A balloon is ascending at a rate of +4.00 m/s to a height of 11.0 m above the ground when a package is dropped. In the absence of air resistance, the velocity of the ball when it hits the ground is

Answer:

Plane spacing, [tex]d=1.4\times 10^{-10}\ m[/tex]

Explanation:

It is given that,

Wavelength of x-ray, [tex]\lambda=1.4\times 10^{-10}\ m[/tex]

Angle the x-ray made with a set of planes in a crystal causing first order constructive interference is 30 degrees

We need to find the plane spacing. It is based on Bragg's law such that,

[tex]2d\sin\theta=n\lambda[/tex]

d is plane spacing

n = 1 here

[tex]d=\dfrac{\lambda}{2\sin\theta}\\\\d=\dfrac{1.4\times 10^{-10}}{2\times \sin (30)}\\\\d=1.4\times 10^{-10}\ m[/tex]

So, the plane spacing is [tex]1.4\times 10^{-10}\ m[/tex].

Answer:

velocity = distance/time

velocity = wavelength × frequency

Both of these are commonly known equations to calculate velocity with different variables.

Answer:

Explanation:

Using equations of motion:

(a)

v=u+at

∴0=19.4−8.57t

∴t=19.4/8.57

=2.3s

B. Using s= ut + 1/2 at²

19.4(2.3)-1/28.57(2.3)²

= 21.92rad

Answer:

0.0665 days

Explanation:

We are given;

The mean distance from the Earth's center to the moon;a1 = 385000 km

The mean distance from the Earth's center to the space craft;a2 = 6965 km

Formula for kepplers third law is;

T² = 4π²a³/GM

However, the proportion of both distances would be;

(T1)²/(T2)² = (a1)³/(a2)³

Where;

T1 is the period of orbit of the moon around the earth. T1 has a standard value of 27.322 days

T2 is the period of the space craft orbit.

Making T2 the subject, we have;

T2 = √((T1)²×(a2)³)/(a1)³)

Thus, plugging in the relevant values;

T2 = √(27.322² × 6965³)/(385000)³

T2 = 0.0665 days

Answer:

The magnitude of the magnetic field is 8.333 x 10⁻⁷ T

Explanation:

Given;

charge on the lightening bolt, C = 15.0 C

time the charge passes by, t = 1.5 x 10⁻³ s

Current, I is calculated as;

I = q / t

I = 15 / 1.5 x 10⁻³

I = 10,000 A

Magnetic field at a distance from the bolt is calculated as;

[tex]B = \frac{\mu_o I}{2\pi r}[/tex]

where;

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

I is the current in the bolt

r is the distance of the magnetic field from the bolt

[tex]B = \frac{\mu_o I}{2\pi r} \\\\B = \frac{4\pi *10^{-7} 10000}{2\pi *24} \\\\B = 8.333 *10^{-5} \ T[/tex]

Therefore, the magnitude of the magnetic field is 8.333 x 10⁻⁷ T

Answer:

The hall  voltage is [tex]\epsilon =1.45 *10^{-6} \ V[/tex]

Explanation:

From the question we are told that

     The magnetic field is  [tex]B = 2.00 \ T[/tex]

     The diameter is  [tex]d = 2.588 \ mm = 2.588 *10^{-3} \ m[/tex]

       The  current is  [tex]I = 20 \ A[/tex]

The radius can be evaluated as

        [tex]r = \frac{d}{2}[/tex]

substituting values

       [tex]r = \frac{2.588 * 10^{-3}}{2}[/tex]

       [tex]r = 1.294 *10^{-3} \ m[/tex]

The hall voltage is mathematically represented as

      [tex]\episilon = B * d * v_d[/tex]

where[tex]v_d[/tex] is the  drift velocity of the electrons on the current carrying conductor which  is mathematically evaluated as

       [tex]v_d = \frac{I}{n * A * q }[/tex]

