Can someone please solve these 6 questions and explain briefly? I really do not understand them. Thank you

Explanation:

∑F = ma

60 N = (40 kg) a

a = 1.5 m/s²

Answer:

[tex] \boxed{\sf Shortest \ possible \ time = 7 \ seconds} [/tex]

Given:

Distance travelled (s) = 8.4 cm

velocity (v) = 1.2 cm/s

To Find:

Shortest possible time (t) in which a bacterium travel a distance 8.4 cm across a Petri Dish

Explanation:

[tex] \boxed{ \bold{\sf Time \ (t) = \frac{Distance \ travelled \ (s)}{Velocity \ (v)}}}[/tex]

Substituting values of Distance travelled (s) & Velocity (v) in the equation:

[tex] \sf \implies t = \frac{8.4}{1.2} [/tex]

[tex] \sf \implies t = \frac{7 \times \cancel{1.2}}{ \cancel{1.2}} [/tex]

[tex] \sf \implies t = 7 \: s[/tex]

Answer:

(I). The sum of the vectors is (7i-5j).

(II). The sum of the vectors is (8i+7j).

Explanation:

Given that,

(I). Vector A [tex]A=3i-12j[/tex]

Vector B [tex]B=4i+7j[/tex]

Suppose, (II). Vector A [tex]A=6i+15j[/tex]

Vector B [tex]B=2i-8j[/tex]

(I). We need to calculate the sum of the vectors

Using formula of sum

[tex]\vec{C}=\vec{A}+\vec{B}[/tex]

Where,

[tex]\vec{A}= vector A[/tex]

[tex]\vec{B}= vector B[/tex]

[tex]\vec{C}= sum of the vector A and b

Put the value into the formula

[tex]\vec{C}=(3i-12j)+(4i+7j)[/tex]

[tex]\vec{C}=7i-5j[/tex]

(II). We need to calculate the sum of the vectors

Using formula of sum

[tex]\vec{C}=\vec{A}+\vec{B}[/tex]

Put the value into the formula

[tex]\vec{C}=(6i+15j)+(2i-8j)[/tex]

[tex]\vec{C}=8i+7j[/tex]

Hence, The sum of the vectors is (7i-5j).

The sum of the vectors is (8i+7j).

Complete question :

A 12 m x 15 m house is built on a 12-cm-thick concrete slab.

What is the heat-loss rate through the slab if the ground temperature is 5°C while the interior of the house is 25°C

Answer:

3kW

Explanation:

Given the following :

Dimension of house :

Length = 12m

Width = 15m

Thickness of concrete slab (t) = 12cm

t in metres :

100cm = 1m

12cm = (12/100)m

= 0.12m

Ground temperature (Tg) = 5°C

Interior temperature = (Th) = 25°C

Thermal conductivity of concrete (K) is approximately 1 Wm/k

Using the relation:

Q = KA * [ (Th - Tg) / d]

A = Length * width = (12 *15) = 180

Q = (1 * 180) * [(25°C - 5°C) / 0.12]

Q = 180 * (20/0.12)

Q = 180 * 16.6666

Q = 3,000W = 3kW

The heat-loss rate is 3kW

Given that,

Dimension of house :

Length = 12m

Width = 15m

Thickness of concrete slab (t) = 12cm

We know that

100cm = 1m

so,

12cm = (12/100)m

= 0.12m

And,

Ground temperature (Tg) = 5°C

Interior temperature = (Th) = 25°C

Q = KA * [ (Th - Tg) / d]

A = Length * width = (12 *15) = 180

Q = (1 * 180) * [(25°C - 5°C) / 0.12]

Q = 180 * (20/0.12)

Q = 180 * 16.6666

Q = 3,000W

= 3kW

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Answer:

6235.5J

Explanation:

Using ( nစ)p= ncp x change in temp

But cp= ( 1+ f/2)R

So cp= ( 1+ 3/2R

Cp= 5R/2

So = n x 5R/2x 150k

= 2 x 5/2x 8.314 x150

= 6235.5J

Answer:

2500 J

Explanation:

Q=(3/2)nRΔT

Q=(3/2)*2 mol*(8.314 J/mol*k)*100 k

Q=2494 J

Answer:

52.7 m

Explanation:

Given that

speed of the vehicle, v = 95 km/h

time of inattentiveness, t = 2 s

distance travelled, s = ?

