A ball is thrown from the top of one building toward a tall building 50 m away. The initial velocity of the ball is 20 m/s at 40° above the horizontal. How far above or below its original level will the ball strike the opposite wall?

Answer:

B = 0.126 T

Explanation:

As per Faraday's law we know that rate of change in magnetic flux will induce EMF in the coil

So here we can say that EMF induced in the coil is given as

[tex]EMF = \frac{\phi_2 - \phi_1}{\Delta t}[/tex]

initially the coil area is perpendicular to the magnetic field

and after one fourth rotation of coil the area vector of coil will be turned by 90 degree

so we can say

[tex]\phi_1 = NBAcos 0 = BA[/tex]

[tex]\phi_2 = NBAcos 90 = 0[/tex]

now we will have

[tex]EMF = \frac{NBA}{t}[/tex]

[tex]10,000 V = \frac{(500)(B)(\pi \times 0.45^2)}{4.01\times 10^{-3}}[/tex]

[tex]B = 0.126 T[/tex]

Answer:

[tex]a = -16 m/s^2[/tex]

Explanation:

As we know that the initial speed of the particle when it enters the nozzle is given as

[tex]v_i = 10 m/s[/tex]

after travelling the distance d = 3 m it will have its final speed as

[tex]v_f = 2 m/s[/tex]

now we know that when acceleration is constant the equation of kinematics is applicable

so we will have

[tex]v_f^2 - v_i^2 = 2 a d[/tex]

[tex]2^2 - 10^2 = 2(a)(3)[/tex]

[tex]a = -16 m/s^2[/tex]

Final answer:

To find the average acceleration from a fluid dynamics perspective, one can use the Eulerian viewpoint to observe velocity changes at a fixed point, or follow the particle through its motion using the Lagrangian viewpoint. However, the provided information is insufficient for precise calculation without the time variable or assumption of constant deceleration.

Explanation:

To find the average acceleration of a particle that slows down from 10 m/s to 2 m/s over a distance of 3 meters, we can use the concepts of Eulerian and Lagrangian viewpoints in fluid dynamics, though it is more common to apply these in the context of fluid flow rather than individual particles in motion.

In the Eulerian viewpoint, we observe the change of velocity at a fixed point in space as the particle passes through. Writing the kinematic equation δv = aδt, where δv is the change in velocity and a is the average acceleration, we can rearrange to find a = δv / δt.

The Lagrangian viewpoint, on the other hand, follows the particle along its path. Given the initial and final velocities (v₀=10 m/s and vf=2 m/s) and the distance traveled (3 m), we can use the kinematic equation vf^2 = v₀^2 + 2aδx to solve for a. In this case, δx is 3m, and vf and v₀ are given. From this equation, a = (vf^2 - v₀^2) / (2δx).

If actual calculations are performed, please note that the given information in the problem statement is insufficient to solve for time, as neither the time taken to travel through the nozzle nor the deceleration time is provided. Assuming the particle moves at a constant deceleration, one can calculate the time through δv = aδt and then average acceleration using that time duration. However, without additional data or time measurement, we cannot find a precise numerical value for acceleration.

Answer:

If x₁=12 cm then k=1.7985 N/m

If x₂=15 cm then k=1.4388 N/m

Explanation:

Hanging mass= 22 g=0.022 kg

Acceleration due to gravity g=9.81 m/s²

If x₁=displacement= 12 cm=0.12 m

k= spring constant

[tex]F=ma\\\Rightarrow F=0.022\times 9.81\\\Rightarrow F=0.21582\ N[/tex]

[tex]\text {For spring}\\F=kx\\\Rightarrow 0.21582=k\times 0.012\\\Rightarrow k=1.7985\ N/m\\[/tex]

∴k = 1.7985 N/m

If x₂=15 cm=0.15 m

Force of the hanging mass is same however the spring constant will change

[tex]\text {For spring}\\F=kx\\\Rightarrow 0.21582=k\times 0.015\\\Rightarrow k=1.4388\ N/m\\[/tex]

∴k = 1.4388 N/m

As the mass is not changing the spring constant has to change. That means that here there are two spring one with k=1.7985 N/m and the other with k= 1.4388 N/m

The potential energy stored in the spring is calculated using the formula U = 1/2kx^2. With a force of 20 N and a spring constant of 10 N/m, the displacement is found to be 2 m, and thus the potential energy is 20 J.

