Torque is dependent on the angle between the force applied and the length of the level arm. When is the torque maximum? Not enough information. θ = 90 θ = 0 θ = 45

Answer:

rate of change in temperature of copper is more than the rate of change in temperature of aluminium.

so here copper will reach to our body temperature first

Explanation:

As we know that rate of energy absorb by the two sphere is same

so here we will have

[tex]\frac{dQ}{dt} = ms\frac{\Delta T}{\Delta t}[/tex]

now for copper sphere we will have

[tex]\frac{dQ}{dt} = 50(0.4)\frac{\Delta T}{\Delta t}[/tex]

[tex]\frac{\Delta T}{\Delta t} = \frac{1}{20}\frac{dQ}{dt}[/tex]

now for Aluminium sphere we will have

[tex]\frac{dQ}{dt} = 25(0.9)\frac{\Delta T}{\Delta t}[/tex]

[tex]\frac{\Delta T}{\Delta t} = \frac{1}{22.5}\frac{dQ}{dt}[/tex]

So rate of change in temperature of copper is more than the rate of change in temperature of aluminium.

so here copper will reach to our body temperature first

Answer:

[tex]p_2 = 664081 N/m^{2}[/tex]

Explanation:

from the ideal gas law we have

PV = mRT

[tex]P = \rho RT[/tex]

[tex]\rho = \frac{P}{RT}[/tex]

HERE  R is gas constant for dry air  =  287  J K^{-1} kg^{-1}

[tex]\rho = \frac{7.00 10^{5}}{287(18+273)}[/tex]

[tex]\rho = 8.38 kg/m^{3}[/tex]

We know by ideal gas law

[tex]\rho = \frac{m_1}{V_1}[/tex]

[tex]m_1 = \rho V_1 = 8.38 *2*10^{-3}[/tex]

[tex]m_1 = 0.0167 kg[/tex]

for m_2

[tex]m_2 = \rho V_i - V_removed[/tex]

[tex]m_2 = 8.38*(.002 - 10^{-4})[/tex]

[tex]m_2 = 0.0159 kg[/tex]

WE KNOW

PV = mRT

V, R and T are constant therefore we have

P is directly proportional to mass

[tex]\frac{p_2}{p_1}=\frac{m_2}{m_1}[/tex]

[tex]p_2 = p_1 * \frac{m_2}{m_1}[/tex]

[tex]p_2 =7*10^{5} * \frac {.0159}{0.0167}[/tex]

[tex]p_2 = 664081 N/m^{2}[/tex]

This problem can be solved using Boyle's Law, which relates the pressure and volume of a gas at a constant temperature. The question asks for the new pressure of a bicycle tire after letting out a certain volume of air. The answer is approximately 7.37 x 10⁵ Pa.

The subject of this question is gas laws, specifically Boyle's Law which states that the pressure and volume of a gas have an inverse relationship when the temperature is kept constant. Assuming the temperature and volume of the tire remain constant before and after you let out the air, when a volume of 100 cm³ (which we will convert to 0.1 L for consistency) of air is let out, the new total volume of the gas is 1.9 L.

According to Boyle's Law, P1*V1 = P2*V2, where P1 and V1 represent the initial pressure and volume, and P2 and V2 represent the final pressure and volume. Plugging the values into this equation, we get:

(7.00 x 10⁵ Pa)(2.00 L) = P2 * (1.9 L)

Which gives us:

P2 = (7.00 x 10⁵ Pa * 2.00 L) / 1.9 L

Therefore, the pressure in the bike tire after letting out 100 cm³ of gas is approximately 7.37 x 10⁵ Pa.

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Answer:

Work done by the gravitational force is 37 mJ.

Explanation:

It is given that,

Mass of the raindrop, [tex]m=3.26\times 10^{-5}\ kg[/tex]

It falls from a height of, h = 115 m

It falls vertically at constant speed under the influence of gravity and air resistance. We need to find the  work done on the raindrop by the gravitational force. It is given by :

[tex]W=mgh[/tex]

[tex]W=3.26\times 10^{-5}\ kg\times 9.8\ m/s^2\times 115\ m[/tex]

W = 0.0367 J

or

W = 0.037 J = 37 mJ

So, the work done on the raindrop by the gravitational force is 37 mJ. Hence, this is the required solution.

Final answer:

The work done on a raindrop of mass 3.26 times [tex]10^{-5}[/tex] kg by the gravitational force.

Explanation:

To calculate the work done on a raindrop by the gravitational force as it falls, we use the formula for work: W = mgh, where W is the work done, m is the mass of the object, g is the acceleration due to gravity (9.8 m/s2), and h is the height the object falls through.

