A free neutron (which is therefore not in an atomic nucleus) decays into a proton and a antineutrino according to

with a half-life of 10.23 minutes. Free neutrons are formed all the time during the nuclear processes i
the sun. How fast must a group of neutrons just formed in the sun travel in order for half of them to reach the earth before they disintegrate?

The rod is hung 8 cm from its endpoint instead of 28 cm, the maximum potential energy and thus the maximum angle of displacement will be smaller.

What is Potential Energy?

Potential energy is the energy possessed by an object due to its position or state. It is the energy that can be stored in an object as a result of its position or configuration. The amount of potential energy an object has depends on its position or configuration relative to other objects or systems, as well as the forces acting on it. Potential energy can be converted into other forms of energy, such as kinetic energy or thermal energy, depending on the situation.

The maximum displacement angle observed in a simple pendulum system is directly related to the initial potential energy and the gravitational potential energy of the system. As the pendulum is pulled away from its resting position, it gains potential energy, which is then converted to kinetic energy as it swings back towards the center.

Learn more about Potential Energy from the given link

https://brainly.com/question/14427111

#SPJ1

the linear diameter of the object is approximately 77.28 meters for an object that has an angular diameter of 10 arcs ends and a distance of 50,000 meters

The angular diameter of an object is the angle it subtends at the observer's eye, while the linear diameter is the physical size of the object. We can use trigonometry to relate the angular diameter, the distance to the object, and the linear diameter.

If an object has an angular diameter of 10 arc seconds (10"), it subtends an angle of:

θ = 10" / 3600 = 0.0027778 radians

The linear diameter, D, is related to the distance, d, and the angle, θ, by the formula:

tan(θ/2) = D/2d

Rearranging this formula gives:

D = 2d * tan(θ/2)

Substituting the given values, we get:

D = 2 * 50,000 m * tan(0.0027778/2)

D = 2 * 50,000 m * tan(0.0013889)

D = 2 * 50,000 m * 0.0007728

D = 77.28 m

Learn more about  linear diameter  here:

https://brainly.com/question/13572468

#SPJ1

the coefficient of kinetic friction is approximately 0.689, the mechanical advantage is 4/3, and the velocity ratio is 1.22.

the coefficient of kinetic friction, mechanical advantage, and velocity at the bottom of the ramp, we need to use the conservation of energy principle. At the top of the ramp, the block has potential energy given by mgh, where m is the mass of the block, g is the acceleration due to gravity, and h is the height of the ramp. At the bottom of the ramp, the block has kinetic energy given by (1/2)m[tex]v^2[/tex], where v is its velocity. Assuming there is no energy loss due to friction, we can equate the potential energy at the top of the ramp to the kinetic energy at the bottom of the ramp.

1-Ep = Ek + Wf

mgh = 1/2 * m[tex]v^2[/tex]+ μk * mg * d

Solving for the coefficient of kinetic friction, we get:

μk = (mgh - 1/2 * m[tex]v^2[/tex]) / (mgd)

μk = (2gh - [tex]v^2[/tex]) / (2gd)

μk = (2 * 9.81 m/[tex]s^2[/tex] * 3 m - [tex]v^2[/tex]) / (2 * 4 m)

μk = 0.689

2-The mechanical advantage of the ramp is given by the ratio of the length of the ramp to the height from which the block falls:

MA = d / h = 4 m / 3 m = 4/3

3-VR = v / sqrt(2gh)

Ep = Ek + Wf

mgh = 1/2 * m[tex]v^2[/tex] + μk * mg * d

Solving for v, we get:

v = sqrt(2gh - 2μkgd) = 5.77 m/s

So the velocity ratio is:

VR = 5.77 m/s / sqrt(2 * 9.81 m/[tex]s^2[/tex] * 3 m) = 1.22

Learn more about kinetic friction here:

https://brainly.com/question/13754413

#SPJ1

The wheel completes approximately 1.91 revolutions during its 2 seconds of acceleration.

The car's uniform acceleration, a = v/t, is provided. The distance it moves in the given amount of time, t, can be calculated using the kinematic equations for linear motion. By multiplying this distance by the tyre's diameter, we can calculate the number of revolutions. The formula f = vf/rtire yields the ultimate angular speed.

To resolve this issue, we can use the kinetic equation shown below:

θ = 1/2 α t²

To begin with, we can use the following method to determine the wheel's ultimate angular velocity:

ωf = ωi + αt

where i represents the starting angular speed. (which is zero in this case).

