Indigenous people sometimes cook in watertight baskets by placing hot rocks into water to bring it to a boil. What mass of 500ºC rock must be placed in 4.00 kg of 15.0ºC water to bring its temperature to 100ºC, if 0.0250 kg of water escapes as vapor from the initial sizzle? You may neglect the effects of the surroundings and take the average specific heat of the rocks to be that of granite. (answer in kg)

1) False

2) True

3) The distance is 17 m

4) The displacement is 2 m south

5) She did not give the direction as either left, or negative.

6) The average speed is 28 mph

7) The average velocity is 12 mph north

8) The average speed is 0.27 m/s

9) False

10) False

Explanation:

1)

Speed is a scalar quantity which tells how fast an object is moving regardless of its direction, and it is calculated as:

[tex]speed=\frac{d}{t}[/tex]

where d is the distance covered by the object and t is the time taken. Being a scalar quantity, speed consists only of a value and its units, so no direction needs to be specified.

2)

Velocity is a vector quantity, defined as

[tex]velocity = \frac{d}{t}[/tex]

where d is the displacement of the object (a vector connecting the initial position to the final position of motion) and t is the time taken. Being a vector, velocity has both a magnitude and a direction (the same direction as the displacement), so direction here should also be specified.

3)

The distance travelled by the object is just the total length of the path taken, regardless of the direction of each part of the motion.

Here the object moves:

10 meters to the right

7 meters to the left

So, the distance travelled is

d = 10 + 7 = 17 m

4)

The displacement is a vector connecting the initial position to the final position of motion, so we have to compare the starting position with the final position.

Taking x = 0 as initial position, and north as positive direction:

- The object moves 5 m north first (+5)

- The object moves 7 m south (-7)

So, the displacement is

d = +5 + (-7) = -2 m

which means 2 meters south.

5)

As we said previously, displacement is a vector connecting the initial position to the final position of motion. Being a vector, it must have:

- A magnitude (the shortest distance between the initial and final position, in a straight line)

- A direction

Here Jenny reported only the magnitude (3 meters), but not the direction, so she forgot to include the direction of the displacement (which is to the left).

6)

The average speed is given by

[tex]speed=\frac{d}{t}[/tex]

where d is the distance and t is the time taken.

The distance is just the total length covered, so:

d = 5 + 2 = 7 miles

The time taken is

t = 1/4 h = 0.25 h

So, the average speed is

[tex]speed=\frac{7}{0.25}=28 mph[/tex]

7)

The average velocity is given by

[tex]velocity=\frac{d}{t}[/tex]

where d is the displacement and t is the time taken.

The displacement is, taking north as positive direction:

d = +5 + (-2) = 3 miles (north)

The time taken is

t = 1/4 h = 0.25 h

So, the average velocity is

[tex]velocity=\frac{3}{0.25}=12 mph[/tex] (north)

8)

We can calculate the average speed by adding the single measurements and dividing by the number of trials done:

[tex]speed_{avg}=\frac{s_1+s_2+s_3}{3}[/tex]

where in this case, N = 3. For this experiment we have:

[tex]s_1 = \frac{0.75 m}{2.5s}=0.30 m/s\\s_2 = \frac{0.75 m}{2.75 s}=0.27 m/s\\s_3=\frac{0.75 m}{2.98 s}=0.25 s[/tex]

So the average is

[tex]speed_{avg}=\frac{0.30+0.27+0.25}{3}=0.27 m/s[/tex]

9)

Data are said to be:

- Accurate, when the average value of the measurements is close to the actual value

- Precise, when the spread of the measurements done in the different trials is small

Therefore, the first part of the sentence "Data that is accurate, is data that is really close to the actual value" is correct, and the second part "data that is precise is data that is repeated over and over again" is not correct, since we may have several measurements but their spread may be large.

10)

As we said in part 9):

- Accuracy refers to how close the measured value is to the actual value

- Precision refers to the spread (or the uncertainty) on the measured value: the smaller it is, the better the precision

For instance, let's assume that the actual value of a certain variable is 3.0. If we get the following set of data:

2.4, 2.5, 2.4, 2.3

it is precise (the spread is small) but not accurate (since the average, 2.4, is far from the actual value)

while the following set:

3.1, 3.6, 2.4, 3.0

is accurate (the average is around 3.0, so close to the actual value), but not precise (the spread is very large).

