A 100 kg individual consumes 1200 kcal of food energy a day. Calculate

(a) the altitude change, in m, if the food energy content was converted entirely into lifting the indi-

vidual under normal earth gravity.

(b) the velocity, in m/s, if the food energy content was converted entirely into accelerating the indi-

vidual from rest.

(c) the final temperature, in ◦C, of a 100 kg mass of liquid water initially at the normal human body

temperature and heated with the energy content of the food. You can use a liquid water specific

heat of 4.1 kJ/kg K.

Answer:

The weight at a distance 4R from the center of earth is 10.37 N.

Explanation:

Given that,

Weight = 166 N

Distance = 4R

Let m be the mass of the object.

We know that,

Mass of earth [tex]M_{e}=5.98\times10^{24}\ kg[/tex]

Gravitational constant[tex]G = 6.67\times10^{-11}\ N-m^2/kg^2[/tex]

Radius of earth [tex]R = 6.38\times10^{6}\ m[/tex]

We need to calculate the weight at a distance 4 R from the center of earth

Using formula of gravitational force

[tex]W = \dfrac{GmM_{e}}{R^2}[/tex]

Put the value in to the formula

[tex]166=\dfrac{6.67\times10^{-11}\times m\times5.98\times10^{24}}{(6.38\times10^{6})^2}[/tex]

[tex]m=\dfrac{166\times(6.38\times10^{6})^2}{6.67\times10^{-11}\times5.98\times10^{24}}[/tex]

[tex]m=16.94 kg[/tex]

Now, Again using formula of gravitational

[tex]W=\dfrac{6.67\times10^{-11}\times 16.94\times5.98\times10^{24}}{(4\times6.38\times10^{6})^2}[/tex]

[tex]W=10.37 N[/tex]

Hence, The weight at a distance 4R from the center of earth is 10.37 N.

Answer:

option (b)

Explanation:

Let the resistance of each resistor is R.

In series combination,

The effective resistance is Rs.

rs = r + R + R + .... + n times = NR

Let V be the source of potential difference.

Power in series

Ps = v^2 / Rs = V^2 / NR ..... (1)

In parallel combination

the effective resistance is Rp

1 / Rp = 1 / R + 1 / R + .... + N times

1 / Rp = N / R

Rp = R / N

Power is parallel

Rp = v^2 / Rp = N V^2 / R    ..... (2)

Divide equation (1) by equation (2) we get

Ps / Pp = 1 / N^2

Explanation:

It is given that,

Mass of an electron, [tex]m=9.11\times 10^{-31}\ kg[/tex]

Electric field, [tex]E=1.45\times 10^4\ N/C[/tex]

Separation between the plates, d = 1.9 cm = 0.019 m

The electron is accelerated from rest near the negative plate and passes through a tiny hole in the positive plate. We need to find the speed of the electron as it leave the hole.

The force due to accelerating electron is balanced by the electrostatic force i.e

qE = ma

[tex]a=\dfrac{qE}{m}[/tex]

[tex]a=\dfrac{1.6\times 10^{-19}\ C\times 1.45\times 10^4\ N/C}{9.11\times 10^{-31}\ kg}[/tex]

[tex]a=2.54\times 10^{15}\ m/s^2[/tex]

Let v is the speed as it leave the hole. It can be calculated using third equation of motion as :

[tex]v^2-u^2=2ad[/tex]

[tex]v=\sqrt{2ad}[/tex]

[tex]v=\sqrt{2\times 2.54\times 10^{15}\times 0.019\ m}[/tex]

v = 9824459.27 m/s

or

[tex]v=9.82\times 10^6\ m/s[/tex]

So, the speed of the electron as it leave the hole is [tex]9.82\times 10^6\ m/s[/tex]. Hence, this is the required solution.

Answer:

Increased by 16 times

Explanation:

F = Gravitational force between two bodies

G = Gravitational constant = 6.67408 × 10⁻¹¹ m³/kg s²

m₁ = Mass of one body

m₂ = Mass of other body

d = distance between the two bodies

[tex]F=\frac{Gm_1m_2}{d^2}\\ F=\frac{1}{d^2}\quad \text {(as G and masses are constant)}[/tex]

[tex]F_{new}=\frac{1}{\left (\frac{d}{4}\right )^2}\\\Rightarrow F_{new}=\frac{1}{\frac{d^2}{16}}\\\Rightarrow F_{new}={16}\times \frac{1}{d^2}\\\Rightarrow F_{new}=16\times F[/tex]

∴Force will increase 16 times

Answer:

The ratio of stopping distances is 4 i.e by a factor 4 the stopping distances differ

Explanation:

Using 3rd equation of motion we have

For car 1

[tex]v_{1}^{^{2}}=u_{1}^{2}+2a_{1}s_{1}[/tex]

For car 2 [tex]v_{2}^{^{2}}=u_{2}^{2}+2a_{2}s_{2}[/tex]