The question is related to the calculation of the potential energy stored in an ideal spring. To find this, we use the formula for elastic potential energy, which is U = 1/2kx2, where U is the potential energy, k is the spring constant, and x is the displacement (or compression) of the spring from its rest position.

In this case, since the force holding the spring in compression is 20 N and the spring constant is 10 N/m, we first need to find the displacement x. The force F applied to a spring is also given by F=kx, so rearranging for x gives us x = F/k = 20 N / 10 N/m = 2 m. Plugging this into the potential energy formula, we get U = 1/2 * 10 N/m * (2 m)2 = 1/2 * 10 * 4 = 20 J.

Therefore, the potential energy stored in the spring is 20 J.

Answer:

When the hunter pulls the polar bear to him, the polar bear will move 3.3 meters.

Explanation:

It is given that, a 640-N hunter gets a rope around a 3200-N polar bear. They are stationary, 20 m apart, on friction less level ice.

The given system is an isolated system which is initially at rest and they both will meet at the center of mass. Then finding the center of mass of the system as :

[tex]X_{com}=\dfrac{m_1x_1+m_2x_2}{m_1+m_2}[/tex]

Multiplying "g" to the numerator and denominator both as :

[tex]X_{com}=\dfrac{gm_1x_1+m_2x_2g}{m_1g+m_2g}[/tex]

[tex]X_{com}=\dfrac{640(0)+3200\times 20}{640+3200}=16.67\ m[/tex]

i.e. 640 N hunter moves at a distance of 16.67 meters and when the hunter pulls the polar bear to him, the polar bear will move, 20 m - 16.67 m = 3.3 meters. Hence, this is the required solution.

answer

50°C

Explanation:

Mw*©=Mi*©

250*20=100*©

©=250*20/100

©=50°C//

To find the final temperature after mixing ice and water, one must calculate the heat required to melt the ice and compare it to the heat the water loses in the process, using the specific heat of water and the enthalpy of fusion of ice.

To determine the final temperature of water after adding 100g of ice at 0°C to 250g of water at 20°C, we must consider the heat transfer involved in the process of melting ice and the subsequent equilibrium between the melted ice and the initial water. The specific heat of water (4.184 J/(g°C)) and the enthalpy of fusion of ice (6.01 kJ/mol) are crucial to this calculation.

The process involves calculating the heat required to melt the ice (Q = mfusion * ΔHfusion) and equating it to the heat lost by the water as it cools (Q = mcwater*ΔT), and solving for the final temperature. However, in this scenario, it's important to note that without the specific values or further calculations included in the question details, we can't provide a precise numerical answer but can outline the method to find it.

Answer:0.642

Explanation:

Given

initially car is at rest i.e u=0

When car hits the truck it's velocity is 4.5 m/s

it hits the truck after 7 sec

Now average acceleration of car is =[tex]\frac{change\ in\ velocity}{time\ taken}[/tex]

average acceleration of car =[tex]\frac{\left ( final velocity\right )-\left ( initial velocity\right )}{time}[/tex]

average acceleration of car=[tex]\frac{\left ( 4.5\right )-\left ( 0\right )}{7}[/tex]

average acceleration of car=[tex]0.642 m/s^{2}[/tex]

Taking Down hill as positive x axis

average acceleration of car=[tex]0.642\hat{i}[/tex]

Answer:

the path of the moving charge will be circular path now

Radius = 1312.5 m

Explanation:

Force on a moving charge due to constant magnetic field is given by

[tex]\vec F = q(\vec v \times \vec B)[/tex]

since here force on the moving charge is always perpendicular to the velocity always as it is vector product of velocity and magnetic field so here magnitude of the speed is always constant

