The total heat required to melt all the ice is 46.44 kcal.
To melt the ice, we need to first raise its temperature to 0 degrees Celsius, at which point it will start to melt. The mass of the ice on the window is given by the formula
m = (density)(volume) = (900 kg/m3)(0.6 cm)(1 m2) = 0.54 kg.To raise the temperature of this ice to 0 degrees Celsius, we need to transfer a certain amount of heat to it. The heat required is given by the formula
Q = (mass)(specific heat capacity)(temperature change) = (0.54 kg)(0.5 cal/g*K)(12 K) = 3.24 kcal.Once the ice has reached 0 degrees Celsius, it will start to melt. The heat required to melt the ice is given by the formula
Q = (mass)(latent heat of fusion) = (0.54 kg)(80 cal/g) = 43.2 kcal.Therefore, the total heat required to melt all the ice is 3.24 kcal + 43.2 kcal = 46.44 kcal.
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WILL GIVE BRAINLIEST.
Objects 1 and 2 attract each other with a gravitational force of 18.0 units. If the distance separating Objects 1 and 2 is doubled, then the new gravitational force will be ____ units.
If the distance separating Objects 1 and 2 is doubled, then the new gravitational force will be 72.0 units.
What is Gravitational force?The force of attraction that operates on all matter is known as gravity, or gravitational force in mechanics. It is by far the weakest known force in nature and plays no role in determining the internal properties of everyday matter. It controls the orbits of objects in places, the structure, and the evolution of stars, galaxies, and the universe as a whole.
On Earth, every object has a weight, or downward gravitational force, proportional to its mass, and the mass of the Earth acts on them. The acceleration that gravity causes in a falling item serves as a gauge of its strength. The acceleration of gravity at the Earth's surface is around 9.8 meters per second (32 feet) per second. For each second her body is in free fall, its velocity increases by about 9.8 meters per second. On the moon, the acceleration of a free-falling object is approximately 1.6 meters per second.
The gravitational force among two objects can be written as:
F = G×m₁×m₂/r²
Where G is the gravitational constant, m₁ and m₂ are the masses of both objects and r is the distance between them.
Now, we have that F = 18 .0 units.
Let's change r to 2r, the new force is:
F' = G×m₁×m₂/(2r)²
F' = G×m₁×m₂/4r²
F'/F = (G×m₁×m₂/4r²)/G×m₁×m₂/r²
F' = 4 F
F' = 4 × 18.0
F' = 72 units
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why does a costal area have less variation in temperature than a noncostal area? 30 points. I need help...
what are the wavelengths of electromagnetic wave in free space that have the following frequencies? (a) 2.00 ✕ 1019 hz pm (b) 4.50 ✕ 109 hz cm
The wavelengths of electromagnetic waves can be calculated using the formula:
wavelength = speed of light / frequency
where the speed of light is approximately 3.00 x 10^8 m/s.
(a) For a frequency of 2.00 x 10^19 Hz, the wavelength can be calculated as:
wavelength = 3.00 x 10^8 m/s / 2.00 x 10^19 Hz
wavelength = 1.50 x 10^-11 meters, or 15 picometers (pm)
(b) For a frequency of 4.50 x 10^9 Hz, the wavelength can be calculated as:
wavelength = 3.00 x 10^8 m/s / 4.50 x 10^9 Hz
wavelength = 6.67 x 10^-2 meters, or 66.7 centimeters (cm)
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What is the mass of a student who weighs 618 Newton?
Answer:
63.01 kg is the mass of the student whose weight is 618 Newton
Mass of student is 63 kilogram (Approx.)
Given that;
Weight of a student = 618 Newton
Find:
Mass of student
Computation:
We know that;
Gravitational acceleration g = 9.8 m/s²
So,
Mass = Weight / Gravitational acceleration
Mass of student = 618 / 9.8
Mass of student = 63.06
Mass of student = 63 kg (Approx.)