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The final velocity of the truck is 6.33 m/s

Explanation:

We can solve this problem by using the law of conservation of momentum: the total momentum of the truck-car system must be conserved before and after the collision (if there are no external forces), so we can write

[tex]p_i = p_f\\m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2[/tex]

where:

[tex]m_1 = 3000 kg[/tex] is the mass of the truck

[tex]u_1 = 8 m/s[/tex] is the initial velocity of the truck

[tex]v_1[/tex] is the final velocity of the truck

[tex]m_2 = 500 kg[/tex] is the mass of the car

[tex]u_2 = 0[/tex] is the initial velocity of the car

[tex]v_2 = 10 m/s[/tex] is the final velocity of the car

And by solving the equation for [tex]v_1[/tex], we find the velocity of the truck after the collision:

[tex]v_1 = \frac{m_1 u_1-m_2 v_2}{m_1}=\frac{(3000)(8)-(500)(10)}{3000}=6.33 m/s[/tex]

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Answer:

Speed by walking is 33 miles per hour

And speed of by car is 88 miles per hour

Explanation:

We have given that it takes same time to walk 1212 miles as 3232 miles by car

Now let the speed by walk is x

As speed by car is 55 miles per hour faster than by walk = x+55

As time is same and we know that time is given as [tex]time=\frac{distance}{speed}[/tex]

So [tex]\frac{1212}{x}=\frac{3232}{x+55}[/tex]

[tex]1212(x+55)=3232x[/tex]

[tex]1212x+66660=3232x[/tex]

x = 33 miles per hour

So speed by walking is 33 miles per hour

And so speed of car = 33+55 =88 miles per hour

The angular velocity of the disk must be 2.25 rpm

Explanation:

The centripetal acceleration of an object in circular motion is given by

[tex]a=\omega^2 r[/tex]

where

[tex]\omega[/tex] is the angular velocity

r is the distance of the object from the axis of rotation

For the space station in this problem, we have

[tex]a=\frac{g}{2}=\frac{9.8}{2}=4.9 m/s^2[/tex] is the centripetal acceleration

The diameter of the disk is

d = 175 m

So the radius is

[tex]r=\frac{175}{2}=87.5 m[/tex]

So, a point on the rim has a distance of 87.5 m from the axis of rotation. Therefore, we can re-arrange the previous equation to find the angular velocity:

[tex]\omega = \sqrt{\frac{a}{r}}=\sqrt{\frac{4.9}{87.5}}=0.237 rad/s[/tex]

And this is the angular velocity of any point along the disk. Converting into rpm,

[tex]\omega=0.236 \frac{rad}{s}\cdot \frac{60 s/min}{2\pi rad/rev}=2.25 rpm[/tex]

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Answer:

h=0.425 L

Explanation:

Given that

θ =  54°

Coefficient of friction μ = 0.32

Mass of rod = m

Lets take mass of man = M  = 4 m

C is the center of mass of the rod.

By balancing force in y and x direction

R= Fr

R = Fr=  μ N

N = mg + Mg = mg + 4 m g                     ( M =4m)

N = 5 m g

Lets take distance cover by man is h along rod before sliding

Now taking moment about the lower end

M g  h cosθ + m g cosθ L/2  =  R L sinθ

2 M g  h cosθ + m g cosθ L  = 2 R L sinθ

Now by putting the value of R  and M

8 m g  h cosθ + m g cosθ L  = 2  μ N L sinθ

8 m g  h cosθ + m g cosθ L  = 10 m g μ  L sinθ

8   h cosθ +  cosθ L  = 10  μ  L sinθ

8 h + L = 10 μ L tanθ

Now putting the value of θ  and μ

8 h + L = 10 x 0.32 x tan54° x L

8 h + L = 4.4 L

8 h = 3.4 L

h=0.425 L

Answer:

Van der waals forces.

Explanation:

When we spread glue to stick any two substances as A and B with adhesives C. then there are adhesive force between substance A and C and adhesive force between substance B and C and cohesive force between C itself will act. In all adhesive and cohesive forces van der waals forces will apply at molecular level because there is no chemical bonding between adhesive and surface but lots of small attractive forces.

Answer:

Van der Waals force

Explanation:

The technical name given to the force that holds glue to its bonding materials is called Van der Waals force.