Also the force is since perpendicular to the velocity always

so here the path of the moving charge will be circular path now

now to find out the radius of this circular path

[tex]F = \frac{mv^2}{R}[/tex]

[tex]qvBsin90 = \frac{mv^2}{R}[/tex]

[tex]R = \frac{mv}{qB}[/tex]

[tex]R = \frac{9.1\times 10^{-31}(1.50 \times 10^7)}{1.6 \times 10^{-19}(6.50 \times 10^{-8})}[/tex]

[tex]R = 1312.5 m[/tex]

Answer:

Float is travelling at speed of 3.86 m/s

Explanation:

As per Doppler's effect we know that when source and observer moves relative to each other then the frequency is different from actual frequency

so here when source moves closer to the observer

[tex]f_1 = f_o(\frac{v}{v - v_s})[/tex]

now we have

[tex]356 = f_o(\frac{v}{v - v_s})[/tex]

again when source moves away from the observer then we have

[tex]f_2 = f_o(\frac{v}{v + v_s})[/tex]

[tex]348 = f_o(\frac{v}{v + v_s})[/tex]

now divide above two equations

[tex]\frac{356}{348} = \frac{v + v_s}{v - v_s}[/tex]

[tex]1.023 = \frac{v + v_s}{v - v_s}[/tex]

[tex]1.023( v - v_s) = (v + v_s)[/tex]

here we know that the speed of sound in air is 340 m/s

so we have

[tex]1.023(340 - v_s) = (340 + v_s)[/tex]

[tex]7.816 = 2.023 v_s[/tex]

now we have

[tex]v_s = 3.86 m/s[/tex]

The speed of the float in the parade is determined using the observed frequencies of the flute when the band is approaching and moving away informed by the Doppler Effect physics theory. You generate equations for both scenarios and solve for the speed of the source, using the average speed of sound in the air.

This problem relates to the Doppler Effect, which explains why the frequency of a sound changes when the source of the sound is moving in relation to the observer. The formula to calculate a Doppler Shift when the source is moving away (as in the float in the parade) is given by: f' = f [(v + v0) / v] and when the source is approaching is given by: f' = f [(v - v0) / v]. Where, f' is the observed frequency, f is the source frequency, v is the sound speed (340 m/s), and v0 is the speed of the source.

In the problem, it's given that the observed frequencies when the band is approaching and moving away are 356 Hz and 348 Hz, respectively. By setting up two equations using the Doppler Shift formula for both observed frequencies, we can solve for v0. In this case, we use the average speed of sound in the air, which is about 340 m/s.

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Answer:

Option C is the correct answer.

Explanation:

We have charge stored in a capacitor

           Q = CV

C is the capacitance and V is the voltage.

A capacitor is connected to a 9 V battery and acquires a charge Q.

That is

          Q = C x 9 = 9C

What is the charge on the capacitor if it is connected instead to an 18 V battery

That is

          Q' = C x 18 = 9C x 2 = 2Q

Option C is the correct answer.      

When the voltage on a capacitor is doubled, the charge on the capacitor doubles as well. Hence, if a capacitor initially has a charge Q at 9V, it will have a charge of 2Q at 18V.

The subject of the question is the behavior of a capacitor when it is connected to various voltage sources. The charge Q on a capacitor is given by the equation Q = CV, where C is the capacitance of the capacitor and V is the voltage across it. So if a capacitor is charged by a 9V battery (Q = C*9V), and then connected to an 18V battery, its new charge (lets call it Q1) would be C*18V. Therefore, Q1 = 2Q, since the voltage is doubled, hence, the charge on the capacitor also doubles.

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Answer:

The potential difference between the plates is 596.2 volts.

Explanation:

Given that,

Capacitance [tex]C=260\ pF[/tex]

Charge [tex]q=0.155\ \mu\ C[/tex]

Separation of plates = 0.313 mm

We need to calculate the potential difference between the plates

Using formula of potential difference

[tex]V= \dfrac{Q}{C}[/tex]

Where, Q = charge

C = capacitance

Put the value into the formula

[tex]V=\dfrac{0.155\times10^{-6}}{260\times10^{-12}}[/tex]

[tex]V=596.2\ volts[/tex]

Hence,The potential difference between the plates is 596.2 volts.