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A uniform bar 15m long balanced on a pivot at its midpoint. A boy of mass 55kg sits on one arm of the bar at a point 5m away from the pivot. What mass can be placed 2m away from the other end of the bar to keep the bar horizontally
The mass at the other end of bar will be 50g .
what is mass
It is the fundamental property of matter , every single property which exist in this world has mass
Mass never can be 0 .
So , the system is in equilibrium
let mass of the body be m
55×5= m×5.5
m= 5 5 × 5 /. 5.5
m= 5 0g
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137.5 kg mass can be placed 2m away from the other end of the bar to keep the bar horizontally.
What does horizontal mean?Any straight line traveling from left to right or right to left is a horizontal line. If two points on a line share the same Y-coordinates, the line is said to be horizontal in coordinate geometry. It is derived from the word "horizon." In other words, the horizon or x-axis is always parallel to the horizontal lines.In the coordinate plane, a horizontal line is a straight line drawn from right to left or from left to right, perpendicular to the x-axis. In other words, a horizontal line is a straight line with an intercept solely on the y-axis, not the x-axis.To keep the bar horizontal, the right and left side torques must be equal:
\(F_{1} d_{1} =F_{2} d_{2}\)
\(F_{2} =F_{1} \frac{d_{1} }{d_{2} }\)
\(=(55.9.8)\frac{5}{2}\)
=1347.5 N.
Convert this force of gravity into mass:
\(F_{2} =m_{2} g,\)
\(m_{2} =\frac{F_{2} }{g}\)
\(=\frac{1347.5}{9.8}\)
=137.5 kg.
The answer is 137.5 kg.
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Vector C is 6.28 m long in a105° direction. Vector D is3.09 m long in a 233° direction.Find the magnitude of theirvector sum.
The magnitude of the vector sum = 5.01 m
Explanations:Step 1: Find the horizontal and vertical components of vector C
\(\begin{gathered} \text{The horizontal component: C}_x=\text{ }6.28\cos 105 \\ C_x=\text{ }-1.625m \\ \text{The vertical componet: C}_y=\text{ 6.28}\sin 105 \\ C_y=\text{ }6.066m \end{gathered}\)Step 2: Find the horizontal and vertical components of vector D
\(\begin{gathered} \text{The horizontal component: D}_x=\text{ 3.09}\cos 233 \\ D_x=\text{ }-1.86m \\ \text{The vertical componet: D}_y=\text{ 3.09}\sin 233 \\ D_y=\text{ }-2.468m \end{gathered}\)Step 3: The vector sum (A) is found by adding the x and y componets of vectors C and D
\(\begin{gathered} A_x=C_x+D_x \\ A_x=\text{ -1.625 + (-1.86)} \\ A_x=\text{ }-3.485m \end{gathered}\)\(\begin{gathered} A_y=C_y+D_y \\ A_y=\text{ 6.066+}(-2.468) \\ A_y=\text{ }3.598m \end{gathered}\)The vector sum is therefore:
\(\begin{gathered} A=A_xi+A_yj \\ V\text{ = }-3.485i+3.598j \end{gathered}\)Step 4: The magnitude of the vector sum is therefore:
\(\begin{gathered} |V|\text{ = }\sqrt[]{(-3.485)^2+(3.598)^2} \\ |V|\text{ = }\sqrt[]{25.09} \\ |V|\text{ = }5.01 \end{gathered}\)The magnitude of the vector sum = 5.01 m
The motor ___________ currents listed in NEC Tables 430.247 through 430.250 shall be used to determine the ampacity of motor circuit conductors and short-circuit and ground-fault protection.
The motor full load currents listed in NEC Tables 430.247 through 430.250 shall be used to determine the capacity of motor circuit conductors and short-circuit and ground-fault protection. This is further explained below.
What is currents?Generally, Moving through an area of water or air where there is less movement than the water or air itself, an eddies
In conclusion, Using the full load currents indicated in NEC Tables 430.247 through 430.250, the capacity of motor circuit conductors and short-circuit and ground-fault protection for motors should be determined.
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The following figures show the spectral types of four main-sequence stars. Rank them based on the time each takes, from longest to shortest, to go from a protostar to a main-sequence star during the formation process.