Where n is the number of electron per cubic meter which for copper is  

        [tex]n = 8.5*10^{28} \ electrons[/tex]

  A is the cross - area of the wire  which is mathematically represented as

           [tex]A = \pi r^2[/tex]

substituting values

          [tex]A = 3.142 * [ 1.294 *10^{-3}]^2[/tex]

          [tex]A = 5.2611 *10^{-6} \ m^2[/tex]

so the drift velocity is  

       [tex]v_d = \frac{20 }{ 8.5*10^{28} * 5.26 *10^{-6} * 1.60 *10^{-19} }[/tex]

       [tex]v_d = 2.7 *10^{-4 } \ m/s[/tex]

Thus the hall voltage is

     [tex]\epsilon = 2.0 * 2.588*10^{-3} * 2.8 *10^{-4}[/tex]

     [tex]\epsilon =1.45 *10^{-6} \ V[/tex]

Answer:

The longer the cord, the lower the illumination

Explanation:

The illumination provided by the light bulb will be reduced as the length of the extension cord increases. This is because the resistance provided by the wire increases with its length.

Long wires have more electrical resistance than shorter ones.

Let us consider this formula:

Resistance =[tex]\frac{\rho L}{A}[/tex]

From this formula, we can see that as the length increases, the resistance to current flow offered by the wire increases also provided the resistivity and cross-sectional area of the wire remain constant. As a result of this, the illumination will drop.

Answer:

The speed of the police car is 294 m/s

Explanation:

Given;

frequency of the siren in air, f = 280 Hz

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

Determine the wavelength of the sound in air to the stationary car:

v = fλ

where;

λ is wavelength of the sound

λ = v/f

λ = 343 / 280

λ = 1.225 m

Now, determine the speed at which the police car is approaching the stationary car;

The actual frequency of the police car, F = 240 Hz

V = Fλ

Where;

V is speed of the police car

λ is the distance between the police car and the stationary car, (wavelength)

V = 240 x 1.225

V = 294 m/s

Therefore, the speed of the police car is 294 m/s

Answer:

[tex]500\text{N} (490\text{N}) (490.5\text{N})[/tex]

Explanation:

The reaction force is the force that is in the perpendicular direction to the wall.

We have an angle and a hypotenuse, we need to find the adjacent angle - so we can just use cos:

[tex]cos(\theta)=\frac{\text{adj}}{\text{hyp}}\\\text{hyp}*cos(\theta)=\text{adj}\\100*cos(60)=100*0.5=50\text{kg}[/tex]

However, we would like a force and not a mass.

[tex]W=mg\\W=50g\\W=500\text{N} (490\text{N}) (490.5\text{N})[/tex]

Answer 1 if you use g as 10, answer 2 if you're studying mechanics in maths, answer 3 if you're studying mechanics in physics.

Answer:

9.82 rads/sec

Explanation:

We are given;

Time taken; t = 1.6 secs

Number of somersaults = 2

Now, we know that,

1 revolution = 2π radians

And number of somersaults is the same thing as number of revolutions

So,

Total radians = 2π × 2 = 5π

Angular velocity = total number of revolutions/time period = 5π/1.6 = 9.82 rads/sec

Answer:

The average induced emf in the loop is 0.3 V

Explanation:

Given:

d = 22 cm

Magnetic field  is  B = 1.5 T

Change in time  Δt = 0.20 sec.

Radius of loop  = r = d/2 = 11 x [tex]10^{-2}[/tex] m

According to the faraday's law,  Induced emf is given by   e = - (ΔФ / Δt)

where Ф = magnetic flux

Ф = BAcos0   (in this occasion, Ф=0)

where area A = pi * r²

note that we have to neglect negative sign due to its lenz law...so

       B * pi * r

e = ----------------

          Δt

       1.5 ( 3.1416) 11 x [tex]10^{-2}[/tex] )²

e =  ------------------------------------

                        0.20

e = 0.3 V

Therefore, the average induced emf in the loop is 0.3 V

Answer:

The moment of inertial of the wheel,  [tex]I = 8(\frac{1}{3}M_sL^2 ) + M_rL^2[/tex]

Explanation:

Given;

8 spokes of uniform diameter

mass of each spoke, = [tex]M_s[/tex]

length of each spoke, = L

mass of outer ring, = [tex]M_r[/tex]

The moment of inertial of the wheel will be calculated as;

[tex]I = 8I_{spoke} + I_{ring}[/tex]

where;

[tex]I_{spoke[/tex] is the moment of inertia of each spoke

[tex]I_{ring[/tex] is the moment of inertia of the rim

Moment of inertia of each spoke [tex]=\frac{1}{3}M_sL^2[/tex]

Moment of inertial of the wheel

[tex]I = 8(\frac{1}{3}M_sL^2 ) + M_rL^2[/tex]

Answer:

The  total energy is  [tex]T = 169.02 \ J[/tex]

Explanation:

From the question we are told that

    The  Poynting vector (energy flux ) is  [tex]k = 0.939 \ W/m^2[/tex]

    The length of the rectangle is  [tex]l = 1.5 \ m[/tex]

    The  width of the rectangle is  [tex]w = 2.0 \ m[/tex]

    The time taken is [tex]t = 1 \ minute = 60 \ s[/tex]

The total electromagnetic energy falls on the area is mathematically represented as

      [tex]T = k * A * t[/tex]

Where A  is the area of the rectangle which is mathematically represented as

           [tex]A= l * w[/tex]

 substituting values

         [tex]A= 2 * 1.5[/tex]

        [tex]A= 3 \ m^2[/tex]

substituting values

        [tex]T = 0.939 * 3 * 60[/tex]

        [tex]T = 169.02 \ J[/tex]

Answer:

Explanation:

When the path difference is half the wave length or λ /2 , destructive interference takes place which results in reduced or zero intensity in case equal intensity waves interfere as in Young's double slit experiment

Hence dark fringe is formed at that place where intensity is zero .

Hence the right option is D

Answer:

x  =  0.27 cm

Explanation:

given data

mass = 150 g

velocity = 10 cm/s = 0.1 m/s

spring constnat = 200 N/m

solution

as we know that here ball is moving with constant speed

so

0.5 × m × v² = 0.5 × k × x²      .......................1

here x is compression in spring

so put here value and we get

0.5 × 150 × (0.1)² = 0.5 × 200 × x²

solve it we get

x  =  0.27 cm

Answer:

20J

Explanation:

The computation of the change in kinetic energy is shown below:

As we know that

Work was done on system =  change in potential energy + change in kinetic energy + change in thermal energy

-430J = -510J + change in kinetic energy + 100J

-430J = -410J + change in kinetic energy

So, the change in kinetic energy is 20J

We simply applied the above formula to find out the change in kinetic energy

Answer:

The  pressure is  [tex]P = 1652 \ Pa[/tex]

Explanation:

From the question we are told that

    The  volume of the container is  [tex]V = 1.83 \ L = 1.83 *10^{-3 } \ m^3[/tex]

     The mass of  [tex]N_2[/tex] is  [tex]m_n = 0.246 \ g = 0.246 *10^{-3} \ kg[/tex]

     The root-mean-square velocity is  [tex]v = 192 \ m/s[/tex]

The  root -mean square velocity is mathematically represented as

      [tex]v = \sqrt{ \frac{3 RT}{M_n } }[/tex]

Now the ideal gas law is mathematically represented as

      [tex]PV = nRT[/tex]

=>   [tex]RT = \frac{PV}{n }[/tex]

Where n is the number of moles which is mathematically represented as

         [tex]n = \frac{ m_n }{M }[/tex]

Where  M  is the molar mass of  [tex]N_2[/tex]

So  

        [tex]RT = \frac{PVM_n }{m _n }[/tex]