Since the initial speed of both the cars are equal and when the cars stop the final velocities of both the cars become zero thus the above equations reduce to

[tex]u^{2}=-2a_{1}s_{1}\\\\s_{1}=\frac{-u^{2}}{2a_{1}}[/tex].............(i)

Similarly for car 2 we have

[tex]s_{2}=\frac{-u^{2}}{2a_{2}}[/tex]..................(ii)\

Taking ratio of i and ii we get

[tex]\frac{s_{1}}{s_{2}}=\frac{a_{2}}{a_{1}}[/tex]

Let

[tex]\frac{a_{2}}{a_{1}}=4[/tex]

Thus

[tex]\frac{s_{1}}{s_{2}}=4[/tex]

The ratio of stopping distances is 4

Final answer:

The stopping distances of two cars with different deceleration rates will differ by the inverse ratio of their decelerations. If one car's deceleration is a quarter of the other's, the car with the lower deceleration will require four times the stopping distance of the other car.

Explanation:

The question at hand is about how the stopping distances of two cars differ when their deceleration rates are different. If one car's deceleration is a quarter of the other's, then to find the factor by which the stopping distances differ, we can use the equation of motion [tex]v^2 = u^2 + 2as[/tex] v is the final velocity, u is the initial velocity, a is the deceleration, and s is the stopping distance.

Since the final velocity (v) for both cars will be zero (they come to a stop), and assuming the initial velocities (u) are the same for both cars, we can set the equation for both as follows: 0 = u^2 + 2a1s1 and 0 = u^2 + 2a2s2, with a1 being the higher deceleration of the first car and a2 being a quarter of that, s1 and s2 being the stopping distances respectively.

When we solve the equations for s1 and s2, we find that s1 is proportional to 1/a1 and s2 is proportional to 1/a2, so if a2 = 1/4 a1, then the ratio of the stopping distances s2/s1 is equal to the inverse ratio of the decelerations, which is 4. Hence, the car with the lower deceleration requires four times the distance to stop compared to the car with the higher deceleration.

Answer:

[tex]Q = 4.40 \times 10^5 Cal[/tex]

Explanation:

Here we know that initial temperature of ice is given as

[tex]T = 0^o C[/tex]

now the latent heat of ice is given as

[tex]L = 80 Cal/g[/tex]

now we also know that the mass of ice is

[tex]m = 5.50 kg[/tex]

so here we know that heat required to change the phase of the ice is given as

[tex]Q = mL[/tex]

[tex]Q = (5.50 \times 10^3)(80)[/tex]

[tex]Q = 4.40 \times 10^5 Cal[/tex]

The total energy required to melt all the 5.50 kg (or 5500g) of ice is 440,000 calories. This is calculated using the given heat of fusion (Lf) value of 80 cal/g for water and the heat exchange formula, Q=mLf.

To calculate the amount of energy required to melt all the ice, we need to use the formula for heat exchange: Q = mLf. Where Q is the heat required, m is the mass, and Lf is the heat of fusion. Given that Lf is 80 cal/g for water, the mass m is 5.50 kg (or 5500g), and you are trying to find Q, you can simply replace the known quantities into the equation:

Q = (5500g) * (80cal/g)

So, the total energy required to melt all the ice is 440,000 calories. This heat is absorbed by the ice, providing the energy required to break the intermolecular bonds in the ice and facilitate the phase transition from solid ice to liquid water. The energy required for a phase change like this is significant, explaining why ice can take a while to melt even on a hot summer day.

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Answer:

at resonance impedence is equal to resistance and quality factor is dependent on R L AND C all

Explanation:

we know that for series RLC circuit impedance is given by

[tex]Z=\sqrt{R^2+\left ( X_L-X_C \}right )^2[/tex]

but we know that at resonance [tex]X_L=X_C[/tex]  

putting  [tex]X_L=X_C[/tex] in impedance formula , impedance will become

Z=R so at resonance impedance of series RLC is equal to resistance only

now quality factor of series resonance is given by

[tex]Q=\frac{\omega L}{R}=\frac{1}{\omega CR}=\frac{1}{R}\sqrt{\frac{L}{C}}[/tex]  so from given expression it is clear that quality factor depends on R L and C

Explanation:

We need to find the speed of an electron that has fallen through a potential difference of  125 volts. It can be calculated using the De-broglie hypothesis as :

(a) V = 125 volts

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

Where

v = speed of electron

V is potential difference

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

[tex]v=\sqrt{\dfrac{2\times 1.6\times 10^{-19}\times 125\ V}{9.1\times 10^{-31}}}[/tex]

v = 6629935.44 m/s

[tex]v=6.62\times 10^6\ m/s[/tex]

(b) V = 125 megavolts

[tex]V=1.25\times 10^8\ V[/tex]

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

[tex]v=\sqrt{\dfrac{2\times 1.6\times 10^{-19}\times 1.25\times 10^8\ V}{9.1\times 10^{-31}}}[/tex]

[tex]v=6.62\times 10^9\ m/s[/tex]

Hence, this is the required solution.