Longest to shortest time:
-M6
-G2
-A5
-O9
G2-type stars take the longest time, while O9-type stars take a shorter time to go from a protostar to a main-sequence star during the formation process.
Based on the spectral types provided, the order of the stars from the longest to the shortest time taken to go from a protostar to a main-sequence star during the formation process is as follows:
1. G2
2. O9
- Stars with lower masses, like G2-type stars, take longer to form because they have a lower rate of fusion and lower pressure at their cores.
- On the other hand, O9-type stars have a higher mass, which results in a higher rate of fusion and higher pressure at their cores.
This means they will form faster than G2-type stars.
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A jet airplane is flying through the very bottom of a vertical circle of radius 4000 m with a constant speed of 300 m/s. What is the magnitude of the plane's acceleration (in m/s/s)
The magnitude of the plane's acceleration is 75 m/s². When a jet airplane is flying through the very bottom of a vertical circle, it is experiencing both centripetal acceleration towards the center of the circle and gravitational acceleration due to the Earth's gravity.
The centripetal acceleration (ac) is given by the formula:
ac = (v² / r)
where v is the velocity of the plane and r is the radius of the circle.
In this case, the velocity of the plane is 300 m/s and the radius of the circle is 4000 m. Plugging these values into the formula, we get:
ac = (300² / 4000)
ac = 22500 / 4000
ac = 5.625 m/s²
Additionally, the gravitational acceleration (ag) experienced by the plane is equal to the acceleration due to gravity (g), which is approximately 9.8 m/s².
Therefore, the magnitude of the plane's acceleration is the vector sum of the centripetal acceleration and the gravitational acceleration:
Magnitude of acceleration = √(ac² + ag²)
Magnitude of acceleration = √((5.625)² + (9.8)²)
Magnitude of acceleration = √(31.640625 + 96.04)
Magnitude of acceleration = √(127.680625)
Magnitude of acceleration ≈ 11.307 m/s²
The magnitude of the plane's acceleration while flying through the very bottom of a vertical circle with a radius of 4000 m and a constant speed of 300 m/s is approximately 75 m/s². This acceleration is a combination of the centripetal acceleration towards the center of the circle and the gravitational acceleration due to the Earth's gravity.
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The energy of the ground state in the bohr model is -13.6 ev. the energy of the n = 2 is:________
The energy of the ground state in the Bohr model is -13.6 eV. Now, we need to find the energy of the n = 2 state.
In the Bohr model, the energy of an electron in any given energy level (n) is given by the formula:
E = -13.6 eV/n^2
Substituting n = 2 into the formula, we get:
E = -13.6 eV/2^2
= -13.6 eV/4
= -3.4 eV
Therefore, the energy of the n = 2 state in the Bohr model is -3.4 eV.
The Bohr model describes the energy levels of electrons in an atom. The ground state is the lowest energy level, corresponding to n = 1. The energy of the ground state is -13.6 eV. As we move to higher energy levels (n > 1), the energy increases. In this case, we are interested in the energy of the n = 2 state. Using the formula E = -13.6 eV/n^2, we substitute n = 2 to find that the energy of the n = 2 state is -3.4 eV. This means that the n = 2 state has higher energy than the ground state, but still lower than higher energy levels.
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A negatively charged balloon touching a wooden wallPulls positive charge on the wall surface toward it Pushed negative charge in a wall away from itPolarizes molecules on the wall All of the above
Given that the balloon is negatively charged and it is touching a wooden wall, the ballon will perform all the actions given in the answer choices.
A negatively charged balloon will pull positive charge on the wall surface towards it, since opposite charges attract each other.
Also, the negatively charged balloon touching a wooden wall will push any negative charge in the wall away from it. This is because like charges repel each other.
The negatively charged balloon also polarizes the molecules on the wall. This is because in molecules, atoms are bonded together since protons in one atom attract the electrons in the cloud of another atom.
Therefore, the correct choice is All of the above
ANSWER:
All of the above
Which force causes all objects with mass to attract one another?
A. Compression
B. Electrical force
C. Magnetic force
D. Gravity
A 600N force is applied to a 3kg lab cart at an angle of 200 (cart is initially at rest). When the cart reaches a speed of 6m/s the force stops
pushing on the cart.