The forces of Van der Waals is defined by  attraction and repulsion between atoms, molecules, and surfaces and other intermolecular forces. They differ from covalent and ionic bond in that they are caused by correlations in the varying polarizations of the nearby particles (as a result of quantum dynamics).

Answer:

Super-critical mass

Explanation:

This term refers to the mass, in which the amount of fission processes per unit of time increases to the point, where some intrinsic feedback mechanism causes the reactor to reach an equilibrium point at a high temperature or power, that is, It becomes critical again, or it is destroyed due to the amount of processes.

"When nuclear material in the reactor is fissioning at an increasing rate, this is known as a ""criticality.""

When nuclear material in the reactor is fissioning at an increasing rate, it is said to be in a state of criticality. This term refers to the condition where the reactor is sustaining a nuclear chain reaction at a steady rate. In a nuclear reactor, criticality is the normal operating condition, where one fission event leads to exactly one subsequent fission event, on average, in the next generation of the reaction. This ensures a controlled and sustained release of energy.

To achieve criticality, the reactor must have enough fissile material (such as uranium-235 or plutonium-239) and the correct geometric arrangement to maintain a chain reaction. Control rods, which are made of materials that absorb neutrons, are used to regulate the rate of the reaction. When the reactor is critical, the rate of neutron production is balanced by the rate of neutron absorption and leakage, resulting in a steady power output.

If the rate of fission increases beyond this balance, the reactor is said to be supercritical, which can lead to an uncontrolled increase in power and is a dangerous condition that must be avoided. Conversely, if the rate of fission decreases, the reactor is said to be subcritical, and the power output will decrease.

In summary, criticality in a nuclear reactor is the state where a self-sustaining chain reaction occurs at a constant rate, providing a stable source of energy for the submarine's propulsion system. It is carefully managed by the reactor's control systems and the vigilance of the Engineering Duty Officer and their team."

Answer:

v1 = 2.76 m/s and v2 = - 0.32 m/s

Explanation:

m1 = 0.140 kg

m2 = 0.299 kg

u1 = 0.80 m/s

u2 = - 2.28 m/s

Let the speed after collision is v1 and v2.

Use conservation of momentum

m1 x u1 + m2 x u2 = m1 x v1 + m2 x v2

0.140 x 0.80 - 0.299 x 2.28 = 0.140 x v1 + 0.299 x v2

0.112 - 0.68 = 0.14 v1 + 0.299 v2

0.14 v1 + 0.299 v2 = - 0.568 ..... (1)

By the use of coefficient of restitution, the value of e = 1 for elastic collision

[tex]e=\frac{v_{1}-v_{2}}{u_{2}-u_{1}}[/tex]

u2 - u1 = v1 - v2

- 2.28 - 0.8 = v1 - v2

v1 - v2 = 3.08

v1 = 3.08 + v2

Put in equation (1)

0.14 (3.08 + v2) + 0.299 v2 = - 0.568

0.43 + 0.44 v2 = - 0.568

v2 = - 0.32 m/s

and

v1 = 3.08 - 0.32 = 2.76 m/s

Thus, v1 = 2.76 m/s and v2 = - 0.32 m/s

Answer:

W = 112.76MJ

Explanation:

the work is:

[tex]W = F_xD[/tex]

where [tex]F_x[/tex] is the force executed in the direction of the displacement and the d the displacement.

so:

W = 12000Ncos(20)(10000)

we use the cos of the angule because it give us the proyection in the axis x of the force, that means the force in the direction of the displacement.

W = 112.76MJ

Answer:

rise in temperature = 333.53°C

Explanation:

mass of lead bullet, m = 5.9 g

initial velocity, u = 410 m/s

specific heat of lead = 0.126 J/gm - K = 126 J/kg K

Initial kinetic energy of the bullet

K = 1/2 mu^2 = 0.5 x 5.9 x 10^-3 x 410 x 410 = 495.895 J

Half of the kinetic energy is used to raise the temperature of lead bullet

K / 2 = mass of bullet x specific heat of lead x rise in temperature

247.95 = 5.9 x 10^-3 x 126 x rise in temperature

rise in temperature = 333.53°C

Thus, the rise in temperature of lead bullet is 333.53°C.

Answer:

sulcus

Explanation:

A sulcus is an indentation or depression in the brain that causes it to look like it  ridges or folds

Cerebral sulci and fissures are grooves between the adjacent gyri on the surface of the cerebral hemispheres.