In this case, the mass m of the raindrop is 3.26 times 10-5 kg, and the height h is 115 m. So:

W = (3.26 times 10-5 kg)(9.8 [tex]m/s^2[/tex])(115 m) = 0.0368134 J

Therefore, the work done on the raindrop by the gravitational force as it falls 115 m is approximately 0.0368134 joules.

Answer:

option (B)

Explanation:

q = 3 c, m = 4 x 10^-3 kg, g  9.8 m/s^2,

In the equilibrium condition, the weight of the charge particle is balanced by the electrostatic force.

q E = mg

Electrostatic force = m g = 4 x 10^-3 x 9.8 = 0.0392 N

Answer:

10042.6 ohm

Explanation:

f = 10 kHz = 10000 Hz, L = 36 mH = 0.036 H, R = 10 kilo Ohm = 10000 ohm

C = 5 nF = 5 x 10^-9 F

XL = 2 x π x f x L

XL = 2 x 3.14 x 10000 x 0.036 = 2260.8 ohm

Xc = 1 / ( 2 x π x f x C) = 1 / ( 2 x 3.14 x 10000 x 5 x 10^-9)

Xc = 3184.7 ohm

Total impedance is Z.

Z^2 = R^2  + (XL - Xc)^2

Z^2 = 10000^2 + ( 2260.8 - 3184.7 )^2

Z = 10042.6 ohm

Answer:

[tex]T_C=256.2^{\circ}C[/tex]

Explanation:

Given that,

Efficiency of heat engine, [tex]\eta=40\%=0.4[/tex]

Temperature of hot source, [tex]T_H=427^{\circ}C[/tex]

We need to find the temperature of cold sink i.e. [tex]T_C[/tex]. The efficiency of heat engine is given by :

[tex]\eta=1-\dfrac{T_C}{T_H}[/tex]

[tex]T_C=(1-\eta)T_H[/tex]

[tex]T_C=(1-0.4)\times 427[/tex]

[tex]T_C=256.2^{\circ}C[/tex]

So, the temperature of the cold sink is 256.2°C. Hence, this is the required solution.

Answer:

Answer to the question is: 1837.65 millimeters of mercury are equal to 245 kPa.

Explanation:

1 kPa are equal to 7.50062 millimeters of mercury.

Final answer:

To convert the pressure from 245 kPa to mmHg, first convert kPa to atm, then multiply by the conversion factor from atm to mmHg. The pressure is 1837.68 mmHg.

Explanation:

To convert the pressure in a container from kilopascals (kPa) to millimeters of mercury (mmHg), we use the conversion factor that 1 atmosphere (atm) is equivalent to 760 mmHg. First, we convert the given pressure in kilopascals to atmospheres:

1 atm = 101.325 kPa

So, to convert 245 kPa to atm, we divide 245 kPa by 101.325 kPa/atm:

245 kPa / 101.325 kPa/atm = 2.418 atm

Next, we convert atmospheres to millimeters of mercury (mmHg) using the conversion factor:

2.418 atm x760 mmHg/atm = 1837.68 mmHg

Therefore, the pressure in the container is 1837.68 mmHg.

Answer : The mass of cereal in two units are, 34.815 oz and 978.075 grams respectively.

Explanation :

As there are two systems for measuring the units which are English and Metric system.

The Metric System measured the things in meters, grams, liters, etc and adds prefixes like kilo, milli and centi to the count orders of the magnitude.

The English system measured the things in feet, inches, pounds, mile, etc.

As we are given the mass of cereal in 978 grams that means 987 grams is in metric unit. Now we have to convert metric unit into English unit.

Conversion factor used :  (1 oz = 28.350 g)

As, 28.350 grams = 1 oz

So, 987 grams = [tex]\frac{987\text{ grams}}{28.350\text{ grams}}\times 1oz[/tex]

                        =  34.815 oz

As we are given the mass of cereal in 34.5 oz that means 34.5 oz is in metric unit. Now we have to convert metric unit into English unit.

Conversion factor used :  (1 oz = 28.350 g)

As, 1 oz = 28.350 grams

So, 34.5 oz = [tex]\frac{34.5\text{ oz}}{1\text{ oz}}\times 28.350\text{ grams}[/tex]

                  =  978.075 grams

Therefore, the mass of cereal in two units are, 34.815 oz and 978.075 grams respectively.

The conversion factor from ounces to grams, divide 978 grams by 34.5 ounces, resulting in approximately 28.3 g/oz when rounded to three significant figures.