(a) Through what distance was the force applied?
(b) The cart continues to roll down the incline plane. What is the change in potential energy of
the cart as it moves from the top of the track to the bottom of the track?
(c) What is the work done by the normal force throughout the motion?
(d) What is the kinetic energy of the cart when it is at the bottom of the track?
A) The force was applied through a distance of 0.03 meters.
B) The change in potential energy of the cart is 18 J.
C) The work done by the normal force throughout the motion is 0
D) The kinetic energy of the cart at the bottom of the track is 18 J.
To find the distance through which the force was applied, we can use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy.
The work done by the force is given by:
W = Fd cos(theta)
where F is the force, d is the distance through which the force is applied, and theta is the angle between the force and the displacement.
Since the cart starts from rest, its initial kinetic energy is zero. When it reaches a speed of 6 m/s, its final kinetic energy is given by:
Kf = (1/2)mv^2 = (1/2)(3 kg)(6 m/s)^2 = 18 J
Therefore, the work done by the force is:
W = Kf - Ki = 18 J - 0 J = 18 J
Using the formula for work, we can solve for the distance d:
d = W / (F cos(theta)) = 18 J / (600 N cos(200)) = 0.03 m
Therefore, the force was applied through a distance of 0.03 meters.
(b) The change in potential energy of the cart as it moves from the top of the track to the bottom of the track can be calculated using the formula:
ΔPE = mgh
where m is the mass of the cart, g is the acceleration due to gravity, and h is the vertical height difference between the top and bottom of the track.
Assuming the track is frictionless, the initial potential energy of the cart at the top of the track is equal to its final kinetic energy at the bottom of the track:
Ki = Kf
(1/2)mv² = mgh
Solving for the change in potential energy, we get:
ΔPE = mgh = (1/2)mv² = (1/2)(3 kg)(6 m/s)² = 18 J
Therefore, the change in the potential energy of the cart is 18 J.
(c) The work done by the normal force throughout the motion is zero, because the normal force is perpendicular to the displacement of the cart. Therefore, the work done by the normal force is:
W = Fd cos(theta) = 0
(d) The kinetic energy of the cart when it is at the bottom of the track is given by:
Kf = (1/2)mv² = (1/2)(3 kg)(6 m/s)² = 18 J
Therefore, the kinetic energy of the cart at the bottom of the track is 18 J.
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It takes the planet Jupiter 12 years to orbit the sun once in a nearly circular orbit. Assuming that Jupiter's orbit is truly circular, what is the distance from Jupiter to the Sun, given that the distance from the earth to the sun is 1.5 × 10 11 m ?
Jupiter is about 5.2 astronomical units away from the Sun.
Jupiter's distance from the Sun, also known as its astronomical unit (AU), can be calculated using Kepler's third law of planetary motion.
Kepler's third law states that the square of the orbital period of a planet (in years) is proportional to the cube of its average distance from the Sun (in astronomical units).
Using the fact that Jupiter takes 12 years to orbit the Sun and the average distance from the Earth to the Sun is 1.5 x 10^11 meters (which is approximately equal to 1 astronomical unit), we can solve for Jupiter's distance from the Sun.
The formula for Kepler's third law can be written as:
(Period of Jupiter)^2 = (Distance of Jupiter from the Sun)^3 / (Distance of Earth from the Sun)^3
Plugging in the values, we get:
(12^2) = (x^3) / (1^3)
where x is Jupiter's distance from the Sun in astronomical units.
Solving for x, we get:
x = (12^2)^(1/3) = 5.2 astronomical units
So, Jupiter is about 5.2 astronomical units away from the Sun.
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Tim is given a new quantity called Electrical Current. Which of the following questions could Tim ask to determine whether the quantitiy is a vector or a scalar?
O A Who discovered electric current?
O B. What are the base units of electric current?
OC. What is the symbol for electric current?
O D. Does electric current have a direction?
Answer:
B. What are the base units of electric current?
To find out that the electric current is a vector or scalar quantity, Tim should ask what is the symbol for electric current. Hence, option C is correct.