Sulci can be basically can be divided into three basic function

limiting sulcus: This happens to  develop between areas differing in structure and function, for example central sulcus

axial sulcus: This develops along the axis of a rapidly growing/developing area (e.g. calcarine sulcus)

operculated sulcus: a sulcus may be between two structurally-different areas and a third sulcus may lie in its wall and does not appear on the surface (e.g. lunate sulcus)

Answer:[tex]\mu [/tex]=0.48

Explanation:

Given

inclination [tex]\theta =31^{\circ}[/tex]

Acceleration of object[tex]=0.99 m/s^2[/tex]

Now using FBD

[tex]mg\sin \theta -f_r=ma[/tex]

[tex]mg\sin \theta -\mu mg\cos \theta =ma[/tex]

[tex]a=g\sin \theta -\mu g\cos \theta [/tex]

[tex]0.99=5.04-\mu 8.4[/tex]

[tex]\mu 8.4=4.057[/tex]

[tex]\mu =0.48[/tex]

Answer:

ΔU= *-26 KJ

Explanation:

Given that

Work done by motor W= 30 KJ

Heat gains by motor Q= 4 KJ

Sign convention:

 If heat is added to the system then it is taken as positive and if heat is rejected from the system then it is taken as negative.

If work done by the system then it is taken as positive and if work is done on the system then it is taken as negative.

From first law of thermodynamics

Q = W + ΔU

ΔU=Change in internal energy

Q=Heat transfer

W=Work

Now by putting the values

4 = 30 + ΔU

ΔU= -26 KJ

Answer:

Internal energy ∆U=-26KJ

Explanation:

Given that:

Work done by the motor=+30KJ

Heat gained by the motor=+4KJ

In solving thermodynamical questions it is reasonable to use the sign convention this

Heat is positive if it is added to a system,but becomes negative if the system rejects heats.

Work is positive if the system does work,but becomes negative if work is done on the system.

Using the thermodynamics first law

∆U=Q-W

∆U= 4-30=-26KJ

Answer:all galaxies Moving away from him

Explanation:

When we talk about the expanding universe, it means it has grown with the Big Bang ever since it started.  

Space expansion makes galaxies seem to move apart from each other. Although the galaxies themselves may seem to move through space, in reality, it is the space that is growing between the galaxies.

Thus the observer sees all the galaxies moving away from him, the more distant galaxies faster they move.

Answer:

9.1°

Explanation:

Torque = distance from pivot * perpendicular force

15 Nm = 0.5 m * perpendicular force

perpendicular force  = 30 N

So the bertical component of the applied force that caused a turning  effect (torque) was 30 N. Now we use this information to find the angle that would produce a vertical component of  30N from an applied force of 95 N.

Fy = FSinθ

15 = 95 Sinθ

θ = 9.1°

Answer:

[tex]\frac{v_p}{v_a}=1.268[/tex]

Explanation:

1) Basic concepts

Apogee: is the maximum distance for an object orbiting the Earth. For this case the distance for the apogee would be the sum of radius for the earth and 2289 km.

Perigee: Minimum distance of an object orbiting the Earth. For this case the distance for the perigee would be the sum of radius for the earth and 459 km.

A good approximation for these terms are related to the figure atached.

Isolated system: That happens when the system is not subdued to an external torque, on this case the change of angular momentum would be 0.

2) Notation and data

[tex]r_{earth}[/tex] radius for the Earth, looking for this value on a book we got [tex]r_{earth}=6.37x10^{3}km[/tex]

[tex]r_p =459km +r_{earth}=459km +6.37x10^3 km=6.829x10^3 km[/tex], represent the radius for perigee

[tex]r_a =2289km +r_{earth}=2289km +6.37x10^3 km=8.659x10^3 km[/tex], represent the radius for perigee

[tex]T=112.7min[/tex], period

[tex]v_p[/tex] velocity of the perigee

[tex]v_p[/tex] velocity of the apogee

[tex]r=\frac{v_p}{v_a}[/tex] is the variable of interest represented the ratio for the speed of the perigee to the speed of the apogee

3) Formulas to use

We don't have torque from the gravitational force since is a centered force. So the change of momentum is 0

[tex]\Delta L=0[/tex]   (1)

[tex]L_a=L_p[/tex]   (2)

From the definition of angular momentum we have [tex]L_i=mv_i r_i[/tex], replacing this into equation (2) we got:

[tex]mv_a r_a =mv_p r_p[/tex]   (3)

We can cancel the mass on both sides

[tex]v_a r_a =v_p r_p[/tex]   (4)

And solving [tex]\frac{v_p}{v_a}[/tex] we got:

[tex]\frac{v_p}{v_a}=\frac{r_a}{r_p}[/tex]   (5)

And replacing the values obtained into equation (5) we got:

[tex]\frac{v_p}{v_a}=\frac{8.659x10^3 km}{6.829x10^3 km}=1.268[/tex]  

And this would be the final answer [tex]\frac{v_p}{v_a}=1.268[/tex]

Answer:

7,157

Explanation:

Hi!