Answer:

Heat flow through walls in 10 hours is

[tex]Q = 6.1 \times 10^6 J[/tex]

Explanation:

Thermal conductivity of all the materials is as follows

1). Concrete = 0.8

2). Brick = 0.6

3). Fibreglass = 0.04

4). Corkboard = 0.04

Area of the wall is given as

[tex]A = (8 \times 4) = 32 m^2[/tex]

now the thermal resistance due to each wall is given as

[tex]R_1 = \frac{0.04}{0.6(32)} = 2.08 \times 10^{-3}[/tex]

[tex]R_2 = \frac{0.08}{0.8(32)} = 3.125 \times 10^{-3}[/tex]

[tex]R_3 = \frac{0.06}{0.04(32)} = 46.87 \times 10^{-3}[/tex]

[tex]R_2 = \frac{0.10}{0.04(32)} = 78.13 \times 10^{-3}[/tex]

Now total thermal resistance of all walls

[tex]R = R_1 + R_2 + R_3 + R_4[/tex]

[tex]R = (2.08 + 3.125 + 46.87 + 78.13) \times 10^{-3}[/tex]

[tex]R = 0.130[/tex]

now rate of heat transfer per second is given as

[tex]\frac{dQ}{dt} = \frac{T_1 - T_2}{R}[/tex]

[tex]Q = \frac{40 - 18}{0.130}(10 \times 3600)[/tex]

[tex]Q = 6.1 \times 10^6 J[/tex]

Answer:

option (d)

Explanation:

There are two types of oscillations.

1. Damped oscillations: The oscillations in which the amplitude of a wave goes on decreasing continuously are called damped oscillations.

For example, the oscillations of a seismic wave.

2. Undamped oscillations: The oscillations in which the amplitude o a wave remains constant are called undamped oscillations.

for example, oscillations of light waves.

The transmission axis of the second sheet makes a right angle (90 degrees) with the vertical given that no light passes through it. This is based on Malus's Law for polarization.

The phenomenon described in your question is polarization, which is a characteristic of transverse waves such as light. The sheet of polarizing material allows only the light polarized in the same direction as the sheet's axis of transmission to pass through it. Following Malus's Law for polarization, we can determine that if no light passes through the second polarizer, its transmission axis must be at a right angle (90 degrees) to the initial polarization direction, which is vertical in this case.

The Malus's Law is an equation that describe the intensity of the light after passing through a polarizer as: I = I0 cos^2 θ where I0 is the initial intensity of the light, θ is the angle between the light polarization direction and the transmission axis of the polarizer. If I = 0, then cos^2 θ = 0, which indicates that θ is 90 degrees. This concept comes under the area of wave optics in Physics.

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The transmission axis of the second sheet of polarizing material makes a 90-degree angle with the vertical because it must be perpendicular to the first sheet's axis for no light to pass through. Hence, with the first polarizer vertical, the second must be horizontal.

The question asks about the angle that the transmission axis of the second sheet of polarizing material makes with the vertical, given that no light passes through. According to the principles of light polarization, if no light passes through a second sheet of polarizing material, it means the transmission axis of the second sheet is perpendicular to the axis of the first one.

Since the first sheet polarizes light vertically, this implies the transmission axis of the second sheet must be horizontal. Therefore, as per common geometric considerations where vertical and horizontal lines are perpendicular, the angle between the vertical (first filter axis) and horizontal (second filter axis) is 90 degrees.