What are vector and scalar quantities?A physical quantity whose size is a complete description of it. Volume, density, speed, energy, mass, and time are a few examples of scalars. Other quantities, like as force and velocity, are referred to as vectors since they have both magnitude and direction.
Real numbers that are typically positive but not always characterize scalars.
In physics, a vector is a quantity with both magnitude and direction. It is often represented by an arrow whose length is proportional to the magnitude of the quantity and whose direction is the same as that of the quantity. A vector does not have position, while having magnitude and direction. In other words, a vector's shape is unaltered if it is shifted parallel to itself as long as its length is unaltered.
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How did Edwin Hubble measure the distance to the Andromeda Galaxy?
He measured its parallax.
He used main-sequence fitting.
He applied the period-luminosity relationship to Cepheid variables.
He deduced it from redshift.
Answer:
D- he applied the period- luminosity relationship to cepheid variables
mix 4 L of 30°C water is 6 L of 40°C water and you’ll have water at what temperature?
Answer:
dont know
Explanation:
need points
Q.7. For a system with a transfer function of G(s)=- co² s² +2a+w² if the natural frequency is 0.5 and the damping ratio is 1.3, which of the following statements is correct regarding the unit step response of the system?
O A) Damped
O B) Undamped
O C) Underdamped
O D) Crittically Damped
O E) Overdamped
The system described by the transfer function G(s) = -co² s² + 2a + w², with a damping ratio of 1.3 and a natural frequency of 0.5, has an overdamped unit step response. So, the correct option is (E)
The transfer function of the system is given as G(s) = -co² s² + 2a + w², where co represents the damping ratio, a represents an arbitrary constant, and w represents the natural frequency of the system. We are given that the natural frequency is 0.5 and the damping ratio is 1.3.
To determine the type of unit step response, we need to analyze the damping ratio (co) in relation to the critical damping value (co_critical).
The critical damping ratio (co_critical) is defined as the value where the system is on the threshold between being overdamped and underdamped. It is given by the formula co_critical = 2 * sqrt(a * w²).
In our case, the natural frequency (w) is 0.5, so we can calculate co_critical as follows: co_critical = 2 * sqrt(a * 0.5²).
Since the damping ratio (co) is given as 1.3, we can compare it with co_critical to determine the type of unit step response.
If co > co_critical, the system is considered overdamped (Option E).
If co = co_critical, the system is considered critically damped (Option D).
If co < co_critical, the system is considered underdamped (Option C).
Based on the given values, we can determine that the system is overdamped (Option E) because the damping ratio (1.3) is greater than the critical damping ratio.
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Drag racer can reach a speed of 53 m/s over a distance of 120 m. What distance can you reach a speed of 85 m/s
Answer:
Explanation:
53m/s = 120m
85m/s = ?
cross multiply
53x = 120 x 85
53x = 10200
x = 192.45m
What most directly determines an object's state of matter? (Please help)
A. the shape and texture of the object
B. the location of the object on Earth
C. the size of the particles in the object
D. the amount of motion and energy that the object's particles have
Answer:
I would say D
Explanation:
because the amount of energy in molecules of matter determines the state of matter
(if I'm wrong I'm sorry)
A hover board is moving at 6 m/s . If it slows down at a rate of -3 m/s per second, how long is the board in the air before coming to rest? Round to 4 decimal places if necessary
Explanation
a uniformly accelerated motion is the one in which the acceleration of the particle throughout the motion is uniform,to fidn the time take we can use the formula:
\(\begin{gathered} t=\frac{v_f-v_1}{a} \\ where \\ v_f\text{ is the final velocity} \\ v_{i\text{ }}\text{ is the initail velocity} \\ a\text{ is the acceleration, so} \end{gathered}\)Step 1
a)Let
\(\begin{gathered} v_i=6\text{ }\frac{m}{s} \\ v_f=0(\text{ rest\rparen} \\ a=-3\frac{m}{s^2} \end{gathered}\)b) now, replace
\(\begin{gathered} t=\frac{v_{f}-v_{1}}{a} \\ t=\frac{0-(-6\frac{m}{s})}{3\frac{m}{s}} \\ t=2\text{ seconds} \end{gathered}\)therefore, the answer is 2 seconds
I
A box with a mass of 5 kg accelerates its speed in a straight line, increasing it from 5 m/s to 8 m/s, due to the application of an external force acting for a duration of 2.0 s. Calculate the average strength of this force.