Use this equation to solve this problem:

Fb=ρfl*g*Vfl

where

Fb=buoyant force

What do we know?

The known values are highlighted in.

An iceberg (density=917 kg/[tex]m^3[/tex]) is floating in seawater, the volume of the iceberg below the waterline is approximately 7168 [tex]m^3[/tex].

To calculate the volume of the iceberg below the waterline, we must apply the concept of buoyancy. The buoyant force acting on an item that floats in a fluid is equal to the weight of the fluid displaced by the object.

The buoyant force (F_b) may be computed using the formula:

F_b = ρ_fluid * V_submerged * g

W_iceberg = ρ_iceberg * V_iceberg * g

F_b = W_iceberg

ρ_fluid * V_submerged * g = ρ_iceberg * V_iceberg * g

Now,

V_submerged = (917 / 1025 ) * 8000

V_submerged = 0.896 * 8000 [tex]m^3[/tex]

V_submerged ≈ 7168 [tex]m^3[/tex]

Therefore, the volume of the iceberg below the waterline is approximately 7168  [tex]m^3[/tex].

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Answer:

The vector a, the answer is the point D

Explanation:

We need to make the make the subtraction from the x,y points. It will be the points of the head minus the points of the tail.

x=(-2 - 0) and y = (3-0) vector = -2 + 3

The Answer is—————————D. a

Answer:

Part a)

[tex]F_f = 692 N[/tex]

Part b)

[tex]F_f = 932 N[/tex]

Explanation:

Part A)

As we know by Force equation on the losing player

[tex]F - F_f = ma[/tex]

so we will have

[tex]800 - F_f = 90\times 1.20[/tex]

[tex]800 - F_f = 108[/tex]

[tex]F_f = 692 N[/tex]

Part b)

As we know that the winning player is also moving with same acceleration

so we will have

[tex]F_f - F = ma[/tex]

[tex]F_f - 800 = 110\times 1.20[/tex]

[tex]F_f = 932 N[/tex]

Answer:

Difference threshold or also Just Noticeable Difference

Explanation:

The above mentioned case between room mates, where one room mate was able to detect a minute change in volume shows an instance of the difference threshold.

Difference threshold can be defined as stimulation at its minimum level that can be detected by an individual almost 50 % of the times.

It is the lowest possible level of sound that is detectable by a person.

That is what happened in the mentioned case that when the volume was increased from 14 to 15, Amber was able to detect it.

Answer:

The measure of angle B equals the measure of angle C.

Explanation:

When a ray of light falls on a smooth polished surface and the light ray bounces back, it is called the reflection of light.

There are two laws of reflection;

1) The incident ray and reflected ray and normal all lie in the same plane.

2) The angle of incidence is equal to angle of reflection.

Here angle of incidence is represented by B and angle of reflection is by C.

So according to law of reflection the measure of angle B equals the measure of angle C.

Answer:

The measure of angle B equals the measure of angle C

Explanation:

"B" is the correct answer on edge

Answer:

F'=  10F (N)

Explanation:

To solve this problem we apply Coulomb's law:

Two point charges (q₁, q₂) separated by a distance (d) exert a mutual force (F) whose magnitude is determined by the following formula:

F = K*q₁*q₂ / d² Formula (1)  

F: Electric force in Newtons (N)

K : Coulomb constant in N*m²/C²

q₁,q₂:Charges in Coulombs (C)  

d: distance between the charges in meters(m)

Calculating of the new force F'

Data:

q'₁ = 5q₁

q'₂ = q₂/2

d' = d/2

We apply the Coulomb's law:

F' = K*q'₁*q'₂ / d'²

F'= K*(5q₁)*(q₂/2) / (d/2)²

F'= K*(5q₁*q₂/2) / (d²/4)

F'= K*20q₁*q₂) / (2d²)

F'=  10(K*q₁*q₂) / (d²)

F'=  10(K*q₁*q₂) / (d²)  , F = K*q₁*q₂ / d²

F'=  10F (N)

Final answer:

The force between two charges can be calculated using Coulomb's Law. We can use the given values to calculate the new force F' and determine its value.