=>    [tex]v = \sqrt{ \frac{3 \frac{P* V * M_n }{m_n } }{M_n } }[/tex]

=>    [tex]v = \sqrt{ \frac{ 3 * P* V }{m_n } } }[/tex]

=>   [tex]P = \frac{v^2 * m_n}{3 * V }[/tex]

substituting values

    =>    [tex]P = \frac{( 192)^2 * 0.246 *10^{-3}}{3 * 1.83 *10^{-3} }[/tex]

=>         [tex]P = 1652 \ Pa[/tex]

Answer:

(a) f

(b) r

(c) s

Explanation:

There are two forces on the sphere: weight and buoyancy.

Sum of forces in the y direction:

∑F = ma

B − mg = 0

B = mg

Buoyancy is equal to the weight of the displaced fluid, or ρVg, where ρ is the density of the fluid and V is the displaced volume.

ρVg = mg

ρV = m

V = m/ρ

(a) The mass decreases, so the displaced volume decreases.

(b) The sphere's density is constant and its radius increases, which means its mass increases, so the displaced volume increases.

(c) The mass stays the same, so the displaced volume is the same.

Answer:

Zack should direct his throw outward and toward the back of the car.

Explanation:

As the car is moving forward, the book will be thrown with a forward component. Therefore, throwing this book backwards at a constant speed would cancel the motion of the car, allowing the book to have a greater chance of ending on the driveway. I say a greater chance as Zack may not have the exact timings as to land the book in his driveway. That too he may not have thrown the book with the right momentum.

The solution is throw 3.

I say a greater chance as Zack may not have the exact timings as to land the book in his driveway. That too he may not have thrown the book with the right momentum as the skydivers.

The statement that best applies Newton’s laws of motion to explain the skydiver’s motion is that an upward force balances the downward force of gravity on the skydiver. Newton's 3rd law often applies to skydiving.

When gravity is not acting upon the skydivers they would continue moving in the direction the vehicle they jumped from was moving. If no air resistance takes place, then the skydivers would still accelerating at 9.8 m/s until they hit the ground.

The skydiver after leaving the aircraft will accelerates downwards due to the force of gravity usually as there is no air resistance acting in the upwards direction, and there is a resultant force acting downwards, the skydiver will accelerates towards the ground.

Therefore, I say a greater chance as Zack may not have the exact timings as to land the book in his driveway. That too he may not have thrown the book with the right momentum as the skydivers.

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Complete question is;

Earth moves in an elliptical orbit with the sun at one of the foci. The length of half of the major axis is 149,598,000 kilometers, and the eccentricity is 0.0167. Find the minimum distance (perihelion) and the maximum distance (aphelion) of Earth from the sun

Answer:

Minimum distance = 147,099,713.4 km

Maximum distance = 152,096,286.6 km

Explanation:

The formula for the eccentricity of an ellipse is given by;

e = c/a

where;

c is distance from the center of the ellipse to the focus of the ellipse.

a is distance from the center of ellipse to a vertex.

From the question, we are given;

a = 149,598,000

e = 0.0167

Thus;

0.0167 = c/149,598,000

c = 0.0167 × 149,598,000

c = 2,498,286.6

Now, formula for the minimum distance (perihelion) is;

Minimum distance = a - c

Minimum distance = 149598000 - 2498286.6

Thus;

Minimum distance = 147,099,713.4 km

Similarly, formula for the maximum distance (aphelion) is;

Max distance = a + c

Max distance = 149598000 + 2498286.6

Maximum distance = 152,096,286.6 km

Answer: W.D = 1/2mv^2

Explanation:

If an external force or a single force is acting on a body. Just like the first law of thermodynamics, the force acting on the body will cause work done on the system.

Work done = force × distance

And the work done on the body will cause the molecules of the body to experience motion and thereby producing kinetic energy.

The work done will be converted to kinetic energy.

W.D = 1/2mv^2

Answer:

The magnitude of the net field located at the center of the square is the same in every of arrangement of the charges.