Answer:

Rhodium has FCC structure.

Explanation:

Formula used :  

[tex]\rho=\frac{Z\times M}{N_{A}\times a^{3}}[/tex]

where,

[tex]\rho[/tex] = density

Z = number of atom in unit cell

M = atomic mass

[tex](N_{A})[/tex] = Avogadro's number  

a = edge length of unit cell

1) If it FCC cubic lattice

Number of atom in unit cell of FCC (Z) = 4

Atomic radius of Rh= 0.1345 nm = [tex]1.345\times 10^{-8} cm[/tex]

Edge length = a

For FCC,  a = 2.828 × r :

a = [tex]2.828\times 1.345\times 10^{-8} cm=3.80366\times 10^{-8}cm[/tex]

Density of Rh= [tex]12.41 g/cm^3[/tex]

Atomic mass of Rh(M) = 102.91 g/mol

On substituting all the given values , we will get the value of 'a'.

[tex]12.41 g/cm^3=\frac{4\times 102.91 g/mol}{6.022\times 10^{23} mol^{-1}\times (3.80366\times 10^{-8}cm)^{3}}[/tex]

[tex]12.41 g/cm^3\approx 12.4214 g/cm^3[/tex]

2) If it BCC cubic lattice

Number of atom in unit cell of BCC (Z) = 2

Atomic radius of Rh= 0.1345 nm = [tex]1.345\times 10^{-8} cm[/tex]

Edge length = a

For BCC,  a = 2.309 × r :

a = [tex]2.828\times 1.345\times 10^{-8} cm=3.105605\times 10^{-8}cm[/tex]

Density of Rh= [tex]12.41 g/cm^3[/tex]

Atomic mass of Rh(M) = 102.91 g/mol

On substituting all the given values , we will get the value of 'a'.

[tex]12.41 g/cm^3=\frac{2\times 102.91 g/mol}{6.022\times 10^{23} mol^{-1}\times (3.105605\times 10^{-8}cm)^{3}}[/tex]

[tex]12.41 g/cm^3[/tex] ≠ [tex]11.41 g/cm^3[/tex]

Rhodium has FCC structure.

Rhodium has a FCC structure because the edge length of the unit cell is smaller than 4 times the atomic radius divided by the square root of 3.

BCC stands for Body-Centered Cubic structure and FCC stands for Face-Centered Cubic structure. To determine which structure rhodium has, we need to compare the atomic radius of rhodium with the edge length of the unit cell for both structures.

For BCC, the diagonal distance of the body-centered cube is equal to 4 times the atomic radius. Therefore, the edge length of the unit cell for BCC is given by 4 times the atomic radius divided by √3.

For FCC, the face diagonal distance of the face-centered cube is equal to 2 times the atomic radius. Therefore, the edge length of the unit cell for FCC is given by 2 times the atomic radius.

By comparing the given atomic radius of 0.1345 nm to the calculated edge lengths, we can determine that rhodium has a FCC structure because 2 times the atomic radius (2 x 0.1345 nm) is smaller than 4 times the atomic radius divided by √3 (4 x 0.1345 nm / √3).

Answer:

21.6 A

Explanation:

n = number density of free electrons in copper = 8.5 x 10²² cm⁻³ = 8.5 x 10²⁸ m⁻³

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

d = diameter of copper wire = 0.790 mm = 0.790 x 10⁻³ m  

Area of cross-section of copper wire is given as  

A = (0.25) πd²

A = (0.25) (3.14) (0.790 x 10⁻³)²

A = 4.89 x 10⁻⁷ m²

v = drift speed = 3.25 mm/s = 3.25 x 10⁻³ m /s

the electric current is given as

i = n e A v

i = (8.5 x 10²⁸) (1.6 x 10⁻¹⁹) (4.89 x 10⁻⁷ ) (3.25 x 10⁻³)

i = 21.6 A

Answer:

The resistance of the heater wire is of R= 0.68 Ω.

Explanation:

1 cal/s = 4.184 W

P= 50 cal/s = 209.2 W

V= 12V

P= V* I

I= P/V

I= 17.43 A

P= I² * R

R= P / I²

R= 0.68 Ω

Answer:

Wavelength of microwaves is 3 m.

Explanation:

In this question, we need to find the wavelength of 100 MHz microwaves in muscle and in fat.

Frequency of the microwaves, [tex]\nu=100\ MHz=100\times 10^6\ Hz=10^8\ Hz[/tex]

The relation between the frequency and the wavelength is given by :

[tex]c=\nu\times \lambda[/tex]

[tex]\lambda=\dfrac{c}{\nu}[/tex]

Where

c is the sped of light

[tex]\lambda=\dfrac{3\times 10^8\ m/s}{10^8\ Hz}[/tex]

[tex]\lambda=3\ m[/tex]

So, the wavelength of microwaves is 3 m. Hence, this is the required solution.