To find a conversion factor between English and metric units using the information that a box of cereal has a mass of 978 grams and 34.5 ounces, you would divide the number of grams by the number of ounces.

Conversion factor = 978 g / 34.5 oz ≈ 28.34783 g/oz

However, we need to consider significant figures in our answer. The number 34.5 has three significant figures, and the number 978 has three significant figures as well. Therefore, we can justify three significant figures in our conversion factor, giving us 28.3 g/oz as the conversion with significant figures properly accounted for.

Answer:

The answer is 1.1A

Explanation:

See the attached file

Answer:

115 m/s, 414 km/hr

Explanation:

There are two forces acting on a skydiver: gravity and air resistance (drag).  At terminal velocity, the two forces are equal and opposite.

∑F = ma

D − mg = 0

D = mg

Drag force is defined as:

D = ½ ρ v² C A

where ρ is the fluid density,

v is the velocity,

C is the drag coefficient,

and A is the cross sectional surface area.

Substituting and solving for v:

½ ρ v² C A = mg

v² = 2mg / (ρCA)

v = √(2mg / (ρCA))

We're given values for m and A, and we know the value of g.  We need to look up ρ and C.

Density of air depends on pressure and temperature (which vary with elevation), but we can estimate ρ ≈ 1.21 kg/m³.

For a skydiver falling headfirst, C ≈ 0.7.

Substituting all values:

v = √(2 × 80.0 kg × 9.8 m/s² / (1.21 kg/m³ × 0.7 × 0.140 m²))

v = 115 m/s

v = 115 m/s × (1 km / 1000 m) × (3600 s / hr)

v = 414 km/hr

The terminal velocity of the skydiver in m/s and km/h is;  115m/s  and  414 km/h

Using Given data :

mass of skydiver ( M ) = 80 kg

Cross sectional surface area ( A ) = 0.14 m^2

p ( fluid density ) ≈ 1.21 kg/m³.

C ( drag coefficient ) = 0.7

Determine the terminal velocity of the skydiver

At terminal velocity drag force and gravity is equal and opposite therefore canceling out each other

∑ F = ma

Drag force - Mg = 0

therefore;  D = Mg ----- ( 1 )

where D ( drag force ) = 1/2 pv² C A ---- ( 2 )

p = fluid density , C = drag coefficient , A = cross sectional area

v = velocity

Back to equations 1 and 2  ( equating them )

1/2 pv² CA = Mg ---- ( 3 )

v² = 2mg / ( p C A )

∴ V = √ ( 2mg / (p C A ))

V = √ ( 2 * 80 * 9.8 ) / ( 1.21 * 0.7 * 0.140 ))

    = 115 m/s  

also  V = 414 km/h

Hence we can conclude that the terminal velocity of the skydiver is in m/s and km/h are 115m/s and  414 km/h

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Answer:

6.45 x 10^5 N/C

Explanation:

q = + e = 1.6 x 10^-19 C

m = 9.99 x 10^-27 kg

V = 13 kV = 13000 V

B = 1 T

Let v be the speed and E be the strength of electric field.

1/2 mv^2 = eV

v^2 = 2 e v / m

v^2 = (2 x 1.6 x 10^-19 x 13000) / (9.99 x 10^-27)

v = 6.45 x 10^5 m/s

As the charge particle is undeflected, the force due to magnetic field is counter balanced by the force due to electric field.

q E = q v B

E = v B = 6.45 x 10^5 x 1 = 6.45 x 10^5 N/C

The result will be the magnitude of the smallest electric field (E) required for the 6Li ions to pass through the magnetic field undeflected.

Here's how to calculate the strength of the electric field required for the 6Li ions to pass through the magnetic field undeflected:

Force Balance:

For the ions to move undeflected, the magnetic force acting on them needs to be balanced by the electric force acting in the opposite direction.

Magnetic Force:

The magnetic force (F_magnetic) on a charged particle moving through a magnetic field is given by: F_magnetic = q * v * B

Where:

q is the charge of the particle (q = +e for 6Li ion)

v is the velocity of the particle

B is the magnetic field strength

Electric Force:

The electric force (F_electric) on the charged particle in an electric field (E) is: F_electric = q * E

Balancing Forces:

For undeflected motion: F_magnetic = F_electric

Substitute the expressions from steps 2 and 3: q * v * B = q * E

Solving for Electric Field (E):

Since the charge (q) of the ion appears on both sides, we can cancel it.

E = v * B

Finding Ion Velocity (v):

The ions are accelerated by a potential difference (V) of 13 kV (13000 V).

The potential difference is related to the ion's kinetic energy (KE) by: KE = q * V

Assuming the ion starts from rest, all the potential energy is converted to kinetic energy.