Explanation:

The force between two charges is given by Coulomb's Law, which states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

Using the given information, we can calculate the new force F' using the formula:

F' = (k * q'1 * q'2) / (d'^2)

Substituting the given values into the formula, we get:

F' = (k * 5q1 * (q2/2)) / ((d/2)^2)

After solving the equation, we can determine the value of the new force F'.

Answer:

(a). The total moment of inertia of the system is 0.0233 kg-m².

(b). The kinetic energy is 0.0011 J.

Explanation:

Given that,

Mass of each particle m= 0.85 kg

Length = 5.6 cm

Mass of each rod M= 1.2 kg

Angular speed = 0.30 rad/s

The moment of inertia of the rod  between  axis of rotation and mass  is

[tex]I_{1}=\dfrac{Md^2}{3}[/tex]

The moment of inertia of the rod  between masses about center of mass is

[tex]I_{cm}=\dfrac{Md^2}{12}[/tex]

Moment of inertial of the rod between masses about point O is

[tex]I_{2}=M(d+\dfrac{d}{2})^2+\dfrac{Md^2}{12}[/tex]

Moment of inertia of two masses is

[tex]I_{m}=md^2+m(2d)^2[/tex]

(a). We need to calculate the total moment of inertia of the system

Using formula of moment of inertia

[tex]I_{t}=I_{1}+I_{2}+I_{m}[/tex]

Put the value into the formula

[tex]I_{t}=\dfrac{Md^2}{3}+M(d+\dfrac{d}{2})^2+\dfrac{Md^2}{12}+md^2+m(2d)^2[/tex]

[tex]I_{t}=\dfrac{Md^2}{3}+\dfrac{9Md^2}{4}+\dfrac{Md^2}{12}+md^2+4md^2[/tex]

[tex]I_{t}=\dfrac{32Md^2}{12}+5md^2[/tex]

[tex]I_{t}=2.67Md^2+md^2[/tex]

Put the value into the formula

[tex]I_{t}=2.67\times1.2\times(5.6\times10^{-2})^2+5\times0.85\times(5.6\times10^{-2})^2[/tex]

[tex]I_{t}=0.0233\ kg-m^{2}[/tex]

(b). We need to calculate the kinetic energy

Using formula of kinetic energy

[tex]K.E=\dfrac{1}{2}I\omega^2[/tex]

Put the value into the formula

[tex]K.E=\dfrac{1}{2}\times0.0233\times(0.30)^2[/tex]

[tex]K.E=0.0011\ J[/tex]

Hence, (a). The total moment of inertia of the system is 0.0233 kg-m².

(b). The kinetic energy is 0.0011 J.

The rotational inertia of the combination is 0.041 kg·m² and the kinetic energy is 80.93 J.

The rotational inertia (moment of inertia) of the combination can be calculated using the formula I = 2mL², where m is the mass and L is the length of the rod. Substituting the given values, the rotational inertia is 0.041 kg·m².

The kinetic energy of rotation can be calculated using the formula K = ½Iω², where I is the moment of inertia and ω is the angular velocity. Substituting the given values, the kinetic energy is 80.93 J.

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Answer:

The temperature required is near about 3 million kelvin

Explanation:

The brilliance of the star results from the nuclear reaction that take place in the core of the star and radiate a huge amount of thermal energy resulting from the fusion of hydrogen into helium.

For this reaction to take place, the temperature of the star's core must be near about 3 million kelvin.

The hydrogen atoms collide and starts and the energy from the collision results in the heating of the gas cloud. As the temperature comes to near about [tex]1.5\times 10^{7 {\circ}C[/tex], the nuclear fusion reaction takes place in the core of the gas cloud.

The huge amount of thermal energy from the nuclear reaction gives the gas cloud a brilliance resulting in a protostar.

The core temperature necessary for hydrogen fusion to begin in a star is approximately 15,000,000 Kelvin, marking its entry into the main sequence. With hydrogen's exhaustion, fusion of helium and other more complex elements happen, each needing significantly higher temperatures.