Answer:

Weight, w = mg

Mass is an intrinsic property.

Explanation:

Mass is the measure of amount of matter in an object. It is an intrinsic that is unchanging property of a body. Mass cannot be destroyed nor be created.

Weight is the product of mass and acceleration due to gravity.

It changes with value of acceleration due to gravity. That is weight in Earth not equal to weight in moon since the value of acceleration due to gravity is different. So, weight is not an intrinsic property. It is a changing property for a body.

          Weight, w = mg, where m is the mass and g is the acceleration due to gravity value.      

Mass is an intrinsic and constant property of a body representing its matter content, while weight, the force of gravity on a body, varies with the gravitational environment. Despite common misuse in everyday language, they are distinct concepts in physics.

Mass and weight are two different but closely related concepts. Mass is an intrinsic property of a body, representing the amount of matter it contains, and it remains constant regardless of the body's location, be it on Earth, the moon, or in orbit.

On the other hand, weight is the force exerted on a body due to gravity. It's a product of the body's mass and the acceleration due to gravity, represented by the formula 'Weight = Mass x Gravity'. Unlike mass, weight changes with the gravitational environment. For example, a person's weight on the moon is only one-sixth of their weight on Earth due to the moon's lower gravity, while their mass remains the same.

In everyday language, mass and weight are often used interchangeably, but in the field of physics, it is important to distinguish between them. For example, when we refer to our 'weight' in kilograms, we're technically referring to our mass. The proper unit of weight, consistent with its definition as a force, is the newton in the International System of Units (SI).

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Answer:

61.85 ohm

Explanation:

L = 12 m H = 12 x 10^-3 H, C = 15 x 10^-6 F, Vrms = 110 V, R = 45 ohm

Let ω0 be the resonant frequency.

[tex]\omega _{0}=\frac{1}{\sqrt{LC}}[/tex]

[tex]\omega _{0}=\frac{1}{\sqrt{12\times 10^{-3}\times 15\times 10^{-6}}}[/tex]

ω0 = 2357 rad/s

ω = 2 x 2357 = 4714 rad/s

XL = ω L = 4714 x 12 x 10^-3 = 56.57 ohm

Xc = 1 / ω C = 1 / (4714 x 15 x 10^-6) = 14.14 ohm

Impedance, Z = [tex]\sqrt{R^{2}+\left ( XL - Xc \right )^{2}}[/tex]

Z = \sqrt{45^{2}+\left ( 56.57-14.14 )^{2}} = 61.85 ohm

Thus, the impedance at double the resonant frequency is 61.85 ohm.

In an LRC circuit, impedance at resonance is equal to resistance. When frequency is doubled, the impedance will increase as the inductive reactance becomes greater than the capacitive reactance. Calculation of the new impedance would involve re-computing inductive and capacitive reactances and substituting these in the impedance formula.

In an LRC series circuit, the impedance (Z) at resonance is equal to the resistance (R), because the reactance of the inductor (L) and the capacitor (C) cancel each other. The resonant frequency is determined by the values of L and C. If we increase the frequency to twice the resonance frequency, the reactance of the inductor becomes higher than the reactance of the capacitor, leading to an increase in total impedance.

Impedance (Z) is given by the square root formula Z = sqrt( R^2 + (X_L - X_C)^2 ). X_L and X_C are the inductive reactance (2πfL) and capacitive reactance (1/2πfC) respectively. If the frequency (f) is doubled, then X_L will be doubled while X_C will be halved.

We can calculate X_L and X_C under these conditions and substitute these values into the impedance formula to find the new impedance. Without the values of R, L, and C, it's not possible to give a numeric answer to this question, but the overall concept of how frequency affects impedance in an LRC circuit can be understood from the explanation.

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Answer:

4.5 Nm (Anticlockwise)

Explanation:

Let the 75 kg kid is sitting at the left end and the 60 kg kid is sitting on the right end.

Anticlockwise Torque = 75 x 1.5 = 112.5 Nm

clockwise Torque = 60 x 1.8 = 108 Nm

Net torque = Anticlockwise torque - clockwise torque

Net Torque = 112.5 - 108 = 4.5 Nm (Anticlockwise)

Answer:

a)

0.245 m/s

b)

0.904 m

Explanation:

a)

[tex]v_{d}[/tex] = speed of duck ahead of wave

[tex]v_{s}[/tex] = speed of surface wave = 0.32 m/s

T = time for paddling = 1.6 s

d = spacing between the waves = 0.12 m

speed of duck ahead of wave is given as

[tex]v_{d}[/tex] = [tex]v_{s}[/tex] - [tex]\frac{d}{T}[/tex]