KE = 1/2 * m * v^2 (where m is the mass of the ion)

Solve for v:

Combine equations from steps 6: 1/2 * m * v^2 = q * V

Solve for v: v = sqrt( 2 * q * V / m )

Substitute v in the equation for E (from step 5):

E = sqrt( 2 * q * V / m ) * B

Plug in the values:

q = +e (elementary charge = 1.602 x 10^-19 C)

V = 13000 V

m = 9.99 x 10^-27 kg

B = 1.0 T

Calculate E using the above values and the constant for elementary charge.

Explanation:

The resistance of a wire is given by :

[tex]R=\rho\dfrac{l}{A}[/tex]

Where

[tex]\rho[/tex] is the resistivity of the wire

l = initial length of the wire

A = initial area of cross section

If length and the area of cross section of the wire is doubled then new length is l' and A', l' = 2 l and A' = 2 A

So, new resistance of the wire is given by :

[tex]R'=\rho\dfrac{l'}{A'}[/tex]

[tex]R'=\rho\dfrac{l}{A}[/tex]

R' = R

So, the resistance of the wire remains the same on doubling the length and the area of wire.

Explanation:

It is given that,

Mass of the shot, m = 7.27 kg

Time taken to accelerate, t = 1.3 s

It is shot from rest to 16 m/s and it raises to a height of 0.9 m. We need to find the power output of the shot-putter. It is given by :

[tex]P=\dfrac{energy}{time}[/tex]

Energy = kinetic energy + potential energy

[tex]E=\dfrac{1}{2}\times 7.27\ kg\times (16\ m/s)^2+7.27\ kg\times 9.8\ m/s^2\times 0.9\ m[/tex]

E = 994.68 J

Power, [tex]P=\dfrac{994.68\ J}{1.3\ s}[/tex]

P = 765.13 Watts

We know that, 1 horse power = 745.7 watts

Or P = 1.02 horse power

Hence, this is the required solution.

Answer:

q = 1.815 \times 10^{-8} C

Charge on one plate is positive in nature and on the other plate it is negative in nature.

Explanation:

E = 8.20 x 10^5 V/m, A = 25 cm^2, d = 22.45 mm

According to the Gauss's theorem in electrostatics

The electric field between the two plates

[tex]E = \frac{\sigma }{\varepsilon _{0}}[/tex]

[tex]{\sigma }= E \times {\varepsilon _{0}}[/tex]

[tex]{\sigma }= 8.20 \times 10^{5} \times {8.854 \times 10^{-12}[/tex]

[tex]{\sigma }= 7.26 \times 10^{-6} C/m^{2}[/tex]

Charge, q = surface charge density x area

[tex]q = 7.26 \times 10^{-6} \times 25 \times 10^{-4}[/tex]

q = 1.815 \times 10^{-8} C

Answer:

3020.68 kg/m^3

Explanation:

r = 5.25 x 10^3 km = 5.25 x 10^6 m, d = 450 km = 450 x 10^3 m

T = 2.15 hours = 2.15 x 3600 second = 7740 second

Let the density of the planet is ρ and M be the mass of planet.

The formula for the orbital velocity is

[tex]v = \sqrt{\frac{GM}{r+d}}[/tex]

Time period is given by

[tex]T = {\frac{2\pi (r+d)}{v}}[/tex]

[tex]T = \frac{2\pi (r +d)^{1.5}}{\sqrt{GM}}[/tex]

[tex]7740= \frac{2\pi (5700\times 1000)^{1.5}}{\sqrt{6.67\times 10^{-11}M}}[/tex]

M = 1.83 x 10^24 kg

Density = mass / Volume

ρ = 1.83 x 10^24 / (4/3 x 3.14 x (5.25 x 10^6)^3)

ρ = 3020.68 kg/m^3

The closest expression for [tex]\( F_2 \)[/tex] in terms of [tex]\( F_1 \)[/tex] is.

[tex]\[ \\F_2 = \frac{3}{4} F_1} \][/tex]

This means that after transferring 2 bricks from one bag to the other, the gravitational attraction [tex]\( F_2 \)[/tex] between the bags is [tex]\( \frac{3}{4} \)[/tex] of the initial attraction [tex]\( F_1 \).[/tex]

When initially each bag contains 4 bricks of mass [tex]\( M \)[/tex] each, the total mass in each bag is [tex]\( 4M \)[/tex]. The bags exert a gravitational attraction [tex]\( F_1 \)[/tex] on each other.

Let's denote:

-[tex]\( F_1 \):[/tex] Initial gravitational attraction between the bags when each bag has 4 bricks.