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Answer:

1.87 A

Explanation:

τ = mean time between collisions for electrons = 2.5 x 10⁻¹⁴ s

d = diameter of copper wire = 2 mm = 2 x 10⁻³ m

Area of cross-section of copper wire is given as

A = (0.25) πd²

A = (0.25) (3.14) (2 x 10⁻³)²

A = 3.14 x 10⁻⁶ m²

E = magnitude of electric field = 0.01 V/m

e = magnitude of charge on electron = 1.6 x 10⁻¹⁹ C

m = mass of electron = 9.1 x 10⁻³¹ kg

n = number density of free electrons in copper = 8.47 x 10²² cm⁻³ = 8.47 x 10²⁸ m⁻³

[tex]i[/tex] = magnitude of current

magnitude of current is given as

[tex]i = \frac{Ane^{2}\tau E}{m}[/tex]

[tex]i = \frac{(3.14\times 10^{-6})(8.47\times 10^{28})(1.6\times 10^{-19})^{2}(2.5\times 10^{-14}) (0.01)}{(9.1\times 10^{-31})}[/tex]

[tex]i[/tex]  = 1.87 A

Answer:

0.01663 Nm

Explanation:

N = 1000, r = 12 cm = 0.12 m, i = 15 A, B = 5.8 x 10^-5 T, θ = 25

Torque = N i A B Sinθ

Torque = 1000 x 15 x 3.14 x 0.12 x 0.12 x 5.8 x 10^-5 x Sin 25

Torque = 0.01663 Nm

Answer:

a) Maximum height reached = 1878.90 m

b) Time of flight = 39.14 seconds.

Explanation:

Projectile motion has two types of motion Horizontal and Vertical motion.  

Vertical motion:  

We have equation of motion, v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration and t is the time taken.  

Considering upward vertical motion of projectile.  

In this case, Initial velocity = vertical component of velocity = u sin θ, acceleration = acceleration due to gravity = -g [tex]m/s^2[/tex] and final velocity = 0 m/s.  

0 = u sin θ - gt  

t = u sin θ/g  

Total time for vertical motion is two times time taken for upward vertical motion of projectile.  

So total travel time of projectile , [tex]t=\frac{2usin\theta }{g}[/tex]

Vertical motion (Maximum height reached, H) :

We have equation of motion, [tex]v^2=u^2+2as[/tex], where u is the initial velocity, v is the final velocity, s is the displacement and a is the acceleration.  

Initial velocity = vertical component of velocity = u sin θ, acceleration = -g, final velocity = 0 m/s at maximum height H

[tex]0^2=(usin\theta) ^2-2gH\\ \\ H=\frac{u^2sin^2\theta}{2g}[/tex]

In the give problem we have u = 192 m/s, θ = 90° we need to find H and t.

a) [tex]H=\frac{u^2sin^2\theta}{2g}=\frac{192^2\times sin^290}{2\times 9.81}=1878.90m[/tex]

Maximum height reached = 1878.90 m

b) [tex]t=\frac{2usin\theta }{g}=\frac{2\times 192\times sin90}{9.81}=39.14s[/tex]

Time of flight = 39.14 seconds.

Answer:

0.278 m/s

Explanation:

We can answer the problem by using the law of conservation of momentum. In fact, the total momentum before the collision must be equal to the total momentum after the collision.

So we can write:

[tex]mu=(m+M)v[/tex]

where

m = 0.200 kg is the mass of the koala bear

u = 0.750 m/s is the initial velocity of the koala bear

M = 0.350 kg is the mass of the other clay model

v is their final combined velocity

Solving the equation for v, we get

[tex]v=\frac{mu}{m+M}=\frac{(0.200)(0.750)}{0.200+0.350}=0.278 m/s[/tex]