Since we have the speed in km/h and the time in s, it would be best if we converted one of them to make sure we have all units in the same rank.

95 km/h = 95 * 1000/3600 m/s

95 km/h = 95000/3600 m/s

95 km/h = 26.38 m/s

Now, we use our derived speed in m/s

Speed of a moving vehicle is given by,

v = s/t, where

v = speed in m/s

s = distance travelled, in m

t = time spent, in s

if we make d the subject of formula by rearranging the equation, we have

s = v * t

distance travelled, s = 26.38 * 2

distance travelled, s = 52.7 m

therefore, during this inattentive period, 52.7 m was travelled.

Answer:

The distance is  [tex]s= 30.3 \ m[/tex]

Explanation:

From the question we are told that

   The  coefficient of static friction is  [tex]\mu_s = 0.42[/tex]

    The  initial speed of the train is  [tex]u = 57 \ km /hr = 15.8 \ m/s[/tex]

For the crate not to slide the friction force must be equal to the force acting on the train i.e

       [tex]-F_f = F[/tex]

The negative sign shows that the two forces are acting in opposite direction

=>   [tex]mg * \mu_s = ma[/tex]

=>   [tex]-g * \mu_s = a[/tex]

=>   [tex]a = -9.8 * 0.420[/tex]

=>   [tex]a = -4.116 m/s^2[/tex]

From equation of motion

  [tex]v^2 = u^2 + 2as[/tex]

Here  v =  0 m/s since it came to a stop

=>   [tex]s= \frac{v^2 - u^2 }{ 2 a}[/tex]

 =>   [tex]s= \frac{0 -(15.8)^2 }{ - 2 * 4.116}[/tex]

=>     [tex]s= 30.3 \ m[/tex]

Answer:

The distance of separation is [tex]d = 9.04 *10^{-6 } \ m[/tex]

Explanation:

From the question we are told that

    The wavelength is [tex]\lambda = 633\ nm = 633 *10^{-9} \ m[/tex]

     The  distance of the screen is [tex]D = 5.0 \ m[/tex]

     The  distance between the fringes is  [tex]y = 35 \ cm = 0.35 \ m[/tex]

Generally the distance between the fringes is mathematically represented as

       [tex]y = \frac{ \lambda * D }{d }[/tex]

Here d is the distance of separation between the slit

=>    [tex]d = \frac{ \lambda * D }{y }[/tex]

=>    [tex]d = \frac{ 633 *10^{-9} * 5 }{ 0.35 }[/tex]

=>   [tex]d = 9.04 *10^{-6 } \ m[/tex]

Answer:

The switching rate between the steady state and the normal state of a capacitor

Explanation:

This was a hard one! Could only find it in my textbook. Anyways this basically is the rate which the capacitors switches back from steady state and normal state from when it charges and discharges over time. This has many purposes as a special type of diode or any other transistor type device etc etc.

Explanation:

We need to solve [tex](5.87\times 10^7)(4.2\times 10^{11})[/tex]

Firstly, multiplying 5.87 and 4.2 = 24.654

Now taking exponent of 10.

We know that : [tex]x^a{\cdot} x^b=x^{a+b}[/tex]

It means, [tex]10^7{\cdot} 10^{11}=10^{11+7}=10^{18}[/tex]

So,

[tex](5.87\times 10^7)(4.2\times 10^{11})=24.654\times 10^{18}[/tex]

In scientific notation,

[tex](5.87\times 10^7)(4.2\times 10^{11})=2.4654\times 10^{19}[/tex]

Hence, the value of [tex](5.87\times 10^7)(4.2\times 10^{11})[/tex] is [tex]2.4654\times 10^{19}[/tex]

Answer:

Explanation:

We need to solve

Firstly, multiplying 5.87 and 4.2 = 24.654

Now taking exponent of 10.