Answer:

Explanation:

Let the velocity of astronaut be u and the velocity of flat sheet of metal plate be v . They will move in opposite direction ,  so their relative velocity

= u + v = 2.3 m /s ( given )

We shall apply conservation of momentum law for the movement of astronaut and metal plate

mu  = M v where m is mass of astronaut , M is mass of metal plate

71 u = 230 x v

71 ( 2.3 - v ) = 230 v

163.3 = 301 v

v = .54 m / s

u = 1.76 m / s

honeycomb will be at rest  because honeycomb surface  is frictionless . Plate will slip over it . Over plate astronaut is walking .

a ) velocity of metal sheet relative to honeycomb will be - 1.76 m /s

b ) velocity of astronaut relative to honeycomb will be + .54 m /s

Here + ve direction is assumed to be the direction of astronaut .  

A wedge of glass of refractive index 1.64 has a silver coating on the bottom, as shown in the image attached below.

Determine the smallest distance x to a position where 450-nm light reflected from the top surface of the glass interferes constructively with light reflected from the silver coating on the bottom. The light changes phase when reflected at the silver coating.

Answer:

the smallest distance x  = 2.74 × 10⁻³ m or 2.74 mm

Explanation:

From the given information:

The net phase change is zero because both the light ray reflecting from the air-glass surface and silver plate undergo a phase change of [tex]\dfrac{\lambda}{2}[/tex] , as such the condition for the  constructive interference is:

nΔy = mλ

where;

n = refractive index

Δy = path length (inside the glass)

So, from the diagram;

[tex]\dfrac{y}{x}=\dfrac{10^{-5} \ m}{0.2 \ m}[/tex]

[tex]\dfrac{y}{x} = 5 \times 10^{-5}[/tex]

[tex]y = 5 \times 10^{-5} x[/tex]

Now;

Δy can now be = 2 ( 5 × 10⁻⁵ [tex]x[/tex])

Δy =1 ×  10⁻⁴[tex]x[/tex]

From nΔy = mλ

n( 1 ×  10⁻⁴[tex]x[/tex] ) = mλ

[tex]x = \dfrac{m \lambda}{n \times 1 \times 10^{-4} }[/tex]

when the thickness is minimum then m = 1

Thus;

[tex]x = \dfrac{1 \times 450 \times 10^{-9} \ m}{1.64 \times 1 \times 10^{-4} }[/tex]

x =  0.00274 m

x = 2.74 × 10⁻³ m or 2.74 mm

Answer: B. The surface of the coating is rough, so light that shines on it gets scattered in many directions.

Explanation: On Edge!!!!!!!!!!!!!!!!!!!!

Answer:

a) 320N (if you take gravity as 10ms^-2) or 313.6N (if you take gravity as 9.8ms^-2

b) 41.6N

c) 6.25ms^-2

d) 1707.317 kg

Explanation:

a) W=mg

    W= 32 x 10 or 9.8

    W = 320N or 313.6N

b) F=ma

   F= 32 x 1.3

   F= 41.6N

c) F=ma

   200 = 32 x a

   a= 6.25ms^-2

d) F=ma

    7000= m x 4.1

     m= 1707.317 kg

I am not completely sure about the d) part because I dont whether you will be taking Friction and Normal Reaction too. As per my knowledge, I think no, as no angles nor the gradient of the floor/road is mentioned here.                  

a) The weight of your shopping cart is 313.6N .

b) The required force is  41.6N

c) The acceleration of the car is 6.25ms^-2

d) The mass of the car is 1707.317 kg.

Acceleration is rate of change of velocity with time. Due to having both direction and magnitude, it is a vector quantity. Si unit of acceleration is meter/second² (m/s²).

a) The weight of the shopping cart:  W=mg

  W= 32 x  9.8 N

 W = 313.6N

b) The required force is to be applied: F=ma

F= 32 x 1.3 N.