Explanation:
acceleration a = v-v0/ t = ∆V/∆t
first we must calculate F = M.A
The average strength of this force will be 7.5 N
What is force?Force is defined as the push or pull applied to the body. Sometimes it is used to change the shape, size, and direction of the body.
Force is defined as the product of mass and acceleration. Its unit is Newton.
Given data;
Force,F = ?
Mass,m = 5 kg
Initial velocity,u=5 m/sec
Final velocity,v==8 m/sec
Time period,t=2.0 sec
The average strength of this force will be;
F=m[(v-u)/t]
F= 5 kg × [(8 m/sec -5 m/sec)/2.0 sec]] m/s²
F= 7.5 N
Hence the average strength of this force will be 7.5 N
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(force on plane surface) a swimming pool is 20 m long and 7.0 m wide. determine (a) the magnitude and (b) location of the resultant force of the water on the vertical end (narrow side) of the pool where the depth is 2.6 m.
(a) The magnitude of the resultant force of the water on the vertical end of the pool can be found using the hydrostatic equation, which states that the pressure at any point in a fluid is equal to the weight of the fluid column above it.
The pressure at the surface of the pool is equal to the weight of the water column above it, which is equal to the density of water multiplied by the gravitational acceleration and the height of the water. This gives us:
F = ρghA
where ρ is the density of water, g is the gravitational acceleration, h is the height of the water, and A is the area of the vertical end of the pool. Substituting the given values into this equation gives us:
F = 1000 kg/m^3 * 9.8 m/s^2 * 2.6 m * 20 m * 7.0 m = 2.68 x 10^6 N
Therefore, the magnitude of the resultant force of the water on the vertical end of the pool is 2.68 x 10^6 N.
(b) The location of the resultant force of the water on the vertical end of the pool is at the surface of the pool, at the point where the depth is 2.6 m.
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A computer hard disk starts from rest, then speeds up with
an angular acceleration of 190 rad/s until it reaches its final
angular speed of 7200 rpm. How many revolutions has the disk
made 10. 0s after it starts up?
The final angular speed of the hard disk is 766.9 rad/s, and it takes 4.04 s to reach this speed with an angular acceleration of 190.0 \(rad/s^2\).
To take care of this issue, we want to utilize the equation that relates the rakish removal of a pivoting object to its precise speed increase, time, and beginning rakish speed. The equation is given by:
θ = 1/2 * α * \(t^2\) + ω0 * t + θ0
Where θ is the complete point pivoted by the plate, α is the precise speed increase, t is the time slipped by, ω0 is the underlying rakish speed, and θ0 is the underlying point.In this issue, the circle begins from rest, so ω0 = 0. The rakish speed increase of the plate is given as 190 \(rad/s^2\), and the last precise speed is 7200 rpm.
We want to change the last precise speed from rpm over completely to rad/s by increasing it with 2π/60. In this manner, the last precise speed is 240π rad/s.We can now substitute these qualities into the recipe and compute the absolute point pivoted by the circle after 10.0 seconds:
θ = 1/2 * 190 \(rad/s^2\) * \((10.0 s)^2\) + 0 rad/s * 10.0 s + 0 rad
θ = 9500 rad
To change this point over completely to the quantity of insurgencies, we partition it by 2π, as one unrest compares to a point of 2π radians. Consequently:
θ in transformations = 9500 rad/(2π rad/unrest) = 1507 upheavals
Accordingly, the plate has made 1507 insurgencies after 10.0 seconds from its underlying state.
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The complete question is:
A computer hard disk starts from rest, then speeds up with an angular acceleration of 190.0 \(rad/s^{2}\)until it reaches a final angular speed of 7300.0 rpm.
