The energy associated with the random motion of molecules or atoms within a substance is

Assume that the average mass of each of the approximately 1 billion people in China is 55 kg.Assume that they all gather in one

Harman [31]

Answer: $5.9(10)^{-8} m$

Explanation:

The equation to calculate the center of mass $C_{M}$ of a particle system is:

$C_{M}=\frac{m_{1}r_{1}+m_{1}r_{1}+...+m_{n}r_{n}}{m_{1}+m_{2}+...+m_{n}}$

In this case we can arrange for one dimension, assuming the geometric center of the Earth and the ladder are on a line, and assuming original center of mass located at the Earth's geometric center:

$C_{M}=\frac{m_{E}(0 m) + m_{p} r_{E-p}}{m_{E}+m_{p}}$

Where:

$m_{E}=5.9(10)^{24} kg$ is the mass of the Earth

$m_{p}=55(10)^{9} kg$ is the mass of 1 billion people

$r_{E}=6371000 m$ is the radius of the Earth

$r_{E-p}=6371000 m- 2m=6370998 m$ is the distance between the center of the Earth and the position of the people (2 m above the Earth's surface)

$C_{M}=\frac{m_{p}55(10)^{9} kg (6370998 m)}{5.9(10)^{24} kg+55(10)^{9} kg}$

$C_{M}=5.9(10)^{-8} m$ This is the displacement of Earth's center of mass from the original center.

8 0

3 years ago

On a winter day with a temperature of -10°C, 500g of snow (water ice) is brought inside where the temperature is 18 °C. The snow

Serjik [45]

Answer:

Explanation:

Mass of ice m = 500g = .5 kg

Heat required to raise the temperature of ice by 10 degree

= mass of ice x specific heat of ice x change in temperature

= .5 x 2093 x 10 J

10465 J

Heat required to melt the ice

= mass of ice x latent heat

0.5 x 334 x 10³ J

167000 J

Heat required to raise its temperature to 18 degree

= mass x specific heat of water x rise in temperature

= .5 x 4182 x 18

=37638 J

Total heat

=10465 +167000+ 37638

=215103 J

7 0

3 years ago

We are running late for school and we want to make our 0.5 kg tea (it’s at 90 C) colder. Let’s assume we can drink tea when it’s

PSYCHO15rus [73]

Answer:

x=0.154kg

Explanation:

(x*L)+(0.5kg*4200*50)+(x*4200*(-50)=0

(x*333 000J/kg*c)+(0.5kg*4200J/kg*C*(-40C))+(x*4200J/kg*C*50C)=0

6 0

2 years ago

The work done by an external force to move a -8.50 μC charge from point a to point b is 6.10×10−4 J . If the charge was started

bekas [8.4K]

Answer:

-54.12 V

Explanation:

The work done by this force is equal to the difference between the final value and the initial value of the energy. Since the charge starts from the rest its initial kinetic energy is zero.

$W=\Delta E\\W=\Delta K+\Delta U\\W=K_f+\Delta U\\\Delta U=W-K_f\\\Delta U=6.10*10^{-4}J-1.50*10^{-4}J\\\Delta U=4.60*10^{-4}J$

The change in electrostatic potential energy $\Delta U$ , of one point charge q is defined as the product of the charge and the potential difference.

$\Delta U=qV\\V=\frac{\Delta U}{q}\\V=\frac{4.60*10^{-4}J}{-8.50*10^{-6}C}\\V=-54.12 V$

5 0

4 years ago

An alternator consists of a coil of area A with N turns that rotates in a uniform field B around a diameter perpendicular to the

svet-max [94.6K]

Answer:

(a): emf = $\rm 2\pi f NBA\sin(2\pi ft).$

(b): Amplitude of alternating voltage = 20.942 Volts.

Explanation:

<u>Given:</u>

Area of the coil = A.
Number of turns of coil = N.
Magnetic field = B
Rotation frequency = f.

(a):

The magnetic flux through the coil is given by

$\phi = \vec B \cdot \vec A=BA\cos\theta$

where,

$\vec A$ = area vector of the coil directed along the normal to the plane of the coil.

$\theta$ = angle between $\vec B$ and $\vec A$ .

Assuming, the direction of magnetic field is along the normal to the plane of the coil initially.

At any time t, the angle which magnetic field makes with the normal to the plane of the coil is $2\pi ft$

Therefore, the magnetic flux linked with the coil at any time t is given by

$\phi(t) = NBA\cos(2\pi ft)$

According to Faraday's law of electromagnetic induction, the emf induced in the coil is given by

$e=-\dfrac{d\phi}{dt}\\=-\dfrac{d(NBA\cos(2\pi ft))}{dt}\\=-NBA(-2\pi f\sin(2\pi ft))\\=2\pi f NBA\sin(2\pi ft).$

(b):

The amplitude of the alternating voltage is the maximum value of the emf and emf is maximum when $\sin(2\pi ft)=1.$

Therefore, the amplitude of the alternating voltage is given by

$e_o = 2\pi ft NBA.$

We have,

$N=100\\A=10^{-2}\ m^2\\B=0.1\ T\\f=2000\ rev/ min = 2000\times \dfrac{1}{60}\ rev/sec=33.33\ rev/sec.$

Putting all these values,

$e_o = 2\pi \times 33.33\times 100\times 0.1\times 10^{-2}=20.942\ Volts.$

7 0

3 years ago