ωf = ωi + αt

ωf = 0 + 6 rad/s² × 2 s

ωf = 12 rad/s

Next, we can calculate the number of rotations made during the two seconds of acceleration using the formula for the angle the wheel made:

θ = 1/2 α t²

θ = 1/2 × 6 rad/s^2 × (2 s)²

θ = 12 rad

We can divide this by 2 (the number of radians in a rotation) to get the number of revolutions:

of revolutions = θ / 2π

of revolutions = 12 rad / 2π

of revolutions ≈ 1.91 revolutions.

To know more about acceleration visit:-

https://brainly.com/question/12550364

#SPJ1

At the start of a race, a cyclist's velocity is zero because they are not yet moving. However, as they begin to pedal and move forward, their velocity increases. The direction of the velocity depends on the direction in which they are moving.

Acceleration is the rate at which velocity changes over time. In the case of a cyclist at the start of a race, their acceleration would be positive, as they are increasing their velocity. The magnitude of the acceleration would depend on various factors such as the force of the cyclist's pedaling, the mass of the cyclist and the bike, and the friction between the tires and the ground.

As the cyclist continues to pedal, their velocity will increase, and their acceleration may either increase or decrease depending on the external factors that influence their motion. Ultimately, the cyclist's velocity and acceleration will determine their position and speed relative to other cyclists in the race.

The density of the pipe is 1.17 × [tex]10^{6}[/tex] kg/m³ (in SI units).

What is density?

To find the density of the pipe, we need to know its volume and mass. We can calculate the volume of the pipe using the formula for the volume of a cylinder:

Volume of cylinder = π * (radius)² * height

where the radius is half of the diameter.

The external radius of the pipe is 21 cm (0.21 m), and the internal radius is 14 cm (0.14 m). We don't know the height of the pipe, but we can assume that it is equal to the difference between the external and internal radii, since the pipe is assumed to have uniform thickness. Therefore, the height of the pipe is:

Height = (external radius) - (internal radius)

Height = 0.21 m - 0.14 m

Height = 0.07 m

Using these values, we can calculate the volume of the pipe:

Volume = π * ((0.21)² - (0.14)²) * 0.07

Volume = 0.00137 m³

Now we can find the density of the pipe by dividing its mass by its volume:

Density = Mass / Volume

Since the mass is given as 1600 kg, we have:

Density = 1600 kg / 0.00137 m³

Density = 1.17 × [tex]10^{6}[/tex] kg/m³

Therefore, the density of the pipe is 1.17 × [tex]10^{6}[/tex] kg/m³ (in SI units).

To know more about density, visit:

https://brainly.com/question/13145021

#SPJ1

Complete question is: a pipe of external and internal diameters of 42cm and 28cm respectively has a mass 1600kg. the density of the pipe is 1.17 × [tex]10^{6}[/tex] kg/m³ (in SI units).

The angular momentum of a system is conserved when there is no external torque acting on the system.

This is known as the law of conservation of angular momentum. Mathematically, it can be expressed as:

L = Iω

where L is the angular momentum of the system, I is the moment of inertia, and ω is the angular velocity. If the net external torque acting on the system is zero, then the angular momentum of the system remains constant.

This law has many applications in physics, including in rotational motion, celestial mechanics, and quantum mechanics. For example, the conservation of angular momentum explains why a spinning ice skater speeds up when they bring their arms inwards, and why the Earth's rotation remains constant over long periods of time.

To know more about torque please refer:

https://brainly.com/question/31248352

#SPJ1

Answer:

A uniformly charge d insulating rod of length 14.0cm is bent into the shape of a semicircle as shown in Figure. The rod has a total charge of −7.50μC. Find (a) the magnitude and (b) the direction of the electric field at O, the center of the semicircle.

1859579

expand

Medium

Solution

verified

Verified by Toppr

Due to symmetry, E

y

=∫dE

y

=0, and E

x

=−∫dEsinθ=−k

e

∫

r

2

dqsinθ

where dq=λds=λrdθ; the component E

x

is negative because charge q=−750μC, causing the net electric field to be directed to the left.