- [tex]\( F_2 \):[/tex] Gravitational attraction after transferring 2 bricks from one bag to the other.

Initial Situation Before Transfer

Each bag has 4 bricks so the mass of each bag is [tex]\( 4M \).[/tex]

Gravitational Attraction [tex]\( F_1 \)[/tex]

[tex]\[ F_1 = G \frac{(4M)(4M)}{d^2} \][/tex]

where [tex]\( G \)[/tex] is the gravitational constant and [tex]\( d \)[/tex] is the distance between the centers of the bags.

After Transferring 2 Bricks:

Now, one bag has 6 brick mass 6m and the other bag has 2 bricks mass2m

Gravitational Attraction[tex]\( F_2 \)[/tex]

[tex]\[ F_2 = G \frac{(6M)(2M)}{d^2} \]s[/tex]

Simplifying [tex]\( F_2 \)[/tex]

[tex]\[ F_2 = G \frac{12M^2}{d^2} \][/tex]

Relation between [tex]\( F_2 \)[/tex] and [tex]\( F_1 \)[/tex]

To find the relation between [tex]\( F_2 \)[/tex] and [tex]\( F_1 \)[/tex] we compare them

[tex]\[ \frac{F_2}{F_1} = \frac{G \frac{12M^2}{d^2}}{G \frac{16M^2}{d^2}} \][/tex]

[tex]\[ \frac{F_2}{F_1} = \frac{12M^2}{16M^2} \][/tex]

[tex]\[ \frac{F_2}{F_1} = \frac{3}{4} \][/tex]

Answer:

Explanation:

When the pendulum falls freely the net acceleration due to gravity is zero.

As we know that the time period of simple pendulum is inversely proportional to the square root of acceleration due to gravity, thus the time period becomes infinity.

In freefall, the pendulum's effective acceleration due to gravity becomes zero, causing the pendulum to not swing, and its period becomes theoretically infinite and immeasurable.

Effect of Freefall on a Pendulum's Period

When considering simple pendulum motion in an elevator under normal conditions, we can determine its periodic time (T) using the formula T = 2π√(L/g), where L is the length of the pendulum and g is the acceleration due to gravity. This equation illustrates that the period of the pendulum (T) is affected by two variables: the length of the pendulum (L) and the acceleration due to gravity (g).

When the elevator is in free fall, the effective acceleration g becomes zero because the elevator and the pendulum are both in a state of free fall with the same acceleration due to gravity. Therefore, in this scenario, the pendulum would experience weightlessness and would not oscillate, resulting in an infinite theoretical oscillation period, making the concept of a period inapplicable.

The period is normally independent of mass or amplitude for small angles, but since freefall changes the acceleration experienced by the pendulum to zero, it significantly affects the pendulum's oscillation, negating the normal conditions for calculating a pendulum's period.

Answer:

2.07 m/s

Explanation:

m = 1.07 x 10^5 kg, u1 = 3.41 m/s, u2 = 1.4 m/s

Let the speed of three coupled car after collision is v

Use conservation of momentum

m x u1 + 2 m x u2 = 3 m x v

u1 + 2 u2 = 3 v

3.41 + 2 x 1.4 = 3 v

v = 2.07 m/s

The angular velocity of the CD is 754.4 rad/s. The time it takes for the CD to rotate through 90 degrees is 0.0021 seconds. The average angular acceleration of the CD is 188.6 rad/s².

To calculate the angular velocity of the CD, we can convert the given 7200 rev/min to radians per second. Since one revolution is equal to 2π radians, we can use the conversion factor to find the angular velocity. Thus, the angular velocity of the CD is 754.4 rad/s.

To calculate the time it takes for the CD to rotate through 90 degrees, we need to find the fraction of the total rotation that corresponds to 90 degrees. Since a full rotation is 360 degrees or 2π radians, 90 degrees is equal to π/2 radians. We can then use the formula Δθ = ωΔt to find the time it takes, where Δθ is the angle in radians, ω is the angular velocity, and Δt is the time. Rearranging the formula, we have Δt = Δθ/ω. Substituting the values, we get Δt = π/2 / 754.4 = 0.0021 seconds.

The average angular acceleration can be found using the formula α = (ωf - ωi) / Δt, where α is the angular acceleration, ωf is the final angular velocity, ωi is the initial angular velocity, and Δt is the time interval. The CD starts from rest and reaches full speed in 4 seconds, so the initial angular velocity is 0. Using the given full speed of 7200 rev/min, we can convert it to radians per second and use it as the final angular velocity. Thus, the average angular acceleration is α = (754.4 rad/s - 0 rad/s) / 4 s = 188.6 rad/s².

