a bag of sugar has a mass of 2.26 kg. what is its weight

Answer:

Equation of motion is x(t) = [tex]-te^{-4t}[/tex] + [tex]\frac{1}{4}[/tex] sin(4t)

Explanation:

P.S - The exact question is -

Given - A mass of 1 slug, when attached to a spring, stretches it 2 feet and then comes to rest in the equilibrium position. Starting at t = 0, an external force equal to  [tex]f(t) = 8 cos(4t)[/tex] is applied to the system.

To find - Find the equation of motion if the surrounding medium offers a damping force that is numerically equal to 8 times the instantaneous velocity.

Proof -

Given that,

Mass = 1 slug

We know that, 1 slug = 32 lb

Now,

Force, f = kx

⇒32 = k(2)

⇒k = 16

Now,

Given that, C = 8 ( 8 times the instantaneous velocity)

Now,

The differential equation of motion is equals to

mx'' + Cx' + kx = 8 cos(4t)

⇒x'' + 8x' + 16x = 8 cos(4t)               ...........(1)

Let the General solution of equation (1) be

x(t) = x(c) + x(p)

Now,

The auxiliary equation is

m² + 8m + 16 = 0

m² + 4m + 4m + 16 = 0

m (m+4) + 4 (m+4) = 0

⇒(m+4)(m+4) = 0

⇒m = -4, -4

So,

The Complimentary equation becomes

x(c) = [tex]Ae^{-4t} + Bte^{-4t}[/tex]                  ...........(2)

Now,

Let the particular solution be

x(p) = C cos(4t) + D sin(4t)

x'(p) = -4C sin(4t) + 4D cos(4t)

x''(p) = -16C cos(4t) - 16D sin(4t)

It also satisfy equation (1)

Equation (1) becomes

-16C cos(4t) - 16D sin(4t) + 8 [ -4C sin(4t) + 4D cos(4t) ] + 16 [ C cos(4t) + D sin(4t) ] = 8 cos(4t)

⇒-16C cos(4t) - 16D sin(4t) - 32C sin(4t) + 32D cos(4t) ] + 16C cos(4t) + 16D sin(4t) ] = 8 cos(4t)

⇒-4C sin(4t) + 4B cos(4t) = cos(4t)

By comparing, we get

4B = 1 , A = 0

⇒ B = [tex]\frac{1}{4}[/tex] , A = 0

So, The particular solution becomes

x(p) =  [tex]\frac{1}{4}[/tex] sin(4t)

Now,

The General solution becomes

x(t) = [tex]Ae^{-4t} + Bte^{-4t}[/tex] + [tex]\frac{1}{4}[/tex] sin(4t)       .......(3)

Now,

Given that, At t = 0, initial velocity is zero and the system starts equilibrium

⇒x(0) = 0, x'(0) = 0

By putting t = 0 in equation (3) , we get

A = 0

Now,

Differentiate equation (3), we get

x'(t) = [tex]-4Ae^{-4t} + Be^{-4t} - 4Bte^{-4t}[/tex] + [tex]\frac{1}{4}[/tex] *4 cos(4t)

Put t = 0, we get

0 = -4A + B + 1

⇒B = -1

∴ we get

The general solution becomes

x(t) = [tex]-te^{-4t}[/tex] + [tex]\frac{1}{4}[/tex] sin(4t)

Equation of motion is x(t) = [tex]-te^{-4t}[/tex] + [tex]\frac{1}{4}[/tex] sin(4t)

Answer:

Right

Explanation:

Coil move right yes

Answer:

the induced electric field is 9.95 V/m

Explanation:

Given the data in the question;

Number of turns N = 52

Diameter of coil D = 17 cm = 0.17 m

Radius r = D/2 = 0.17/2 = 0.085 m

Now,

cross-section area A of the coil  = πr²

A = π × ( 0.085 m )²

A = 0.0227 m²

Also given that;

Initial magnetic field B₁ = 0.45 T

Final magnetic field B₂ = 0

∴ change in magnetic field ΔB = B₁ - B₂ = 0.45 T - 0 = 0.45 T

Time taken dT = 0.10 seconds

Now, we know that;

Induced emf ∈ = N[tex](\frac{d\eta }{dt} )[/tex]

where η = BAcosθ

We know that, magnetic field is cylindrically symmetric, coil is also perpendicular to magnetic field.