E

x

=−

r

k

e

λ

0

∫

π

sinθdθ=−

r

k

e

λ

(−cosθ)∣

0

π

=−

r

2k

e

λ

where λ=

and r=

π

L

. Thus,

E

x

=−

L

2

2k

e

∣q∣π

=−

(0.140m)

2

2(8.99×10

9

N⋅m

2

/C

2

)(7.50×10

−6

C)π

E

x

=−2.16×10

7

N/C

(a) magnitude E=

2.16×10

7

N/C

to minimize the change in motion of Car A due to the collision, we should decrease the mass of Car A relative to the mass of Car B.

Newton's Third Law states that for every action, there is an equal and opposite reaction. This means that in a collision between two objects, the force that Car A exerts on Car B is equal and opposite to the force that Car B exerts on Car A.

To minimize the change in motion of Car A due to the collision, we need to minimize the force that Car B exerts on Car A. This can be achieved by decreasing the mass of Car A relative to the mass of Car B.

We can see evidence of this from the system model in the activity. When Car A and Car B have equal masses, they experience equal and opposite forces during the collision, and their velocities are both affected to the same degree. However, when Car A has less mass than Car B, Car B experiences a greater force during the collision, but Car A experiences a smaller force. As a result, Car A experiences less of a change in velocity than it would if the masses were equal.

Learn more about velocities here:

https://brainly.com/question/17127206

#SPJ1

Because the cable was not connected properly is the most likely cause of the experiment's failure.

The coils of wire that make up an electromagnet have electricity running through them. When an electric current flows through the wire coils of an electromagnet, the coils act like a magnet because moving charges produce magnetic fields.

There are numerous factors to examine. Make sure an ordinary magnet can attract safety pins as a start. Then, verify that current is actually flowing through your wire. To do this, you need a strong enough battery, a wire with a low enough resistance, and a complete circuit connecting the two.

To learn more about electromagnet visit:

brainly.com/question/3427992

#SPJ1

Explanation:

speed = wavelength * frequency

          = 2 m * .0025/s = .005 m/s

The direction of the magnetic field with respect to your screen is d) to the left.

The upward force experienced by the proton indicates that the magnetic field is acting perpendicular to both the motion of the proton (due east) and the force it experiences. According to the right-hand rule for magnetic forces, if you point your thumb in the direction of the velocity of the charged particle (due east in this case) and your fingers in the direction of the force (vertically upward), then the direction your palm faces represents the direction of the magnetic field.

In this scenario, if you extend your left hand and point your thumb to the right (due east) and your fingers vertically upward, your palm will face to the left, indicating that the magnetic field is directed to the left. Therefore, option d) to the left is the correct answer. The magnetic field is perpendicular to the plane of the screen and points into the screen.

To learn more about magnetic field, here

https://brainly.com/question/14848188

#SPJ2

False. Not all online typing programs are free.

Online typing programs are software applications or websites that provide typing lessons, exercises, and tests to help individuals improve their typing skills.

These programs typically include a variety of lessons and exercises designed to help users learn proper typing techniques, improve their typing speed, and increase their accuracy.

There are online typing programs that are available for free. While some online typing programs do require a fee to access all features or to remove ads, there are also many free typing programs available that provide basic typing lessons and exercises.

More on online typing can be found here: https://brainly.com/question/16266184

#SPJ1

Consequently, the light's wavelength that caused the multiply-slit interference pattern was around 546 nm.

Solution and Justification: Interference patterns are produced when waves of identical (or what very similar) frequencies collide. The amplitudes of these waves may then either be raised (via constructive interference) or lowered.

Fringes are the light lines that alternate with the black lines in the interference pattern. The following equation can be used to calculate the wavelength for the double-slit experiment: dissipates ≈ xd / L.

To know more about interference patterns visit:

https://brainly.com/question/13081724

#SPJ1

The correct question is

Problem 4: Suppose a double-slit interference pattern has its third minimum at an angle of 0.256° with slits that are separated by 293 μm.

Randomized Variables

0 = 0.256°

d=293 μm

Calculate the wavelength of the light in nm.

Gra

Ded

Pote

Answer:

Q = h . A . (T (t) - T env)

the rate of loss of heat from a body is directly proportional to the difference in the temperature of the body and its surroundings.

Explanation:

Q = rate of heat transfered out of the body

h = heat transfers coefficient

A = heat transfer to surface area

T = temperature of the objects surface

T env = temperature of the environment

T (t) = time dependent temperature

The velocity of the ball 3 seconds after reaching the peak height is 30 m/s.

What is Velocity?

Velocity is a vector quantity that describes the speed and direction of motion of an object. It is defined as the rate of change of displacement of an object over time. In other words, velocity tells us how fast an object is moving and in what direction.