Hydrogen fusion, also known as thermonuclear fusion, initiates within a star when its core temperature reaches approximately 15,000,000 Kelvin (K). At these temperatures, all molecules dissociate into atoms, and the atoms ionize, forming plasma. This process of hydrogen fusion occurring in the core of a star is critical for a star's energy balance and longevity.

A star reaches the main sequence when its core temperature is high enough (about 12 million K) to fuse hydrogen into helium. However, once the hydrogen fuel is exhausted in a star's core, fusion of helium, and later, other more complex elements can occur, with each requiring significantly higher temperatures than previous fusion reactions.

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Answer:

Iris

Explanation:

The pupil is where the light enters the eye, however, the iris is pupil tissue and is the one who regulates the amount of light that it lets through.

The iris opens or closes to allow a greater or lesser flow of light through the pupil.

In summary, the iris is responsible for regulating the amount of light that enters the eye.

The amount of light entering the eye is mainlly regulated by the pupil, which adjusts its size based on the surrounding light levels. This is achieved by the action of muscles connected to the iris. Furthermore, the light that enters the eye is focused on the retina and processed to the brain via the optic nerve.

The amount of light entering the eye is majorly managed by the pupil. The pupil is the small opening in the center of the eye that adjusts its size based on the light levels in the environment. This adjustment is achieved by the contraction and relaxation of muscles connected to the iris, which is the colored part of the eye.

When the light levels are high, the pupil contracts (or constricts) to limit the amount of light that enters the eye. On the other hand, when the light levels are low, the pupil expands (or dilates) to allow more light to enter the eye. This process is regulated by specific nerves and structures, specifically the optic nerve and the oculomotor nerve in a process called the Pupillary Light Response.

Furthermore, light waves cross the cornea and focus on the retina, a light-sensitive layer lining the back of the eye. The image processing is then carried forward to the brain through the optic nerve.

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Answer:

[tex]\Delta U = 64218.9 J[/tex]

Explanation:

As we know that power of the heater is given as

P = 100 W

now the energy given by the heater for 11 min of time

[tex]E = P \times t[/tex]

[tex]E = 100 \times 11 \times 60[/tex]

[tex]E = 100\times 11 \times 60[/tex]

[tex]E = 66000 J[/tex]

now from 1st law of thermodynamics we know that

[tex]E = \Delta U + W[/tex]

work done under constant pressure condition we have

[tex]W = P \Delta V[/tex]

[tex]W = (3.527 \times 1.01 \times 10^5)(6 - 1) \times 10^{-3}[/tex]

[tex]W = 1781.13 J[/tex]

now from first equation we have

[tex]66000 = 1781.13 + \Delta U[/tex]

[tex]\Delta U = 64218.9 J[/tex]

The change in the internal energy of the system is 67.787 kJ.

The given parameters;

The heat added to the system by the heater;

Q = Pt = 100 x 660 = 66,000 J = 66 kJ

The work done on the system is calculated as follows;

W = PΔV

W = 3.527(6 - 1)

W = 17.64 L.atm

1 Latm = 0.1013 kJ

17.64 Latm = 1.787 kJ

The change in the internal energy of the system is calculated by applying the first law of thermodynamics as follows;

ΔU = Q + W

ΔU = 66 kJ  +  1.787 kJ

ΔU = 67.787 kJ.

Thus, the change in the internal energy of the system is 67.787 kJ.

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Answer:

c. Jupiter's greater mass compresses it more, thus increasing its density.

Explanation:

The mass of Jupiter is greater in its interior, this mass compresses Jupiter to some extent. Thus, its density is increased. Now, more mass is compressed in the lesser volume. Hence, its size does not increase enormously. On the other hand the mass of Saturn is lesser  and also density lower. this gives Saturn a reasonably higher volume.

Hence, option C is correct.

Saturn appears almost as large as Jupiter due to its lower mass leading to less gravitational compression of its hydrogen and helium composition, resulting in a larger volume for its mass. The correct answer from the provided choices is c. Jupiter's greater mass compresses it more, thus increasing its density.

The reason why Saturn appears almost as large as Jupiter despite having a smaller mass is largely due to its composition and structure. We see that Jupiter, which is 318 times more massive than Earth, has a significantly higher density because its greater mass compresses the planets' internal hydrogen and helium more than Saturn, which is about 25% as massive as Jupiter. In comparison, Saturn's lower mass results in less compression and hence a larger volume for its mass. So, the correct answer is c. Jupiter's greater mass compresses it more, thus increasing its density.