F= 41.6N.

c) Let the acceleration of the cart is a.

Then, force:  F=ma

200 = 32 x a

a= 6.25ms^-2

Hence,  the acceleration of the cart is  6.25ms^-2.

d) Let the mass of the car is m.

Force applied on the car: F=ma

7000= m x 4.1

m= 1707.317 kg

The mass of the car is 1707.317 kg.

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Answer:

The power required by the pump is nearly 230.588 kW

Explanation:

Flow rate of the pump Q = 1 m^3/s

the head flow H = 20 m

specific weight of water γ = 9800 N/m^3

efficiency of the pump η = 85%

First note that specific gravity of water is the product of the density of water and acceleration due to gravity.

γ = ρg

where ρ is density. For water its value is 1000 kg/m^3

g is the acceleration due to gravity = 9.81 m/s^2

The power to lift this water at this rate will be gotten from the equation

P = ρgQH

but ρg = γ

therefore,

P = γQH

imputing values, we'll have

P = 9800 x 1 x 20 = 196000 W

But the centrifugal pump that will be used will only be able to lift this amount of water after the efficiency factor has been considered. The power of pump needed must be greater than this power.

we can say that

196000 W is 85% of the power of the pump power needed, therefore

196000 = 85% of [tex]P_{p}[/tex]

where [tex]P_{p}[/tex] is the power of the pump needed

85% = 0.85

196000 = 0.85[tex]P_{p}[/tex]

[tex]P_{p}[/tex] = 196000/0.85 = 230588.24 W

Pump power = 230.588 kW

Answer:

the three possible movements by the change in electric potential energy (Ue) of the object are NORTH EAST SOUTH

Explanation:

This is because When the object moves south, the force is in the direction of the displacement, and positive work is done with decreasing electric potential energy.

The opposite is true if the particle moves north—that is, negative work is done with increasing electric potential energy.

No work is done and the electric potential energy is constant if the motion is perpendicular to the electric field.

Answer:

D &B

Explanation:

Using Fleming right hand rule that States that if the fore-finger, middle finger and the thumb of left hand are stretched mutually perpendicular to each other, such that fore-finger points in the direction of magnetic field, the middle finger points in the direction of the motion of positive charge, then the thumb points to the direction of the force

Answer:

Explanation:

The volume of the spherical balloon is expressed as V = 4/3πr³ where r is the radius of the spherical balloon. If the spherical balloon is inflated with gas at the rate of 500 cubic centimetres per minute then dV/dt = 500cm³.

Using chain rule to express dV/dt;

dV/dt = dV/dr*dr/dt

dr/dt is the rate at which the radius of the gallon is increasing.

From the formula, dV/dr = 3(4/3πr^3-1))

dV/dr = 4πr²

dV/dt = 4πr² *dr/dt

500 =  4πr² *dr/dt

If radius r = 40;

500 = 4π(40)² *dr/dt

500 = 6400π*dr/dt

dr/dt = 500/6400π

dr/dt = 5/64π

dr/dt  = 0.245cm/min

Hence, the radius of the balloon is increasing at the rate of 0.245cm/min

Answer:

a) before immersion

C = εA/d = (8.85e-12)(25e-4)/(1.31e-2) = 1.68e-12 F

q = CV = (1.68e-12)(255) = 4.28e-10 C

b) after immersion

q = 4.28e-10 C

Because the capacitor was disconnected before it was immersed, the charge remains the same.

c)*at 20° C

C = κεA/d = (80.4*)(8.85e-12)(25e-4)/(1.31e-2) = 5.62e-10 F

V = q/C = 4.28e-10 C/5.62e-10 C = 0.76 V

e)

U(i) = (1/2)CV^2 = (1/2)(1.68e-12)(255)^2 = 5.46e-8 J

U(f) = (1/2)(5.62e-10)(0.76)^2 = 1.62e-10 J

ΔU = 1.62e-10 J - 5.46e-8 J = -3.84e-8 J