Assuming that air resistance is negligible, we can use the kinematic equations of motion to solve for the velocity of the ball 3 seconds after reaching the peak height.

Let's use the following variables:

a = acceleration = 10 m/[tex]s^{2}[/tex] (since the ball is continuing to accelerate downwards)

t = time = 3 seconds (since we want to find the velocity 3 seconds after reaching the peak)

v₀ = initial velocity = 0 m/s (since the ball has zero velocity at the peak)

v = final velocity (what we want to find)

Using the kinematic equation for velocity with constant acceleration:

v = v₀ + at

Substituting the given values:

v = 0 + 10 m/[tex]s^{2}[/tex] × 3 s

v = 30 m/s

Learn more about Velocity from the given link

https://brainly.com/question/24445340

#SPJ1

The frequency ratio between fi = 256 Hz and f2 = 320 Hz is 4:5.Adding the interval of a fifth to f2 (320 Hz) results in fs (400 Hz). The frequency ratio falfi is 5:8.The frequency of fs is 400 Hz.

The interval of a fifth in music theory is the distance between two notes that are five notes apart in a diatonic scale. For example, the distance between C and G is a fifth.

Frequency and pitch are related in music because the pitch of a note is determined by its frequency. Lower frequencies result in lower pitches, whereas higher frequencies result in higher pitches.

The relationship between frequency and pitch is logarithmic, meaning that a doubling of frequency results in an increase of one octave (a doubling of pitch).

To know more about frequency,visit:

https://brainly.com/question/5102661

#SPJ1

For a given length of the pendulum and acceleration of the cart, the maximum displacement angle can be determined using the above formulas.

What is Acceleration?

Acceleration can be positive or negative depending on the direction of the change in velocity. If an object is speeding up, the acceleration is positive, while if it is slowing down, the acceleration is negative.

(1) The maximum displacement angle observed in a pendulum experiment can be determined by the length of the pendulum and the acceleration due to gravity. According to the theory of simple harmonic motion, the period of a pendulum is directly proportional to the square root of its length and inversely proportional to the square root of the acceleration due to gravity.

The formula for the period of a pendulum is:

T = 2π * sqrt(L/g)

where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity (approximately 9.8 m/[tex]s^{2}[/tex]).

For a given length of the pendulum, the maximum displacement angle occurs when the pendulum is at the highest point in its swing (i.e., when its velocity is momentarily zero). At this point, all of the energy of the pendulum is potential energy (i.e., gravitational potential energy), and the angle is known as the maximum displacement angle or the amplitude.

The maximum displacement angle (θ) can be calculated using the formula:

θ = [tex]sin^{^-1(a/g)}[/tex]

where a is the acceleration of the cart.

Therefore, for a given length of the pendulum and acceleration of the cart, the maximum displacement angle can be determined using the above formulas.

(2) If the rod is hung 8 cm from its endpoint instead of 28 cm, the length of the pendulum (L) would be 20 cm. Using the same formula as above, the period of the pendulum would be:

T = 2π * sqrt(0.2/9.8) = 0.898 seconds

The maximum displacement angle can be calculated using the same formula as above:

θ = sin^[tex]sin^{^-1(a/g)}[/tex]

where a is the acceleration of the cart.

Learn more about Acceleration from given link

https://brainly.com/question/605631

#SPJ1

Answer: The sound level produced by a chorus of 43 singers will be 97.66 dB.

Explanation:

Let I, the intensity of a sound produced by a singer, therefore, the intensity of the sound produced by 43 singers is equal to 43I. Therefore, the intensity is:

x = 10log(43I/Io)

x = 10log(43) + 10log(I/Io)

The second term in the equation is the sound intensity produced by a single singer. We calculate that the sound intensity of 36:

x = 10log(36) + 82.1  = 97.66 dB

The zeros of the function f(x) are x = 3 and x = -12.

To find the zeros of a function, we need to solve the equation f(x) = 0. In this case, we have:

f(x) = -x^2 - 9x + 36

Setting f(x) = 0, we get:

-x^2 - 9x + 36 = 0

We can solve this quadratic equation by factoring or by using the quadratic formula. Factoring, we get:

-(x - 3)(x + 12) = 0

Setting each factor equal to zero, we get:

x - 3 = 0 or x + 12 = 0

Solving for x, we get:

x = 3 or x = -12

These zeros represent the horizontal distances from the diving board where the vertical distance of the diver from the pool's surface is zero. In other words, they represent the points where the diver enters the water. The zero x = 3 represents the point where the diver enters the water at a distance of 3 feet from the diving board, while the zero x = -12 represents the point where the diver enters the water at a distance of 12 feet behind the diving board. However, the negative solution x = -12 is not meaningful in this context since it represents a point that is behind the diving board, so we discard it. Therefore, the zero x = 3 is the meaningful solution, which represents the point where the diver enters the water at a distance of 3 feet from the diving board.