Hence, the angle between B & A is 0°

∴ θ = 0°

Induced emf ε = N[tex](\frac{d }{dt} )BAcos\theta[/tex]

we substitute

ε = N[tex](\frac{d }{dt} )[/tex] (BAcos0°)

A is constant and cos0° = 1

so

ε = NA[tex](\frac{dB }{dt} )[/tex]  

We now substitute in our values;

ε = 52 × 0.0227 m² ×  [tex](\frac{0.45T }{0.10s} )[/tex]

ε  =  5.3118 V

we know that, from the relation between electric and emf

ε = ∫∈.dl or ε = ∈∫dl         { for coil; ∫dl = πD }

so we have;

ε = ∈πD

solve for ∈

∈ = ε/πD

we substitute

∈ = 5.3118 V / ( π × 0.17 m )

∈ = 9.95 V/m

Therefore, the induced electric field is 9.95 V/m

Answer: the answer is B

Explanation: 80 is not the same as 150 so it will go the way 150 units of force is pulling.

Answer74.3

:

Explanation:

Answer:

option (C) is right answer

Explanation:

I think it's helps you

Answer:

Option C is correct

Explanation:

hope it helps you

Answer:

v = 6.195 m / s

Explanation:

For this exercise we can use the conservation of energy, for the system formed by the ball and the pulley

starting point. Higher before releasing the system

        Em₀ = U = M g h

final point. When the ball has lowered h = 2

        Em_f = K = ½ M v² + ½ I w²

the energy is preserved

        Em₀ = Em_f

        M g h = ½ M v² + ½ I w²

angular and linear velocity are related

         v = w r

        w = v / r

indicate that the moment of inertia is

         I = ½ m r²

we substitute

          M g h = ½ M v² + ½ (½ m r²)  (v/r) ²

          ½ v² (M + [tex]\frac{1}{2}[/tex] m) = M g h

          v² = [tex]2gh \ \frac{M}{M + \frac{m}{2} }[/tex]

let's calculate

          v = [tex]\sqrt{ 2 \ 9.8 \ 2 \ \frac{70}{70 + 1.5} }[/tex]

          v = 6.195 m / s

Answer:

m = 1.31 kg

Explanation:

Given that,

The speed of duck, v = 9.1 m/s

The magnitude of momentum, p = 12 kg-m/s

We need to find the mass of the duck. We know that the momentum of an object is given by :

p = mv

Where

m is the mass of the duck

[tex]m=\dfrac{p}{v}\\\\m=\dfrac{12\ kg-m/s}{9.1\ m/s}\\\\m=1.31 kg[/tex]

So, the mass of the duck is equal to 1.31 kg.

Answer:

i am guessing for reflection but not so sure

Answer:

okay

Explanation:

please I don't know

Answer:

the correct answer is C     +, - , +

Explanation:

The electric field for positive charges is outgoing and for negative charges it is directed towards the charge.

Let's apply this to our case:

On plates A and B the field goes to the right, therefore plate A must be positive

In plates B and C the way it goes to the left, so the field is selected from it, this implies that plate C is positive

therefore plate B must be negative for both cases

when checking the correct answer is C     +, - , +

Answer:

Universe

Explanation:

I took the quiz.

Answer:

can you explain in Hindi language

because i learn hindi

Answer:

b) 1.63x10-9N

Explanation:

i dont think this is right answer

Answer:

C or 8.17x10^-10 N

Explanation:

I was looking for the explanation but the answer is correct.

Answer:

All of the above.

Explanation:

A person is said to be at rest when he or she is not performing any action. The heartbeat stays normal in this condition.

A person is said to perform a moderate activity when his heart beats faster than the normal rest condition. It requires extra effort within the limit. For example, walking and dancing are examples of moderate activity.

A person is said to perform a vigorous activity when his heart beats much than in moderate activity. It requires a lot of effort over the limit. Running is an example of vigorous activity.

In view of the above information, all the options given in the question are true. Hence, the correct answer will be:

All of the above.

Answer:

They are right.