Answer:

work is 130.5 kJ/kg

entropy change is 1.655 kJ/kg-k

maximum  theoretical work is 689.4 kJ/kg

Explanation:

piston cylinder assembly

100 bar, 360°C to 1 bar, 160°C

to find out

work  and amount of entropy  and magnitude

solution

first we calculate work i.e heat transfer - work =   specific internal energy @1 bar, 160°C  - specific internal energy @ 100 bar, 360°C    .................1

so first we get some value from steam table with the help of 100 bar @360°C and  1 bar @ 160°C

specific volume = 0.0233 m³/kg

specific enthalpy = 2961 kJ/kg

specific internal energy = 2728 kJ/kg

specific entropy = 6.004 kJ/kg-k

and respectively

specific volume = 1.9838 m³/kg

specific enthalpy = 2795.8 kJ/kg

specific internal energy = 2597.5 kJ/kg

specific entropy = 7.659 kJ/kg-k

now from equation 1 we know heat transfer q = 0

so - w =   specific internal energy @1 bar, 160°C  - specific internal energy @ 100 bar, 360°C

work = 2728 - 2597.5

work is 130.5 kJ/kg

and entropy change formula is i.e.

entropy change =  specific entropy ( 100 bar @360°C)  - specific entropy ( 1 bar @160°C )

put these value we get

entropy change =  7.659 - 6.004

entropy change is 1.655 kJ/kg-k

and we know maximum  theoretical work = isentropic work

from steam table we know specific internal energy is 2038.3 kJ/kg

maximum  theoretical work = specific internal energy - 2038.3

maximum  theoretical work = 2728 - 2038.3

maximum  theoretical work is 689.4 kJ/kg

The work and entropy produced in the adiabatic expansion of steam can be calculated using the First Law of Thermodynamics and thermodynamic principles. Maximum theoretical work corresponds to an isentropic process, which is an ideal, reversible adiabatic process that occurs without an increase in entropy.

The question regards the calculation of work and entropy of an adiabatic expansion process of steam in a piston-cylinder assembly. We'd need specific heat capacity, initial and end states temperatures data and the thermodynamic equations for adiabatic processes. The First Law of Thermodynamics equation dEint = CyndT will be used to calculate internal energy changes. Final work, W, can be calculated using the equation W = pΔV. Entropy change can be obtained using the formula ΔS=Q/T, where Q represents heat transfer, which is 0 for adiabatic processes.

As for the maximum theoretical work obtainable, this corresponds to a reversible adiabatic process or an isentropic process - entropy remains constant. This requires a quasi-static or reversible deformation. The work obtained in this case is at its maximum because there are no irreversibilities or entropy generation, which are responsible for decreasing the performance of real processes and engines.

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Answer:

2069.76 N

Explanation:

density of wood = 824 kg/m^3

density of water = 1000 kg/m^3

Volume of wood = 1.2 m^3

True weight of wood = volume of wood x density of wood x gravity

True weight of wood = 1.2 x 824 x 9.8 = 9690.24 N

Buoyant force acting on wood = volume of wood x density of water x gravity

Buoyant force acting on wood = 1.2 x 1000 x 9.8 = 11760 N

Tension in the rope = Buoyant force - True weight

tension in rope = 11760 - 9690.24 = 2069.76 N

Explanation:

It is given that,

Mass of lithium, [tex]m=1.16\times 10^{-26}\ kg[/tex]

It is accelerated through a potential difference, V = 224 V

Uniform magnetic field, B = 0.724 T

Applying the conservation of energy as :

[tex]\dfrac{1}{2}mv^2=qV[/tex]

[tex]v=\sqrt{\dfrac{2qV}{m}}[/tex]

q is the charge on an electron

[tex]v=\sqrt{\dfrac{2\times 1.6\times 10^{-19}\ C\times 224\ V}{1.16\times 10^{-26}\ kg}}[/tex]

v = 78608.58 m/s

[tex]v=7.86\times 10^4\ m/s[/tex]

To find the radius of the ion's path in the magnetic field. The centripetal force is balanced by the magnetic force as :

[tex]qvB=\dfrac{mv^2}{r}[/tex]

[tex]r=\dfrac{mv}{qB}[/tex]

[tex]r=\dfrac{1.16\times 10^{-26}\ kg\times 7.86\times 10^4\ m/s}{1.6\times 10^{-19}\ C\times 0.724\ T}[/tex]

r = 0.0078 meters

So, the radius of the path of the ion is 0.0078 meters. Hence, this is the required solution.