(a) What is the final angular speed in units of rad/s? rad/s.
(b) How long does it take for the disk to reach this angular speed? s
(c) How many revolutions (not radians) does it make in getting to the final angular speed? rev
(d) Once the disk reaches its final angular speed, it continues rotating at this same speed. How many revolutions has the disk made 10.0 s after it started up from rest?
If you want brainiest, can you help me?
Answer
?????
Explanation:
Which of the following is true about an object's weight but NOT about its mass? (S8P3.b)
A. It may vary depending on the object's location.
B. It is a measure of the amount of matter in the object.
C. It is measured in kilograms or grams.
D. It would be the same on the moon as it is on Earth.
The mass of a body is 12 kg. What is the resulting acceleration if a forced 6 N is applied on it in the direction of motion ?
Answer:
0.5 m/s²Explanation:
The acceleration of an object given it's mass and the force acting on it can be found by using the formula
\(a = \frac{f}{m} \\ \)
f is the force
m is the mass
We have
\(a = \frac{6}{12} = \frac{1}{2} = 0.5 \\ \)
We have the final answer as
0.5 m/s²Hope this helps you
The steps for conducting a basic search are listed below. Put the steps in the correct order.
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What is basic research?Basic research can be used to learn more about a particular issue; it might not produce an idea or a solution, but it can be used to develop theories and scientific understanding.
Fundamental information from basic research can be used to carry out applied research. Applied research is utilized to address relevant, concrete issues. Research into and examination of materials and sources with the goal of establishing facts and drawing new findings.
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expalin how waves energy and matter are related
a 4.4-kg block attached to a spring of force constant 284 n/m undergoes simple harmonic motion of amplitude 0.21 m. what is the energy of the mass-spring system?
The energy of the mass-spring system is approximately 12.407 J.
The energy of a mass-spring system can be calculated using the formula for the total mechanical energy, which is the sum of the potential energy and the kinetic energy.
To find the potential energy, we can use the formula for the potential energy of a spring:
Potential energy = (1/2) x k x x²
where k is the force constant of the spring and x is the displacement from the equilibrium position.
Given that the force constant of the spring is 284 N/m and the amplitude of the motion is 0.21 m, we can calculate the potential energy as follows:
Potential energy = (1/2) x 284 N/m x (0.21 m)²
Simplifying this expression gives:
Potential energy = 0.5 x 284 N/m x 0.0441 m²
Potential energy = 6.12984 Nm
To find the kinetic energy, we can use the formula for kinetic energy:
Kinetic energy = (1/2) x m x v²
where m is the mass of the block and v is the velocity of the block.
Since the motion is simple harmonic, the maximum velocity occurs at the equilibrium position, where the block passes through the midpoint of its oscillation. At this point, the velocity is maximum and equal to the angular frequency (ω) times the amplitude (A). The angular frequency can be calculated using the formula:
Angular frequency (ω) = √(k/m)
Given that the mass of the block is 4.4 kg and the force constant of the spring is 284 N/m, we can calculate the angular frequency as follows:
Angular frequency (ω) = √(284 N/m / 4.4 kg)
Simplifying this expression gives:
Angular frequency (ω) = √(64.5455 N/kg)
Angular frequency (ω) = 8.0345 rad/s
Therefore, at the equilibrium position, the maximum velocity is:
v = ω x A
v = 8.0345 rad/s 0.21 m
v = 1.6872 m/s
Now we can calculate the kinetic energy:
Kinetic energy = (1/2) x 4.4 kg x (1.6872 m/s)²
Simplifying this expression gives:
Kinetic energy = 0.5 x 4.4 kg x 2.8439 m²/s²
Kinetic energy = 6.27716 J
The total mechanical energy of the mass-spring system is the sum of the potential energy and the kinetic energy:
Total mechanical energy = Potential energy + Kinetic energy
Total mechanical energy = 6.12984 J + 6.27716 J
Total mechanical energy = 12.407 J
Therefore, the energy of the mass-spring system is approximately 12.407 J.
In conclusion, the energy of the mass-spring system is approximately 12.407 J.
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