Learn more about pool's surface here:

https://brainly.com/question/22661403

#SPJ1

The air pressure that will produce a force of the given magnitude is 135 times the pressure transmitted by the liquid. The value of P2, the pressure transmitted by the liquid, is not given in the problem, so we cannot determine the exact value of P1.

The planet's gravitational pull on the gases above its surface produces atmospheric pressure, which depends on the planet's mass, the radius of its surface, the quantity, makeup, and vertical distribution of the gases in the atmosphere.

The following equations describe the force that compressed air exerts on a tiny piston:

F1 = P1 * A1

The larger piston, which has a larger area A2, receives the power via the liquid. The larger piston's power is determined by:

F2 = P2 * A2

Pascal's rule states that the larger piston receives the same amount of pressure P1 as the smaller piston, so we have:

P1 = P2

Since the forces F1 and F2 are equal, we have:

F1 = F2

Therefore:

P1 * A1 = P2 * A2

P1 * (pi * (5.00 cm)²) = P2 * (pi * (15.0 cm)²)

Simplifying and solving for P1, we get:

P1 = (P2 * A2 * (5.00 cm)²)/ (A1 * (15.0 cm)²)

Substituting A1 = pi * (5.00 cm)² and A2 = pi * (15.0 cm)², we get:

P1 = (P2 * 15.0²) / 5.00²

P1 = 135 * P2.

To know more about magnitude visit:-

https://brainly.com/question/28173919

#SPJ1

If Cv reduces by 2%, calculate the percentage gain in efficiency of the a diesel cycle with a bit rate of 16 and a cut-off ratio of 10% of a swept volume. Taking Cv = 0.717 & 1.4; the answer is 1.23%.

In cubic units, the volume answer is displayed. Volume is determined by multiplying the length, breadth, and height.

The 3-dimensional space that is occupied by matter or surrounded by a surface is measured in volume, which is expressed in cubic units. A derived measure called a cubic meter (m3) serves as the SI volume measurement unit.

To know more about volume visit:

https://brainly.com/question/17322215

#SPJ1

To calculate the energy gained when changing the temperature of 100g of solid candle wax at 20°C to liquid at 68°C, we need to consider two processes:

(1) raising the temperature of the wax from 20°C to 68°C

(2) melting the wax at its melting point of 68°C.

The first process requires an energy input of Q1 = mcΔT, where m is the mass of the wax (100 g), c is the specific heat capacity of the wax (29 J/g°C), and ΔT is the change in temperature (68°C - 20°C = 48°C). Thus, Q1 = (100 g)(29 J/g°C)(48°C) = 139,200 J.

The second process requires an energy input of Q2 = mL, where L is the specific latent heat of fusion of the wax (220 J/g). Thus, Q2 = (100 g)(220 J/g) = 22,000 J.

Therefore, the total energy gained when changing the temperature of 100g of solid candle wax at 20°C to liquid at 68°C is Q = Q1 + Q2 = 139,200 J + 22,000 J = 161,200 J.

To know more about melting point, visit:

https://brainly.com/question/29578567

#SPJ1

Answer:

b

Explanation:

Long answers are always the correct answer. FAXS

Observations of a Milky Way have brought out that stars close to the galaxy's edge rotate rather quickly, which implies that there is more solar masses that we are unable to perceive.

The Sun-like star is known as a 1-solar mass star. At the rightmost to the bottom left in the stars, the primary structure region is where this type of star begins. Nearing the end its main-sequence existence, the star transforms into a red giant as it keeps burning its fuel.

As far as I'm aware, "massive stars" are defined as having masses equal or greater than to eight solar masses.