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Answer:

(a) 0.33 second

(b) 6 cm/s

Explanation:

Frequency, f = 3 waves per second

wavelength, λ = 2 cm = 0.02 m

(a) The period of wave is defined as the time taken by the wave to complete one oscillation. It is the reciprocal of frequency.

T = 1 / f = 1 / 3 = 0.33 second

(b) the relation between wave velocity, frequency and wavelength is given by

v = f x λ

v = 3 x 0.02 = 0.06 m /s

v = 6 cm /s

Final answer:

The period of the waves generated by a grasshopper in water is 0.333 seconds, and the wave velocity is 0.06 m/s.

Explanation:

Calculating the Period and Wave Velocity

When dealing with waves generated by a grasshopper floating in water, two key properties to determine are the period of the waves and the wave velocity.

(a) The Period of the Waves

The period (T) of a wave is the amount of time it takes for one complete wave cycle to pass. It can be calculated as the inverse of the frequency (f), which is the rate at which waves are generated. The formula to find the period is:

T = 1/f

In this case, the grasshopper generates waves at a frequency of 3 waves per second (3 Hz). Therefore, the period is:

T = 1/3 Hz = 0.333 seconds

(b) The Wave Velocity

The velocity (v) of a wave is determined by multiplying the frequency (f) of the wave by its wavelength (λ). The formula for wave velocity is:

v = f × λ

Here, the wavelength given is 2 cm, which we need to convert to meters (since the SI unit for velocity is m/s). Thus:

λ = 2 cm = 0.02 m

The velocity of the waves generated by the grasshopper is then:

v = 3 Hz × 0.02 m = 0.06 m/s

Answer:

Weight in planet X = 0.413 N

Explanation:

Weight = Mass x Acceleration due to gravity.

W = mg

Mass, m = 100 g = 0.1 kg

We have equation of motion s = ut + 0.5 at²

Displacement, s = 10 m

Initial velocity, u = 0 m/s

Time, t = 2.2 s

Substituting

        s = ut + 0.5 at²

        10 = 0 x 2.2 + 0.5 x a x 2.2²        

        a = 4.13 m/s²

Acceleration due to gravity, a = 4.13 m/s²

W = mg = 0.1 x 4.13 = 0.413 N

Weight in planet X = 0.413 N

In Planet X, a 100-g ball is released from rest from a height of 10.0 m and it takes 2.2 s for it to reach the ground. The weight of the ball on the surface of Planet X is 0.41 N.

In physics, gravitational acceleration is the acceleration of an object in free fall within a vacuum (and thus without experiencing drag).

A 100-g (m) ball is released from rest from a height of 10.0 m (s) and it takes 2.2 s (t) for it to reach the ground. We can calculate the gravitational acceleration using the following kinematic equation.

s = 1/2 × g × t²

g = 2 s / t² = 2 (10.0 m) / (2.2 s)² = 4.1 m/s²

We will use Newton´s second law of motion.

w = m × g = 0.100 kg × 4.1 m/s² = 0.41 N

In Planet X, a 100-g ball is released from rest from a height of 10.0 m and it takes 2.2 s for it to reach the ground. The weight of the ball on the surface of Planet X is 0.41 N.

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Answer:

Final velocity, v = 1.74 m/s

Explanation:

Given that,

Mass of car 1, m₁ = 22509 kg

Velocity of car 1, v₁ = 4.21 m/s

Mass of car 2, m₂ = 31647 kg

It is stationary, v₂ = 0

Let v be the velocity of the two cars after they collide and attach. It can be calculated using law of conservation of momentum as :

[tex]m_1v_1+m_2v_2=(m_1+m_2)v[/tex]

[tex]v=\dfrac{m_1v_1+m_2v_2}{(m_1+m_2)}[/tex]

[tex]v=\dfrac{22509\ kg\times 4.21\ m/s+0}{22509\ kg+31647\ kg}[/tex]

v = 1.74 m/s

So, the velocity of two cars after the collision is 1.74 m/s. Hence, this is the required solution.

Answer:

Spongebob: Bye Mr. Krabs! Bye Squidward! BYE SQUIDWARD!

Patrick: (clearly triggered) Why'd you say "bye squidward" twice?

Spongebob: I LiKe SqUiDwArD

Answer:

d

Explanation:

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The speed of an electron with a kinetic energy of 1.25 eV is approximately 1.57 x 10⁶ m/s, and the speed of a proton with the same kinetic energy is approximately 5.29 x 10⁵ m/s.