[tex]v_{d}[/tex] = 0.32 - [tex]\frac{0.12}{1.6}[/tex]

[tex]v_{d}[/tex] = 0.245 m/s

b)

[tex]v_{w}[/tex] = speed of wave behind the duck

speed of wave behind the duck is given as

[tex]v_{w}[/tex] = [tex]v_{s}[/tex] + [tex]v_{d}[/tex]

[tex]v_{w}[/tex] = 0.32 + 0.245

[tex]v_{w}[/tex] = 0.565 m/s

D = spacing between the crests

spacing between the crests is given as

D = [tex]v_{w}[/tex] T

D = (0.565) (1.6)

D = 0.904 m

Answer:

847.45 N

Explanation:

F₁=force of exerted by smaller piston

F₂=force of exerted by larger piston=1.44×10⁴ N

A₁=Area of smaller piston= 2.62 cm =0.0265 m

A₂=Area of larger piston= 10.8 cm =0.108 m

Pressure exerted by both the pistons will be equal

[tex]P_1=P_2\\\Rightarrow \frac{F_1}{A_1}=\frac{F_2}{A_2}\\\Rightarrow F_1=\frac{F_2}{A_2} A_1\\\Rightarrow F_1=\frac{14400}{\pi\times  0.108^2}\pi\times  0.0262^2\\\Rightarrow F_1=847.45\ N[/tex]

Hence, force exerted to lift a 14400 N car is 847.45 N

Answer:

a)

346.67 N/C, downward

b)

1.3 m

Explanation:

(a)

q = magnitude of charge on the particle = 1.95 x 10⁻⁹ C

r = distance of location from the charged particle = 0.225 m

E = magnitude of electric field at the location

Magnitude of electric field at the location is given as

[tex]E = \frac{kq}{r^{2}}[/tex]

Inserting the values

[tex]E = \frac{(9\times 10^{9})(1.95 \times 10^{-9})}{(0.225)^{2}}[/tex]

E = 346.67 N/C

a negative charge produce electric field towards itself.

Direction :  downward

(b)

E = magnitude of electric field at the location = 10.5 N/C

r = distance of location from the charged particle = ?

q = magnitude of charge on the particle = 1.95 x 10⁻⁹ C

Magnitude of electric field at the location is given as

[tex]E = \frac{kq}{r^{2}}[/tex]

Inserting the values

[tex]10.5 = \frac{(9\times 10^{9})(1.95 \times 10^{-9})}{r^{2}}[/tex]

r = 1.3 m

The magnitude and direction of the electric field due to a particle of charge -1.95 nC at a point 0.225 m directly above it is approximately -3.57 x 10^5 N/C towards the particle. The distance from this particle at which its electric field has a magnitude of 10.5 N/C is approximately 0.036 m or 36 mm.

The magnitude of the electric field (E) due to a charged particle can be calculated using Coulomb's Law, which states E = k*Q/r^2, where k is Coulomb's constant (k ≈ 8.99 × 10^9 N m^2/C^2), Q is the charge of the particle, and r is the distance from the particle.

(a) Incorporating the given values: Q = -1.95 nC = -1.95 × 10^-9 C, and r = 0.225 m, we find E = k*Q/r^2 = (8.99 × 10^9 N m^2/C^2) * (-1.95 × 10^-9 C) / (0.225 m)^2 ≈ -3.57 x 10^5 N/C. The negative sign indicates the direction of the electric field is towards the particle.

(b) To find the distance at which the electric field has a magnitude of 10.5 N/C, we rearrange the equation to solve for r. That is r = sqrt(k*Q/E). By plugging in the given values, we find r = sqrt((8.99 × 10^9 N m^2/C^2 * -1.95 × 10^-9 C) / 10.5 N/C) ≈ 0.036 m or 36 mm.

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Answer:

112.5 J

Explanation:

F = 250 N, x = 30 cm = 0.3 m

Let the spring constant be K.

By using the Hooke's law

F = k x

250 = k x 0.3

k = 833.3 N / m

xi = 30 cm = 0.3 m, xf  60 cm = 0.6 m

Work done = 1/2 k (xf^2 - xi^2)

Work done = 0.5 x 833.33 x (0.6^2 - 0.3^2)

Work done = 112.5 J

Answers: (1) a. weight, (2)b. Force changes by 2/9, (3)b. movement, (4)a. 40,000 Joules, (5)c. the soil will be 5°C.

Mass and weight are very different concepts.  

Mass is the amount of matter that exists in a body, which only depends on the quantity and type of particles within it. This means mass is an intrinsic property of each body and remains the same regardless of where the body is located.  

On the other hand, weight is a measure of the gravitational force acting on an object and is directly proportional to the product of the mass [tex]m[/tex] of the body by the acceleration of gravity [tex]g[/tex]:  

[tex]W=m.g[/tex]  

Then, since the Earth and the Moon have different values ​​of gravity, the weight of an object in each place will vary, but its mass will not.