To know more about solar masses visit:

https://brainly.com/question/30003952

#SPJ1

Using the formula given, the Schwarzschild radius are calculated below;

Problem 1:

Given: R = 2GM/c² and R = 1.48 × 10⁻²⁷M

Using c = 3x10^8 m/s and G = 6.67x10^-11 Nm^2/kg^2

G = gravitational constant, c = speed of light

Substituting the values, we get:

1.48 × 10⁻²⁷M = 2GM/c²

R = 2GM/c² = (2 x 6.67x10^-11 x M)/(9x10^16)

R = 1.48 x 10^-27 M

The radius is 1.48 * 10^-27M

Problem 2:

To calculate the Schwarzschild radius, we simply need to substitute the values into the equation

Given: M = 5.7 x 10^24 kg

Using R = 2GM/c² = (2 x 6.67x10^-11 x M)/(9x10^16)

R = 8.45 * 10^-3m

Problem 3:

Given: M = 1.9 x 10^30 kg

Using R = 2GM/c² = (2 x 6.67x10^-11 x M)/(9x10^16)

R = 2816.2 kilometers

Problem 4:

Given: M = 250 billion suns = 250 x 10^9 x 1.9 x 10^30 kg

Using R = 2GM/c² = (2 x 6.67x10^-11 x 2.5 x 10^11 x 1.9 x 10^30)/(9x10^16)

R = 7.04 x 10^14 kilometers

Problem 5:

Given: M = 60 kg

Using R = 2GM/c² = (2 x 6.67x10^-11 x 60)/(9x10^16)

R = 8.9 x 10^-26 meters

Learn more on Schwarzschild radius here;

https://brainly.com/question/30011727

#SPJ1

Answer:

x² = ((n-1)s²)/o²

x² = (39 - 1) * (3.15)² / (2.94)²

x² = 38 * 9.9225 / 8.6436

x² = 43.7598

Rounding to three decimal places, x² = 43.760. Therefore, the value of x² is 43.760 when o = 2.94, n = 39, and s = 3.15.

Explanation:

Math

Answer: The mass of the remaining ice in the jar is 1.3e+2 g.

Explanation: Let’s denote the mass of the remaining ice as m_ice. The heat gained by the ice is equal to the heat lost by the tea. The heat gained by the ice is given by m_ice * L_f, where L_f is the latent heat of fusion of water (334000 J/kg). The heat lost by the tea is given by m_tea * c_w * (T_initial - T_final), where m_tea is the mass of tea (0.187 kg), c_w is the specific heat capacity of water (4186 J/kg·°C), T_initial is the initial temperature of the tea (33.3°C), and T_final is the final temperature of the tea (31.8°C).

Equating the heat gained by the ice to the heat lost by the tea, we get:

m_ice * L_f = m_tea * c_w * (T_initial - T_final)

Substituting in the values, we get:

m_ice * 334000 = 0.187 * 4186 * (33.3 - 31.8)

Solving for m_ice, we get:

m_ice = 0.187 * 4186 * (33.3 - 31.8) / 334000

m_ice ≈ 0.130 kg

Converting to grams and rounding to two significant figures, we get:

m_ice ≈ 130 g

Hope this helps, and have a great day! =)

Answer:

14.46°C

Explanation:

Given:

Find:

Solution:

1. Calculate the heat required to warm the ice from its initial temperature to its melting point: Heat to warm ice = Mass of ice * Specific heat of ice * (Melting point of ice - Initial temperature of ice) Heat to warm ice = 0.028 kg * 2090 J/(kg*°C) * (0°C - (-78°C)) = 4579.44 J

2. Calculate the heat required to melt the ice at its melting point: Heat to melt ice = Mass of ice * Latent heat of fusion of water Heat to melt ice = 0.028 kg * 3.33e5 J/kg = 9324 J

3. Calculate the heat lost by the water and calorimeter as they cool down to the final temperature: Heat lost by water and calorimeter = Mass of water * Specific heat of water * (Initial temperature of water and copper calorimeter - Final temperature) + Mass of copper calorimeter * Specific heat of copper * (Initial temperature of water and copper calorimeter - Final temperature)

4. The total heat gained by the ice must be equal to the total heat lost by the water and calorimeter: Heat to warm ice + Heat to melt ice + Mass of ice * Specific heat of water * (Final temperature - Melting point of ice) = Heat lost by water and calorimeter 4579.44 J + 9324 J + 0.028 kg * 4186 J/(kg°C) * (Final temperature - 0°C) = [0.562 kg * 4186 J/(kg°C) + 0.080 kg * 387 J/(kg*°C)] * (21°C - Final temperature)

Solving for the final temperature, we get: Final temperature ≈ 14.46°C

So, the final temperature of the system is approximately 14.46°C