To calculate the speed of an electron and a proton with a kinetic energy of 1.25 electron volts (eV), we can use the kinetic energy formula and relate it to the speed of the particles. The kinetic energy (KE) of a particle is given by:

KE = (1/2) * m * v²

Where:

KE = kinetic energy

m = mass of the particle

v = speed of the particle

We are given the kinetic energy in electron volts (eV), but we need to convert it to joules (J) since the mass is given in kilograms (kg). The conversion factor is 1 eV = 1.60219 x 10⁻¹⁹ J.

So, the kinetic energy in joules is:

KE = 1.25 eV * 1.60219 x 10⁻¹⁹ J/eV = 2.0027375 x 10⁻¹⁹ J

Now, we can rearrange the kinetic energy formula to solve for the speed (v):

v = √((2 * KE) / m)

For an electron:

Mass of electron (mₑ) = 9.11 x 10⁻³¹ kg

v(electron) = √((2 * 2.0027375 x 10⁻¹⁹ J) / (9.11 x 10⁻³¹ kg))

Calculating this gives us the speed of the electron.

For a proton:

Mass of proton (m_p) = 1.67 x 10⁻²⁷ kg

v(proton) = √((2 * 2.0027375 x 10⁻¹⁹ J) / (1.67 x 10⁻²⁷ kg))

Calculating this gives us the speed of the proton.

Now, let's calculate these speeds.

After performing the calculations, the speed of the electron is approximately 1.57 x 10⁶ m/s, and the speed of the proton is approximately 5.29 x 10⁵ m/s.

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Answer:

The tip of the needle to move from the highest point to the lowest point in 0.4 sec and the needle tip to travel a total distance in 0.9 sec.

Explanation:

Given that,

Frequency = 2.5 Hz

Amplitude = 1.27 cm

(a). We need to calculate the time

The frequency is the reciprocal of the time.

[tex]f=\dfrac{1}{T}[/tex]

[tex]T=\dfrac{1}{f}[/tex]

[tex]T=\dfrac{1}{2.5}[/tex]

[tex]T=0.4\ sec[/tex]

The time taken from highest point to lowest point

[tex]T'=\dfrac{T}{2}[/tex]

[tex]T'=\dfrac{0.4}{2}[/tex]

[tex]T'=0.2\ sec[/tex]

(b).  We need to calculate the time

The time taken in one cycle = 0.4 sec

The distance covered  in one sec= 4 times x amplitude

[tex]d=4\times1.27[/tex]

[tex]d=5.08\ m[/tex]

We need to calculate the speed

Using formula of speed

[tex]v=\dfrac{5.08}{0.4}[/tex]

[tex]v=12.7[/tex]

We need to calculate the time

[tex]t=\dfrac{11.43}{12.7}[/tex]

[tex]t= 0.9 sec[/tex]

Hence,  The tip of the needle to move from the highest point to the lowest point in 0.4 sec and the needle tip to travel a total distance in 0.9 sec.

The amount of time it took the tip of the needle to move from the highest point to the lowest point in its travel is equal to 0.2 seconds.

Given the following data:

Mathematically, the frequency of an object in simple harmonic motion is give by:

[tex]F=\frac{1}{T} \\\\T=\frac{1}{F}\\\\T=\frac{1}{2.5}[/tex]

T = 0.4 seconds.

Now, we can calculate the time it took the needle to move from the highest point to the lowest point:

[tex]t = \frac{T}{2} \\\\t = \frac{0.4}{2}[/tex]

Time, t = 0.2 seconds.

The distance traveled by the needle per seconds is given by:

[tex]d=4A\\\\d=4 \times 1.27\\\\[/tex]

Distance, d = 5.08 cm.

For the speed:

[tex]Speed = \frac{distance}{time} \\\\Speed =\frac{5.08}{0.4}[/tex]

Speed = 12.7 cm/s.

For the time:

[tex]Time = \frac{distance}{speed} \\\\Time =\frac{11.43}{12.7}[/tex]

Time = 0.9 seconds.