Answer:

64.08 rad

Explanation:

f = 78 rpm = 76 / 60 rps

θ = 0.45 rad, t = 8 s

(θ2 - θ1) / t = ω

θ2 - θ1 = 2 x 3.14 x 76 x 8 / 60 = 63.63

Angle turns from initial position = 0.45 + 63.63 = 64.08 rad

Answer:

The final speed of the train car is 8.57 m/s.

Explanation:

Given that,

Mass of train car = 1000 kg

Mass of sand = 400 kg

Speed of train car = 12 m/s

We need to calculate the final speed of the train car after the sand is dumped

Using conservation of momentum

[tex]m_{1}u_{1}=(m_{1}+m_{2})v[/tex]...(I)

Put the value in the equation (I)

[tex]1000\times12=(1000+400)v[/tex]

[tex]v=\dfrac{1000\times12}{1400}[/tex]

[tex]v=8.57\ m/s[/tex]

Hence, The final speed of the train car is 8.57 m/s.

Answer:

783.63 Watt

Explanation:

T = 111 degree C = 111 + 273 = 384 K

T0 = 45 degree C = 45 + 273 = 318 K

A = 1.6 m^2

e = 0.75

According to the Stefan's law, the energy radiated per second is given by

[tex]E = \sigma eA\left ( T^{4}- T_{0}^{4}\right )[/tex]

[tex]E = 5.67\times 10^{-8}\times 0.75\times 1.6 ( 384^{4}- 318^{4}\right ))[/tex]

E = 783.63 Watt

Answer:

Explanation:

Number of oscillations in 100 s is 68.

time taken to complete one oscillation = 100 / 68 s = 1.47 s

Use the formula for the time period of an oscillating body

[tex]T = 2\pi \sqrt{\frac{L}{g}}[/tex]

[tex]T^{2} = 4\pi^{2} \frac{L}{g}}[/tex]

In this equation substitute the value of T amd L and then find the value of g.

Answer:

[tex]I_1 = 32.5 kg m^2[/tex]

Explanation:

Here as we know that total angular momentum is always conserved for child + round system

so here by angular momentum conservation we have

[tex]I_1 \omega_1 = (I_1 + I_2)\omega_2[/tex]

here we have

[tex]I_2 = mR^2[/tex] (inertia of boy)

[tex]I_2 = (34.5)(1.45^2)[/tex]

[tex]I_2 = 72.5 kg m^2[/tex]

now we have

[tex]I_1(2\pi 55) = (I_1 + 72.5)(2 \pi 17)[/tex]

[tex]I_1 = (I_1 + 72.5)(0.31)[/tex]

[tex]I_1(1 - 0.31) = 22.4[/tex]

[tex]I_1 = 32.5 kg m^2[/tex]

The total moment of inertia of the merry-go-round with the child can be calculated by considering the child as a point mass at a given distance from the axis of rotation. The decrease in the angular velocity of the merry-go-round when the child jumps on is due to the increase in the moment of inertia. The moment of inertia of the merry-go-round itself is close to the total moment of inertia because it has far more mass distributed away from the axis.

The subject is based on the physics concept of moment of inertia, which depends not only on the object's mass but also on its distribution relative to the axis of rotation. The moment of inertia initially decreases when the child, initially at rest, grabs onto the already spinning merry-go-round. This abrupt decrease in angular velocity is because of the increase in moment of inertia caused by the child.

To find the total moment of inertia (I), we first calculate the child’s moment of inertia (Ic) by considering the child as a point mass at a distance of 1.45 m from the axis of rotation. The formula for this is Ic = mR², where m is the child's mass (34.5 kg) and R is the distance from the center (1.45 m).

Then, we calculate for the angular velocity change from 55 rpm to 17 rpm. The goal is to find the moment of inertia of the merry-go-round itself, which should be close to the total moment of inertia because it has much more mass distributed away from the axis than the child does.