We know that :

It means,

So,

In scientific notation,

Hence, the value of  is

Answer:

The force per unit between the two parallel wires with same current flowing in the same direction is 5 x 10⁻⁶ N/m repulsive force.

Explanation:

Given;

current though the two parallel wires, I₁ and I₂ = 5A

distance between the two wires, R = 1 m

The force per unit of the wires is calculated as;

[tex]\frac{F}{L} = \frac{\mu_o I_1I_2}{2\pi R}[/tex]

Where;

μ₀ is permeability of free space = 4π x 10⁻⁷ m/A

Substitute in the given values into the equation and determine the force per unit length (F/L).

[tex]\frac{F}{L} = \frac{\mu_o I_1I_2}{2\pi R} \\\\ \frac{F}{L} = \frac{4\pi *10^{-7}*5*5}{2\pi *1}\\\\ \frac{F}{L} = 5*10^{-6} \ N/m \ (repulsive)[/tex]

Therefore , the force per unit between the two parallel wires with same current flowing in the same direction is 5 x 10⁻⁶ N/m repulsive force.

Answer:

L = L0 ( 1 - v^2/c^2))1/2     where L0 is the proper length

L = 10 L-y (1 - .9^2)^1/2 = 4.36 L-y   length of pole measured by ship

t = 4.36 L-y / .9 c = 4.84 y  since the ship travels at .9 c

Answer:

The average force of wind on the building is 4.728 x 10¹² N

Explanation:

Given;

speed of the air wind, v = 124 km/h

dimension of the building, 42 m wide by 73 m high

density of the air, ρ = 1.3 kg/cm³ =

speed of the air in m/s = 124/3.6 = 34.44 m/s

Area of the building, A = 42 m x 73 m = 3066 m²

density of the air in (k.g/m³);

[tex]\rho = \frac{1.3 \ kg}{cm^3} *(\frac{100\ cm}{1 \ m} )^3\\\\\rho = \frac{1.3 \ kg}{cm^3} *\frac{10^6\ cm^3}{1 \ m^3} = \frac{1.3*10^6 \ kg}{m^3}[/tex]

The average force of wind on the building;

F = mass flow rate x velocity

F = (ρvA) x V

F = ρAv²

F = 1.3 x 10⁶ x 3066  x (34.44)²

F = 4.728 x 10¹² N

Therefore, the average force of wind on the building is 4.728 x 10¹² N

Answer:

The type of medium affects a sound wave as sound travels with the help of the vibration in particles.

Explanation:

As different mediums have different amount and size of particles, for example, the speed of sound is faster through solid than liquid as solids have closely packed particles whereas liquids are loosely packed.

The speed of sound in a given medium is determined by its density and stiffness (or compressibility in the case of gases).The speed of sound increases with the rigidity (or lack of compressibility) of the medium. The speed of sound decreases with increasing medium density.

Any material or area through which a wave is transmitted is referred to as a medium. Four variables impact a wave's speed: wavelength, frequency, medium, and temperature. The wavelength and frequency are multiplied to determine the wave speed (speed = l × f).

Therefore, The rate at which energy is transferred through a medium depends on the amplitude of the vibrations of its constituent particles; the higher this rate, the more powerful the sound wave.

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Answer:

The correct treatment of uncertainties for the volume is shown below

Explanation:

In order to estimate the uncertainty in the volume which is derived via the formula:

[tex]V = w*l*h[/tex]

you normally start with the relative errors  [tex](\frac{\delta Q}{Q})[/tex]  of each quantity (Q) measured, since they are so easy to handle, stating that the relative error in the Volume is the addition of the relative errors in each quantity:

[tex]\frac{\delta V}{V} =\frac{\delta w}{w} +\frac{\delta l}{l} +\frac{\delta h}{h}[/tex]

and finally solve for [tex]\delta V[/tex] by multiplying both sides by the volume you calculated.