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Answer:

[tex]C = 2.48 \times 10^{-4} Farad[/tex]

Explanation:

As per the equation of voltage on capacitor we know that

[tex]V = V_{max}(1 - e^{-\frac{t}{\tau}})[/tex]

now we know that voltage reached to its 80% of maximum value in 4 second time

so we will have

[tex]0.80 V_{max} = V_{max}(1 - e^{-\frac{4}{\tau}})[/tex]

[tex]0.20 = e^{-\frac{4}{\tau}}[/tex]

[tex]-\frac{4}{\tau} = ln(0.20)[/tex]

[tex]-\frac{4}{\tau} = -1.61[/tex]

[tex]\tau = 2.48[/tex]

as we know that

[tex]\tau = RC[/tex]

[tex](10 k ohm)(C) = 2.48[/tex]

[tex]C = 2.48 \times 10^{-4} Farad[/tex]

Answer:

[tex]F_{applied} = 45.8 N[/tex]

Explanation:

When maximum force is applied on the crate along the plane so that it will not move then in that case friction force and component of the weight of the crate is along the plane opposite to the applied force

So here we will have

[tex]mgsin\theta + F_f = F_{applied}[/tex]

now we know that

[tex]F_f = \mu F_n[/tex]

also we know that

[tex]F_n = mg cos\theta[/tex]

so we will have

[tex]F_f = \mu ( mg cos\theta)[/tex]

now we will have

[tex]mg sin\theta + \mu (mg cos\theta) = F_{applied}[/tex]

[tex](5)(9.81)sin30 + (0.5)(5)(9.81)cos30 = F_{applied}[/tex]

so we will have

[tex]F_{applied} = 45.8 N[/tex]

The maximum force that can be applied parallel to the plane without moving the 5.0-kg crate on a 30° incline, considering a static friction coefficient of 0.5, is 45.7N.

To determine the maximum force that can be applied without moving the crate, we need to consider the effect of static friction, gravity, and the angle of the incline. The weight of the crate (W) is its mass (m) times acceleration due to gravity (g), which equals 5kg*9.8m/s² = 49N. However, this is the weight vertically down, so the force from gravity parallel to the incline is less, and we should multiply W by sin30⁰, getting 24.5N. The normal force (N) on the incline is W*cos30⁰, equal to 42.4N. Therefore, the maximum static friction force (fs) is coef. of static friction (μs) times N, which equals 0.5*42.4N = 21.2N. The max force applied to keep the crate from moving is the sum of the force of gravity and the static friction forces on the incline, which equals 24.5N + 21.2N = 45.7N.

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Answer:

The amplifier gain is 30 dB.

(c) is correct option.

Explanation:

Given that,

Output power = 100 mW

Input power = 0.1 mW

We need to calculate the amplifier gain in dB

Using formula of power gain

[tex]a_{p}=10\ log_{10}(A_{p})[/tex]....(I)

We calculate the [tex]A_{p}[/tex]

[tex]A_{p}=\dfrac{P_{o}}{P_{i}}[/tex]

[tex]A_{p}=\dfrac{100}{0.1}[/tex]

[tex]A_{p}=1000[/tex]

Now, put the value of  [tex]A_{p}[/tex] in equation (I)

[tex]a_{p}=10\ log_{10}(1000)[/tex]

[tex]a_{p}=10\times log_{10}10^{3}[/tex]

[tex]a_{p}=10\times 3log_{10}10[/tex]

[tex]a_{p}=30\ dB[/tex]

Hence, The amplifier gain is 30 dB.

The gain of an amplifier, given a power output of 100 mW and an input power of 0.1 mW, can be calculated using the gain formula in decibels, which results in a gain of 30 dB.

In this context, the gain of the amplifier can be calculated using the formula for Gain in decibels (dB), which is 10 times the log base 10 of the output power divided by the input power. Therefore, we first divide 100 mW by 0.1 mW, which gives us 1000. Taking the log base 10 of 1000 returns 3, and multiplying 3 by 10 gives us a gain of 30 dB.

So the correct answer to your question: 'An amplifier has a power output of 100 mW when the input power is 0.1 mW, what is the amplifier gain?' is option c which states that the gain is 30 dB.

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The International Space Station's operational weight in orbit is effectively zero due to its state of continuous free-fall around Earth, even though the gravitational force at its altitude is not significantly less than on Earth's surface.

The question relates to the weight of the International Space Station (ISS) when in orbit. Weight in physics is defined as the force exerted on an object due to gravity, calculated as the product of mass and gravitational acceleration (g). On Earth's surface, g is approximately 9.81 m/s2, but this value decreases with altitude due to the equation g = GME / r2, where G is the gravitational constant, ME is Earth's mass, and r is the distance from Earth's center. At the ISS's altitude (> 350 km), g is about 8.75 m/s2. However, it's crucial to understand that while the ISS has a significant mass, leading to a large weight calculation on Earth, its apparent weight in orbit is effectively zero due to it being in a continuous free-fall state around Earth, experiencing microgravity. This explains why astronauts appear weightless, even though the actual gravitational force at that altitude is not much less than on Earth's surface. Therefore, while the ISS has a calculable weight based on its mass and Earth's gravitational pull at its altitude, its operational weight in orbit, in terms of the experience within it, is zero.