According to the law of universal gravitation, which is a classical physical law that describes the gravitational interaction between different bodies with mass:  

[tex]F=G\frac{m_{1}m_{2}}{r^2}[/tex] (1)

Where:  

[tex]F[/tex] is the module of the force exerted between both bodies  

[tex]G[/tex] is the universal gravitation constant

[tex]m_{1}[/tex] and [tex]m_{2}[/tex] are the masses of both bodies.

[tex]r[/tex] is the distance between both bodies

If we double the mass of one object (for example [tex]2m_{1}[/tex]) and triple the distance between both (for example [tex]3r[/tex]). The equation (1) will be rewritten as:

[tex]F=G\frac{2m_{1}m_{2}}{(3r)^2}[/tex] (2)

[tex]F=\frac{2}{9}G\frac{m_{1}m_{2}}{r^2}[/tex] (3)

If we compare (1) and (2) we will be able to see the force changes by 2/9.

The Work [tex]W[/tex] done by a Force [tex]F[/tex] refers to the release of potential energy from a body that is moved by the application of that force to overcome a resistance along a path.  

When the applied force is constant and the direction of the force and the direction of the movement are parallel, the equation to calculate it is:  

[tex]W=(F)(d)[/tex]

Now, when they are not parallel, both directions form an angle, let's call it [tex]\alpha[/tex]. In that case the expression to calculate the Work is:  

[tex]W=Fdcos{\alpha}[/tex]

Therefore, pushing on a rock accomplishes no work unless there is movement (independently of the fact that movement is parallel to the applied force or not).

The Kinetic Energy is given by:

[tex]K=\frac{1}{2}mV^{2}[/tex]   (4)

Where [tex]m[/tex] is the mass of the body and [tex]V[/tex] its velocity

For the first case (kinetic energy [tex]K_{1}=10000J[/tex]  for a car at [tex]V_{1}=30 mph=13.4112m/s[/tex]):

[tex]K_{1}=\frac{1}{2}mV_{1}^{2}[/tex]   (5)

Finding [tex]m[/tex]:

[tex]m=\frac{2K_{1}}{V_{1}^{2}}[/tex]   (6)

[tex]m=\frac{2(10000J)}{(13.4112m/s)^{2}}[/tex]   (7)

[tex]m=111.197kg[/tex]   (8)

For the second case (unknown kinetic energy [tex]K_{2}[/tex]  for a car with the same mass at [tex]V_{2}=60 mph=26.8224m/s[/tex]):

[tex]K_{2}=\frac{1}{2}mV_{2}^{2}[/tex]   (9)

[tex]K_{2}=\frac{1}{2}(111.197kg)(26.8224m/s)^{2}[/tex]   (10)

[tex]K_{2}=40000J[/tex]   (11)

The formula to calculate the amount of calories [tex]Q[/tex] is:

[tex]Q=m. c. \Delta T[/tex]   (12)

Where:

[tex]m[/tex]  is the mass

[tex]c[/tex]  is the specific heat of the element. For water is [tex]c_{w}=1 kcal/g\°C[/tex]  and for soil is [tex]c_{s}=0.20 kcal/g\°C[/tex]  

[tex]\Delta T[/tex]  is the variation in temperature (the amount we want to find for both elements)

This means we have to clear [tex]\Delta T[/tex] from (12) :

[tex]\Delta T=\frac{Q}{m.c} [/tex]   (13)

For Water:

[tex]\Delta T_{w}=\frac{Q_{w}}{m_{w}.c_{w}} [/tex]   (14)

[tex]\Delta T_{w}=\frac{1kcal}{(1kg)(1 kcal/g\°C)}[/tex]   (15)

[tex]\Delta T_{w}=1\°C)}[/tex]   (16)

For Soil:

[tex]\Delta T_{s}=\frac{Q_{s}}{m_{s.c_{s}} [/tex]   (17)

[tex]\Delta T_{s}=\frac{1kcal}{(1kg)(0.20 kcal/g\°C)}[/tex]   (18)

[tex]\Delta T_{s}=5\°C)}[/tex]   (19)

Hence the correct option is c.

Answer:

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Answer:

I) It becomes two times larger

II) It becomes four times larger

Explanation:

I) Electric field is directly proportional to Magnetic field and as such, if one is increased, the other is also increased by the same proportion.

The formula is given as

[tex]E_{1}  = cB_{1}[/tex]

c = speed of light, therefore

[tex]2E_{1}  = c2B_{1}[/tex]

II) Intensity of is proportional to the square of amplitude, as such

If amplitude is doubled ([tex]X2^{2}[/tex]), intensity is [tex]X4^{}[/tex]

This means the intensity becomes four times bigger.