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Answer:

144540.16735 hp

Explanation:

Diameter of pipe = 36 in

Specific gravity of oil = 0.89

ρ = Density of oil = 0.89×62.2407

Q = Flow rate of oil = 1×10⁶ bbl/day = 1×10⁶×5.61458/86400 =  64.9836033565 ft³/s

hf = 13 ft/1000ft = 0.013 ft/ft

for 10 miles

hf = 0.013×10×5280 = 686.4 ft

g = Acceleration due to gravity = 32.17405 ft/s²

Power

P = ρQghf

⇒P = 0.89×62.2407×64.9836033565×32.17405×686.4

⇒P = 79497097.342 ft lbf/s

1 ft lbf/s = 0.0018181817 hp

79497097.342 ft lbf/s = 144540.16735 hp

∴ Horsepower which must be delivered to the oil by each pump is  144540.16735 hp

Answer:

Explanation:

The half-life of a radioisotope, in this case carbon-14, is the time that a sample requires to reduce its amount to half, and it is a constant for every radioisotope (it does not change with the amount of sample).

Then, the formula for the remaining amount of a radioisotope is:

Where:

The number of half-lives for carbon-14 elapsed for the dinosaur fossil is:

Then, A / A₀ = (1/2)ⁿ = (1/2)¹¹⁸⁶⁷ ≈ 0.00000 .

The number is too small, and when you round to five decimal places the result is zero. That is why carbon-14 cannot be used to date dinosaur fossils, given that they are too old.

C-14 dating is not applicable to a 68 million years old dinosaur fossil, because the half-life of C-14 (5730 years) only allows for accurate dating up to about 50,000-57,000 years. After such time period, the remaining C-14 would be too small to measure accurately. Therefore, for a 68 million year old fossil, the remaining C-14 would be effectively zero.

The question is asking about the amount of Carbon-14 (C-14) remaining in a dinosaur fossil that is approximately 68 million years old. However, C-14 dating is not applicable to such old samples. This is because C-14 decays back to Nitrogen-14 (N-14) with a half-life of approximately 5,730 years. Because of this half-life, the best-known method for determining the absolute age of fossils with C-14 allows for reliable dating of objects only up to about 50,000 years old. After 10 half-lives, which would be about 57,000 years, any original C-14 existing in a sample would become too small to measure accurately

For very old samples like a 68 million year old dinosaur fossil, isotopes with much longer half-lives are used for dating, such as uranium-235 and potassium-40. Therefore, for a 68 million year old dinosaur fossil, the remaining C-14 would effectively be zero.

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Answer:

Temperature change in the wire is 625°C

Explanation:

Let the initial current in the wire be I₀

Thus,

the final current in the wire will be, I = (1 - 0.20) × I₀ = 0.80I₀

Given α = 0.0004 1/°C

Now,

Resistance = (potential difference (E))/current  (I)

also

R = R₀ [1 + αΔT]

Where ΔT is the increase in temperature , thus

E/I = E/I₀ [1 + α × ΔT)

on substituting the values in the above equation, we get

1/(0.80I₀) = 1/(I₀) × [1 + 0.0004 × ΔT]

or

1/(0.80) = [1 + 0.0004 × ΔT)]

or

ΔT = 625°C

The temperature change in the Nichrome wire, based on a 20% drop in current, is calculated to be approximately 625°C.

A Nichrome wire's resistance increases with temperature, primarily determined by its temperature coefficient.

Step-by-Step Solution :

      E/I = E/I₀ [1 + α × ΔT)

on substituting the values in the above equation, we get

= 1/(0.80I₀) = 1/(I₀) × [1 + 0.0004 × ΔT]

= 1/(0.80) = [1 + 0.0004 × ΔT)]

= ΔT = 625°C

The temperature change in the Nichrome wire is  approximately 625°C.

A cool experiment with a testable hypothesis is testing an apple and if it will be able to oxidize in different temperatures with the inside exposed to Oxygen.  

Hypothesis: If the cut piece of an apple is exposed to warm air then the apple will turn brown and oxidize faster than a cut piece of apple in a cooler temperature.

Supplies: Three thermometers, An apple, an apple cutter, a plate, etc.

Directions place the three thermometers in a cool cold area,