Jupiter and Saturn are both composed mainly of hydrogen and helium, which become liquid at great depths due to their large size and the resulting high pressure. However, Saturn, with its lower density, is the least dense planet in the solar system, even less dense than water. Contrary to the choices provided, Saturn's rings do not play a significant role in making the planet appear larger in terms of its physical size, and the effect of distance from the Sun on the compactness of the planets is negligible compared to the impact of their massive gravitational compression.

Answer:

Explained.

Explanation:

Only the first question has been answered

In a period from left to right the nuclear charge increases and hence nucleus size is compressed. Thus,  atomic radius decreases.

In transition elements, electrons in ns^2 orbital remain same which is the outer most orbital having 2 electrons and the electrons are added to (n-1) d orbital. So, outer orbital electron experience almost same nuclear attraction and thus size remains constant.

The atomic radius of main-group elements decreases as you move to the right across a period due to increased positive charge, while the atomic radius of transition elements remains relatively constant.

The atomic radius of main-group elements decreases as you move to the right across a period because the number of protons in the nucleus increases. This increased positive charge pulls the electrons closer to the nucleus, reducing the size of the atom. In contrast, the atomic radius of transition elements remains relatively constant as you move across a period because their outermost electrons are in different energy levels or subshells. The addition of protons does not significantly affect the size of the atom.

Moving across a period, the number of protons in the nucleus increases, leading to a greater positive charge. This increased positive charge exerts a stronger pull on the electrons, pulling them closer to the nucleus and resulting in a smaller atomic radius.

However, electron shielding, or the repulsion between electrons in different energy levels, also plays a role. As you move across a period, the number of electrons in the same energy level (shell) remains constant, providing consistent shielding effects. This partial counteraction to the increased positive charge contributes to the overall trend of decreasing atomic radius.

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Answer:

There is a constant emf induced in the loop.

Explanation:

In the uniform magnetic field suppose the rectangular wire loop of length L and width b is moved out with a uniform velocity v. suppose any instance x length of the loop is out of the magnetic field and L-x length is inside the loop.

Area of loop outside the field = b(L-x)

we know that flux φ= BA

B= magnitude of magnetic field , A=  area

and emf [tex]\epsilon= \frac{d\phi}{dt}[/tex]

[tex]\epsilon=B\frac{dA}{dt}[/tex]

[tex]\epsilon=B\frac{db(L-x)}{dt}[/tex]

[tex]\epsilon=Bb\frac{d(L-x)}{dt}[/tex]

B,b and L are constant and dx/dt = v

⇒ε = -Bbv

which is a constant hence There is a constant emf induced in the loop.

Final answer:

The work done by gravity on a block dropped onto a spring is 0.22638 J, the spring does 1.815 J of work compressing, and if the speed at impact is doubled, the maximum spring compression becomes 22 cm. The speed of the block before impact cannot be determined without the drop height.

Explanation:

A 210 g block is dropped onto a relaxed vertical spring that has a spring constant of k = 3.0 N/cm. The block becomes attached to the spring and compresses it 11 cm before momentarily stopping.

(a) To calculate work done by gravity, use Work = mgh, where m is the mass of the block, g is the acceleration due to gravity (9.8 m/s²), and h is the height (11 cm = 0.11 m, since we need consistent units). The work done by gravity is (0.21 kg)(9.8 m/s²)(0.11 m) = 0.22638 J (since potential energy lost by the block is equal to the work done by gravity).

(b) The work done by the spring is Work = 1/2 kx², converting k to N/m gives us 300 N/m. The compression x is 0.11 m, so the work done is (1/2)(300 N/m)(0.11 m)² = 1.815 J.

(c) Since we're assuming friction is negligible and using energy conservation, the potential energy (mgh) at the beginning will be equal to the kinetic energy (1/2 mv²) just before impact. Solving for v gives v = √(2gh), where h is the drop height. However, without the drop height, we cannot calculate the exact velocity.

(d) Doubling the speed will increase the kinetic energy by a factor of four (since KE = 1/2 mv²). To find the new compression distance, we set the new kinetic energy equal to the spring potential energy (1/2 kx²) and solve for x. The maximum compression x will be twice the original compression, or 22 cm.