Answer:

Minimum uncertainty in position is [tex]\Delta x= 1157808.48\ m[/tex]

Explanation:

It is given that,

Uncertainty in the position of an electron, [tex]\Delta x=0.1\ nm=0.1\times 10^{-9}\ m[/tex]

According to uncertainty principle,

[tex]\Delta x.\Delta p\geq \dfrac{h}{4\pi}[/tex]

[tex]\Delta x.m\Delta v\geq \dfrac{h}{4\pi}[/tex]

[tex]\Delta v\geq \dfrac{h}{4\pi \times \Delta x\times m}[/tex]

[tex]\Delta v\geq \dfrac{6.62\times 10^{-34}\ J-s}{4\pi \times 0.1\times 10^{-9}\ m\times 9.1\times 10^{-31}\ kg}[/tex]

[tex]\Delta v\geq 578904.24\ m/s[/tex]

Let [tex]\Delta x[/tex] is the uncertainty in position after 2 seconds such that,

[tex]\Delta x=\Delta v\times t[/tex]

[tex]\Delta x=578904.24\ m/s\times 2\ s[/tex]

[tex]\Delta x= 1157808.48\ m[/tex]

or

[tex]\Delta x= 1.15\times 10^6\ m[/tex]

Hence, this is the required solution.

Answer:

66.2 sec

Explanation:

C₁ = 1.0 F

C₂ = 1.0 F

ΔV = Potential difference across the capacitor = 6.0 V

C = parallel combination of capacitors

Parallel combination of capacitors is given as

C = C₁ + C₂

C = 1.0 + 1.0

C = 2.0 F

R = resistance = 33 Ω

Time constant is given as

T = RC

T = 33 x 2

T = 66 sec

V₀ = initial potential difference across the combination = 6.0 Volts

V = final potential difference = 2.2 volts

Using the equation

[tex]V = V_{o} e^{\frac{-t}{T}}[/tex]

[tex]2.2 = 6 e^{\frac{-t}{66}}[/tex]

t = 66.2 sec

Answer:

A) Option 1 is the correct answer.

B) Option 4 is the correct answer.

Explanation:

A) Weight of liquid = 7 N

    Volume of liquid = 1 L = 0.001 m³

    Specific weight =  [tex]\frac{7}{0.001}=7000N/m^3[/tex]

    Density = [tex]\frac{7000}{9.81}=713.5kg/m^3[/tex]

    Specific gravity = [tex]\frac{713.5}{1000}=0.7135[/tex]

    Option 1 is the correct answer.

B) The Stokes(St) is the cgs physical unit for kinematic viscosity, named after George Gabriel Stokes.

We have

             1 St = 10⁻⁴ m²/s

    Option 4 is the correct answer.        

After evaluating all the options we have:

A. From all of the options of specific weight, density, and specific gravity of 1 liter of liquid, the correct is option 1: 7000 N/m³, 713.5 kg/m³, 0.7135.  

B. The correct option of the multiplying factor for converting one stoke into m²/s is 4: 10⁻⁴.  

A. Let's calculate the specific weight, density, and specific gravity of 1 L of the liquid that weighs 7 N.

[tex] \gamma = dg [/tex]   (1)

Where:

γ: is the specific weight

d: is the density

g: is the gravity = 9.81 m/s²

We need to find the density which is:

[tex] d = \frac{m}{V} [/tex]   (2)

Where:

m: is the mass

V: is the volume = 1 L = 0.001 m³

The mass can be found knowing that the liquid weighs (W) 7 N, so:

[tex] W = mg [/tex]  

[tex] m = \frac{W}{g} [/tex]   (3)  

By entering equations (3) and (2) into (1) we have:

[tex] \gamma = dg = \frac{mg}{V} = \frac{W}{V} = \frac{7 N}{0.001 m^{3}} = 7000 N/m^{3} [/tex]

Hence, the specific weight is 7000 N/m³.

[tex] d = \frac{m}{V} = \frac{W}{gV} = \frac{7 N}{9.81 m/s^{2}*0.001 m^{3}} = 713.5 kg/m^{3} [/tex]

Then, the density is 713.5 kg/m³.

[tex] SG = \frac{d}{d_{H_{2}O}} = \frac{713.5 kg/m^{3}}{1000 kg/m^{3}} = 0.7135 [/tex]

Hence, the specific gravity is 0.7135.

Therefore, the correct option is 1: 7000 N/m³, 713.5 kg/m³, 0.7135.

B. A Stokes is a measurement unit of kinematic viscosity.

One m²/s is equal to 10⁴ stokes, so to convert 1 stokes to m²/s we need to multiply for 10⁻⁴.

Hence, the correct option is 4: 10⁻⁴.

You can find more about specific weight here: https://brainly.com/question/13178675?referrer=searchResults    

I hope it helps you!