In your case, this becomes:

[tex]\delta V =V \left \{\frac{\delta w}{w} +\frac{\delta l}{l} +\frac{\delta h}{h}\right \} \\\delta V = 244.296 \left \{\frac{0.1}{5.4} +\frac{0.1}{8.7} +\frac{0.1}{5.2}\right \}\\\delta V = 244.296 \, (0.04924354)\\\delta V = 12.03 \,\,cm^3[/tex]

Then, since the standard practice is to write the uncertainty with ONLY ONE significant figure, the rounding of your uncertainty becomes:

[tex]\delta V=10\,\,cm^3[/tex]

Giving this, you need to express the final measurement as:

[tex]V=240\,\,cm^3\,+/- 10 \,\,cm^3[/tex]

making sure that the expression for the volume doesn't have significant figures passed the limitation imposed by its uncertainty (in this case the tenths).

Please notice as well that in the treatment you did, you:

1) ended up with an uncertainty even smaller than the relative uncertainty of each measurement (which cannot be possible since relative uncertainties add-up)

2) are not rounding your uncertainty to ONE SIG FIG.

Answer:

its an interaction that can move an object; push or pull makes it or gravity, magnetism

Explanation:

its all in the answer

Answer:

In physics, a force is any interaction that, when unopposed, will change the motion of an object. A force can cause an object withmass to change its velocity (which includes to begin moving from a state of rest), i.e., toaccelerate. 

Explanation:

e(t) = 9t² − 6t + 3

The velocity is the first derivative:

e'(t) = 18t − 6

The acceleration is the second derivative:

e"(t) = 18

Explanation:

It is given that,

Momentum in y direction is [tex]2.4\times 10^4\ kg-m/s[/tex]

Momentum in x direction is [tex]7\times 10^4\ kg-m/s[/tex]

We need to find the angle of the motion of the two vehicles, with respect to the x-axis. The angle between two vectors is given by :

[tex]\tan\theta=\dfrac{p_y}{p_x}\\\\\tan\theta=\dfrac{2.4\times 10^4}{7\times 10^{4}}\\\\\theta=\tan^{-1}\left(0.342\right)\\\\\theta=18.88^{\circ}[/tex]

So, the angle of the motion of the two vehicles is 18.88 degrees.

Answer:

The force is  [tex]F = 21.48 \ N[/tex]

Explanation:

From the question we are told that

   The diameter of the wire is  [tex]d = 1.5 \ mm = 1.5 *10^{-3} \ m[/tex]

     The  pressure is  [tex]P = 120 \ a.t.m = 120 * 101.3 *10^{3} = 12156000 Pa[/tex]

Generally the radius of the of the wire is  

     [tex]r = \frac{d}{2}[/tex]

=>    [tex]r = \frac{ 1.5 *10^{-3}}{2}[/tex]  

=>    [tex]r = 7.5 *10^{-4} \ m[/tex]

The Area is evaluated as

     [tex]A = \pi r^2[/tex]

=>    [tex]A = 3.142 * 7.5 *10^{-4}[/tex]

=>    [tex]A = 1.7673*10^{-6} \ m^2[/tex]

Generally pressure is mathematically represented as

     [tex]P = \frac{F}{A }[/tex]

=>   [tex]F = P* A[/tex]

=>    [tex]F = 12156000 * 1.767*10^{-6}[/tex]

=>    [tex]F = 21.48 \ N[/tex]

Answer:

The mass of the rule is 56.41 g  

Explanation:

Given;

mass of the object suspended at zero mark, m₁ = 200 g

pivot of the uniform meter rule = 22 cm

Total length of meter rule = 100 cm

0                          22cm                                  100cm

-------------------------Δ------------------------------------

↓                                                                       ↓

200g                                                                 m₂  

Apply principle of moment

(200 g)(22 cm - 0)     = m₂(100 cm - 22 cm)

(200 g)(22 cm) = m₂(78 cm)

m₂ =  (200 g)(22 cm)  / (78 cm)

m₂ = 56.41 g  

Therefore,  the mass of the rule is 56.41 g                                            

Answer:

[tex]F_x=208.25\ N[/tex]

Explanation:

Given that,

Mass of a crate is 22 kg

It moved up along the 15 degrees incline without tipping.

We need to find the corresponding magnitude of force P. The force P is acting in horizontal direction.

It means that the horizontal component of force is given by :

[tex]F_x=F\cos\theta\\\\F_x=mg\cos\theta\\\\F_x=22\times 9.8\times \cos(15)\\\\F_x=208.25\ N[/tex]

So, the horizontal component of force is 208.25 N.

Answer:

A

Explanation:

Answer:

A

Explanation:

No evaporation or precipitation in the water cycle occurs over the ocean.

The angular acceleration of the tires is -2.2 rad/s².

If the car continues to decelerate at this rate, the time required to stop is 27.66 s.

The total distance traveled by the car before stopping is 210.96 revolutions.

The given parameters;

The angular acceleration of the tire is calculated as follows;

[tex]\omega _f^2 = \omega _i ^2 + 2\alpha \theta\\\\(\frac{16.67}{0.42} )^2 = (\frac{25.56}{0.42} )^2 + 2( 77 \ rev \times \frac{2 \pi \ rad}{1 \ rev} ) \alpha \\\\1575.33 = 3703.59 \ + \ 967.736 \alpha \\\\-2128.26 = 967.736 \alpha\\\\\alpha = \frac{-2128.26}{967.736} \\\\\alpha = - 2.2 \ rad/s^2[/tex]

When the car stops, the final angular speed = 0. The time for the motion is calculated as;

[tex]\omega _f = \omega _i + \alpha t\\\\0 = \omega _i + \alpha t\\\\0 = 60.86 + (-2.2)t\\\\0 = 60.86 - 2.2t\\\\2.2t = 60.86\\\\t = \frac{60.86}{2.2} \\\\t = 27.66 \ s[/tex]

The total distance traveled by the car before stopping;

[tex]\theta = \omega_i t + \frac{1}{2} \alpha t^2\\\\\theta = (60.86 \times 27.66) \ + \ (0.5 \times -2.2\times 27.66^2)\\\\\theta = 841.8 \ rad\\\\\theta = 841.8 \ rad \times\frac{1 \ rev}{2\pi \ rad} = 133.96 \ rev[/tex]

total distance = 133.96 + 77 = 210.96 revolutions.

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Answer:

The  correct option is  H

Explanation:

From the question we are told that

    The index of refraction of  coating is  [tex]n_1[/tex]

       The  index of refraction of material  is  [tex]n_2[/tex]

Generally the condition for constructive for a thin film interference is mathematically represented

            [tex]2 * t = [ m + \frac{1}{2}] \frac{\lambda}{n_1 }[/tex]

Here  t represents the thickness

For minimum thickness  m =  0

So

           [tex]2 * t =0 + \frac{1}{2}\frac{\lambda}{n_1 }[/tex]

=>        [tex]t =\frac{\lambda}{4n_1 }[/tex]

Answer:

Explanation:

To focus object at .7m , the image distance can be measured as follows

object distance u = .7m

focal length f = .05 m

image distance v = ?

from lens formula

[tex]\frac{1}{v} -\frac{1}{u} = \frac{1}{f}[/tex]

[tex]\frac{1}{v} +\frac{1}{.7} = \frac{1}{.05}[/tex]

[tex]\frac{1}{v} =\frac{1}{.05} -\frac{1}{.7}[/tex]

v = .054 m

= 54 mm

when the object is at infinity , image is formed at focus ie at distance of

50 mm .

