N, how far will the car go before coming to a stop?
With the application of third equation of motion, the car go as far as 451.3 meters before coming to a stop
What is Braking Force ?Braking Force is the force applied for an object to decelerate or stop. It is also the product of mass and its deceleration.
Given that a car with a mass of 1260 kg is travelling at 38.0 m/s when the driver sees a traffic jam ahead. If the average braking force in modern vehicles is 2010 N,
The given parameters are;
Mass m = 1260 KgInitial velocity u = 38 m/sForce F = 2010 NAcceleration a = ?Distance s = ?Before we know how far will the car go before coming to a stop, we need to know its deceleration.
F = ma
2010 = 1260a
a = 2010/1260
a = 1.6 m/s²
Now, let us applied third equation of motion
v² = u² - 2as
v = 0 since the car is coming to rest.
0 = 38² - 2 × 1.6 × s
0 = 1444 - 3.2s
3.2s = 1444
s = 1444/3.2
s = 451.25 m
Therefore, the car go as far as 451.3 meters before coming to a stop.
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What is the torque experienced by a magnetic dipole moment m placed
with its axis at angle theta with a uniform magnetic field B?
The torque experienced by a magnetic dipole moment M placed with its axis at angle theta with a uniform magnetic field B is τ = MB sin θ
Torque = Force * Perpendicular distance
F = m * B
F = Force
m = Magnetic pole strength
B = Magnetic field
τ = Torque
τ = m * B * 2 * l * sin θ
Magnetic dipole moment, M = 2 * m * l
τ = ( 2 * m * l ) * B * sin θ
τ = M B sin θ
Therefore, the torque experienced by a magnetic dipole moment M placed with its axis at angle theta with a uniform magnetic field B is τ = MB sin θ
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Which type of material is the best thermal conductor?
A.nonmetal
B.metalloid
C.metal
if you set out to explore the surface of the moon, you would wear a thermally insulated space suit. in such activity, you might expect to generate roughly 4 kj of heat per kilogram of mass per hour. if all this heat were retained by your body, how much would your body temperature increase per hour owing to this rate of heat production? (assume that your heat capacity is roughly that of water) what time limit would you recommend for a moon walk under these conditions?
Temperature rise hourly = 0.956 degree Celsius
2.3245 hours are the time limit for the process.
How would you define specific heat?The amount of heat needed to raise a substance's temperature by one degree Celsius in one gram is known as specific heat. Calories or joules per gram per degree Celsius are frequently used as the units of specific heat. For instance, water has a specific heat of 1 calorie (4.186 joules) per gram per degree Celsius.
Heat produced per hour per 1kg = 4 KJ
Heat absorbed per kg per hour = temperature rise x specific heat of body
4 = temp rise x 4.184 KJ/kgK
temperature rise per hour = 4/4.184 = 0.956 C
For calculation of time limit
increase of C = ( increase in F) x 5/9
= 4 x 5/9 = 2.22
Now per hour rise = 0.956 C
time required to rise per 2.22 C = ( 2.22 /0.956)
= 2.3245 hours
Hence time limit = 2.3245 hours
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Earth's mass is approximately 80 times the moon's mass. The centers of Earth and the moon are 384,000,000 meters apart. Earth exerts a gravitational force of 1.99x10²⁰ newtons on the moon. What is the magnitude of the gravitational force the moon exerts on Earth?
The magnitude of the gravitational force the moon exerts on Earth if Earth exerts a gravitational force of 1.99 x 10²⁰ newtons on the moon is 1.99 x 10²⁰ N
F = G m1 m2 / r²
F = Gravitational force of attraction
m1 = Mass of Earth
m2 = Mass of moon
r = Distance between moon and Earth
In this equation all the mentioned variables are constant for both gravitational force exerted by moon on Earth and by Earth on moon. So the value will be equal for both.
The equation mentioned above is the result of Newton's law of gravitation. This law states that any object in the universe attracts another object with a force which is directly proportional to product of both the masses and inversely proportional to the squared value of distance between them.
Therefore, the magnitude of the gravitational force the moon exerts on Earth is 1.99 x 10²⁰ N.
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which of these stars has the greatest surface temperature? which of these stars has the greatest surface temperature? a 30msun main-sequence star a supergiant a star a cepheid variable star
A 30MSUN main-sequence star has the greatest surface temperature.
What is a star's main sequence stage?A star spends the majority of its life in the main sequence. It is incredibly long compared to other phases of a star's "life"; Our Sun formed in around 20 million years, but it will remain a main sequence star for roughly 10 billion years (1 × [tex]10^{10}[/tex] years) before transforming into a red giant.What main-sequence star is the biggest?Despite being the largest star known, R136a1 is not the largest because it only has a radius of around 30 times that of the sun. UY Scuti, a hypergiant with a radius almost 1,700 times greater than the sun, is the biggest star currently known to science.What occurs during the star phase of the main sequence?During the main-sequence stage, stars emit energy in the form of heat and light. Deep inside of them, nuclear fusion reactions produce this energy. Helium is created when reactions between hydrogen nuclei fuse. Stars stay in this stage for almost 90% of their lives.
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A fridge uses about 200 watts of power. This means that the fridge uses 200 joules per second of energy. If managed to turn 1 g of matter into energy, according to Einstein's equation E = mc², how long would I be able to power my fridge with that energy?
Answer:
Approximately [tex]4.50 \times 10^{11}\; {\rm s}[/tex].
Explanation:
The speed of light is [tex]c \approx 3.00\times 10^{8}\; {\rm m\cdot s^{-1}}[/tex].
Note that the standard unit of energy, joule, is a derived unit. In terms of the standard base units:
[tex]\begin{aligned}1\; {\rm J} &= (1\; {\rm N})\, (1\; {\rm m}) \\ &= (1\; {\rm kg \cdot m \cdot s^{-2}})\, (1\; {\rm m}) \\ &= 1\; {\rm kg \cdot m^{2} \cdot s^{-2}} \end{aligned}[/tex].
Apply unit conversion and ensure that the unit of mass is in the standard unit kilogram ([tex]{\rm kg}[/tex]):
[tex]\begin{aligned} m &= 1\; {\rm g} \times \frac{1\; {\rm kg}}{10^{3}\; {\rm g}} &= 10^{-3}\; {\rm kg}\end{aligned}[/tex].
Apply the equation [tex]E = m\, c^{2}[/tex] to find the energy equivalent to [tex]m = 10^{-3}\; {\rm kg}[/tex] of matter:
[tex]\begin{aligned}E &= m\, c^{2} \\ &= (10^{-3}\; {\rm kg})\, (3.00 \times 10^{8}\; {\rm m\cdot s^{-1}})^{2} \\ &= 9.00\times 10^{13}\; {\rm kg \cdot m^{2} \cdot s^{-2}} \\ &= 9.00\times 10^{13}\; {\rm J} \end{aligned}[/tex].
Divide energy [tex]E[/tex] by power [tex]P[/tex] to find the duration [tex]t[/tex] of the power consumption:
[tex]\begin{aligned} t &= \frac{E}{P} \\ &\approx \frac{9.00 \times 10^{13}\; {\rm J}}{200\; {\rm J \cdot s^{-1}}} \\ &= 4.50 \times 10^{11}\; {\rm s}\end{aligned}[/tex].
In other words, the energy equivalent to [tex]1\; {\rm g}[/tex] of matter could power this fridge for approximately [tex]4.50 \times 10^{11}\; {\rm s}[/tex].