Answer:

The output power is 2 kW

Explanation:

It is given that,

Number of turns in primary coil, [tex]N_p=250[/tex]

Number of turns in secondary coil, [tex]N_s=500[/tex]

Voltage of primary coil, [tex]V_p=200\ V[/tex]

Current drawn from secondary coil, [tex]I_s=5\ A[/tex]

We need to find the power output. It is equal to the product of voltage and current. Firstly, we will find the voltage of secondary coil as :

[tex]\dfrac{N_p}{N_s}=\dfrac{V_p}{V_s}[/tex]

[tex]\dfrac{250}{500}=\dfrac{200}{V_s}[/tex]

[tex]V_s=400\ V[/tex]

So, the power output is :

[tex]P_s=V_s\times I_s[/tex]

[tex]P_s=400\ V\times 5\ A[/tex]

[tex]P_s=2000\ watts[/tex]

or

[tex]P_s=2\ kW[/tex]

So, the output power is 2 kW. Hence, this is the required solution.

Explanation:

The speed of light in vacuum is, c = 3 × 10⁸ m/s

We have to find the speed of light :

(a) In air :

[tex]n_1_{air}=1.0003[/tex]

The equation of refractive index is given as :

[tex]n_1=\dfrac{c}{v_1}[/tex]

[tex]v_1=\dfrac{c}{n_1}[/tex]

[tex]v_1=\dfrac{3\times 10^8\ m/s}{1.0003}[/tex]

[tex]v_1=299910026.9\ m/s[/tex]

[tex]v_1=2.99\times 10^8\ m/s[/tex]

(b) In diamond :

[tex]n_2_{diamond}=2.42[/tex]

The equation of refractive index is given as :

[tex]n_2=\dfrac{c}{v_2}[/tex]

[tex]v_2=\dfrac{c}{n_2}[/tex]

[tex]v_2=\dfrac{3\times 10^8\ m/s}{2.42}[/tex]

[tex]v_2=123966942.1\ m/s[/tex]

[tex]v_2=1.23\times 10^8\ m/s[/tex]

(c) In crown glass :

[tex]n_3_{glass}=1.5[/tex]

The equation of refractive index is given as :

[tex]n_3=\dfrac{c}{v_3}[/tex]

[tex]v_3=\dfrac{c}{n_3}[/tex]

[tex]v_3=\dfrac{3\times 10^8\ m/s}{1.5}[/tex]

[tex]v_3=200000000\ m/s[/tex]

[tex]v_3=2\times 10^8\ m/s[/tex]

(4) In water :

[tex]n_4_{glass}=1.34[/tex]

The equation of refractive index is given as :

[tex]n_4=\dfrac{c}{v_4}[/tex]

[tex]v_4=\dfrac{c}{n_4}[/tex]

[tex]v_4=\dfrac{3\times 10^8\ m/s}{1.34}[/tex]

[tex]v_4=223880597.01\ m/s[/tex]

[tex]v_4=2.23\times 10^8\ m/s[/tex]

Hence, this is the required solution.

Answer:

90 miles

Explanation:

speed = 30 miles per hour, time = 3 hour

The formula for the speed is given by

speed = distance / time

Distance = speed x time

distance = 30 x 3 = 90 miles

Answer:

90 Miles

Explanation:

This is more simple than you thought...

The equation is 30 miles per hour,in 3 hours you would travel  (30*3)=90 miles.

Formula used Distance = Speed x Time

Speed = 30 mph

Time = 3 hours

So, Distance = Speed * Time = 30 * 3 = 90 miles.

So all in all, the answer is 90 miles

Answer:

0.4375 cm

Explanation:

f = frequency of the chirp emitted by the bats = 7.84 x 10⁴ Hz

v = speed of sound in air = 343 m/s

λ = smallest wavelength = size of the smallest insect a bat can detect

Using the equation

v = f λ

inserting the values

343 = (7.84 x 10⁴) λ

λ = [tex]\frac{343}{7.84\times 10^{4}}[/tex]

λ = 43.75 x 10⁻⁴ m

λ = 0.4375 cm

Answer:

a) 12.23 N

b) 2.2 m/s²

Explanation:

m = mass of the block = 3.9 kg

F = applied force = 27 N

θ = angle of the applied force with the horizontal = 40°

μ = Coefficient of kinetic friction = 0.22

[tex]F_{n}[/tex] = normal force

[tex]F_{g}[/tex] = weight of the block = mg

Along the vertical direction, force equation is given as

[tex]F_{n}[/tex] = F Sinθ + [tex]F_{g}[/tex]

[tex]F_{n}[/tex] = F Sinθ + mg

Kinetic frictional force is given as

f = μ [tex]F_{n}[/tex]

f = μ (F Sinθ + mg)

f = (0.22) (27 Sin40 + (3.9)(9.8))

f = 12.23 N

b)

Force equation along the horizontal direction is given as

F Cosθ - f = ma

27 Cos40 - 12.23 = 3.9 a

a = 2.2 m/s²