So lens position from sensor  where image is formed , varies from 54 mm to 50 mm .

Answer:

The value is  [tex]h = 32.91 \ m[/tex]

Explanation:

From the question we are told that

    The diameter of each wheel is  [tex]d = 52 \ cm = 0.52 \ m[/tex]

    The mass of the motorcycle is  [tex]m = 320 \ kg[/tex]

    The rotational kinetic inertia is  [tex]I = 2.1 \ kg \ m^2[/tex]

    The  mass of the  rider is  [tex]m_r = 75 \ kg[/tex]

     The  velocity is  [tex]v = 85 \ km/hr = 23.61 \ m/s[/tex]

      Generally the radius of the wheel is mathematically represented as

      [tex]r = \frac{d}{2}[/tex]

=>     [tex]r = \frac{0.52}{2}[/tex]

=>    [tex]r = 0.26 \ m[/tex]

Generally from the law of energy conservation

     Potential energy  attained  by  system(motorcycle and rider )  =  Kinetic  energy of the system  +  rotational kinetic energy of  both wheels of the motorcycle

=>  [tex]Mgh = \frac{1}{2} Mv^2 + \frac{1}{2} Iw^2 + \frac{1}{2} Iw^2[/tex]

=>    [tex]Mgh = \frac{1}{2} * Mv^2 + Iw^2[/tex]

Here  [tex]w[/tex] is the angular velocity which is mathematically represented as

     [tex]w = \frac{v }{r }[/tex]

So

    [tex]Mgh = \frac{1}{2} * Mv^2 + I \frac{v}{r} ^2[/tex]

Here [tex]M = m_r + m[/tex]

         [tex]M = 320 + 75[/tex]

          [tex]M = 395 \ kg[/tex]

[tex]395 * 9.8 * h = 0.5 * 395 * (23.61)^2 + 2.1 *[\frac{ 23.61}{ 0.26} ] ^2[/tex]

=>   [tex]h = 32.91 \ m[/tex]

Answer:

0.182C

Explanation:

Using Q= It

= 13x10^3 . 14x10^-6

= 0.182C

Answer:

C. the motion of a spacecraft under gravitational influence

Answer:

f = 127.48 Hz ,  T = 7.844 1⁻³ s ,  Ф = 3.38 ,     λ = 12.49 m

Explanation:

The general equation for the motion of a wave in a string is

          y = A sin (kx -wt + fi)

the expression they give is

         y = ym sin (0.503x + 801 t + 3.38 )

the veloicda that accompanies time is

      w = 801   rad / s

angular velocity is related to frequency

      w = 2π f

      f = w / 2π

      f = 801 / 2π

      f = 127.48 Hz

The period is the inverse of the frequency

      T = 1 / f

       T = 1 / 127.48

      T = 7.844 10⁻³ s

the csntnate of phase fi is the independent term

      Ф = 3.38

the wave vector accompanies the position k = 0.503 cm

       ka = 2pi /λ

       λ = 2 π / k

       λ = 2 π / 0.503

       λ = 12.49 m

Answer:

A static observer hears a sound whose frequency is appreciably different from actual frequency because here the change in frequency of the sound due to doppler effect.

Explanation:

Given that,

Frequency = f

We know that,

The sound source of frequency f moves with constant velocity through a medium that is at rest.

A static observer hears a sound whose frequency is significantly different from actual frequency due to doppler effect.

We know that,

The doppler effect is defined as

[tex]f=f_{0}(\dfrac{v+v_{0}}{v-v_{s}})[/tex]

Where, f₀ = actual frequency

f = observe frequency

v = speed of sound

[tex]v_{o}[/tex] = speed of observer

[tex]v_{s}[/tex] = speed of source

Hence, A static observer hears a sound whose frequency is significantly different from actual frequency because here the change in frequency of the sound due to doppler effect.