Explanation:

Answer:

Mechanical Energy : KE + PE

Conversion : "When energy transfers from one form to another"

Potential Energy: the energy possessed by a body by virtue of its position relative to others , stresses within itself, electric charge , and other factors .'

Kinetic Energy: energy of an object in motion

Law of conservation of energy: KE+PE+friction=KE

Explanation:

First of all mechanical energy is kinetic energy plus potential energy (it is the energy of movement) So:

Mechanical Energy : KE + PE

Conversion is when energy converts or becomes a different form. So:

Conversion : "When energy transfers from one form to another"

Potential energy is stored energy, in Physics I or AP Physics I, it is often due to it being at a height, but batteries, foods, etc. are also example of it, so:

Potential Energy: the energy possessed by a body by virtue of its position relative to others , stresses within itself, electric charge , and other factors .'

Kinetic energy is for objects in motion so you got it right!

Kinetic Energy: energy of an object in motion

The law of conservation of energy means there is the same amount of energy before, as there is after, so when you see an equation with energy on both sides, it is usually this. Also, this is the last question left, so this has to be the answer.

Law of conservation of energy: KE+PE+friction=KE

Answer:

electromagnetic waves only

Explanation:

I just took the test, Hope it helps!

Answer:

A: Electromagnetic waves only

Explanation:

Answer: 1.  walking across a carpet and touching a metal door handle            2. pulling your hat off and having your hair stand on end.

Explanation

:)

Answer:D

Explanation:

Answer:

C.

Explanation:

This is what we call a permanent magnet. By the  way, the magnetic phenomena were first observed about 2500 years ago near the ancient city of Magnesia, what is today Manisa, located in western Turkey, when people saw fragments of magnetized iron. So what happens if you cut a magnet in half? Well, a magnet has two ends, the first one is called a north pole or N pole while the  other end is a south pole or S pole, so if you break a bar magnet, each piece  has a north and south pole, no matter the size of each new bar although the smaller the  piece, the weaker its magnetism. This is true because unlike electric charges, you always find magnetic poles  in pairs, that is, ¡they can't be isolated! The option is C. because in the great bar the north pole is to the left while the south pole is to right.

Answer:

Increases

Explanation:

This is because if there are more gas particles available within a given area, the greater the air density. Therefore, the greater the air density, there will be more gas particles per unit volume. Which indicate that there are more air particles bombarding with a surface. Therefore, the air pressure increases as the air density increases and visa versa.

Answer:

its a. and jusing that youl

Explanation:

Since the balloon is not accelerating means that the net force on the balloon is zero. This implies that the weight of balloon must be equal to the buoyant force on balloon.

Hence, the buoyant force equals the weight of air displaced by the balloon, also 20,000 N.

Weight of the air displaced = density of air × volume

The density of air at 1 atm pressure and 20º C is 1.2 kg/m³  

the volume V = 20,000/(1.2×9.8) =  1700 m³

Answer:

A

Explanation:

Answer:

Diagram (3).

Explanation:

N3L states that if object A exerts a force on object B, then object B must exert a force of equal magnitude and opposite direction back on object A ([tex]F_{A} = -F_{B}[/tex]).

The diagram which best represents the gravitational forces, F, between a satellite, S, and Earth is; Choice (3).

The law clearly states a Force of attraction; the two objects come towards each other.

Consequently, Choice (3) best represents the gravitational forces, F, between a satellite, S, and Earth.

Read more:

https://brainly.com/question/11460810

Answer:

  a = [tex]\frac{m}{m+ \frac{1}{2} m_p} \ g \ sin \beta[/tex]  ,       t = [tex]\sqrt{ \frac{2d}{a} }[/tex]

Explanation:

To solve this exercise we must use Newton's second law

For the block

let's set a reference system with the x axis parallel to the plane

X axis

         Wₓ - T = m a

Y axis  

         N- W_y = 0

         N = W_y

for pulley

          ∑τ = I α

           T R = (½ m_p R²) α

let's use trigonometry for the weight components

         sin β = Wₓ / W

         cos β = W_y / W

         Wx = W sin β

angular and linear variables are related

          a = α R

          α = a / R

we substitute and group our equations

         W sin β - T = m a

         T R = ½ m_p R² (a / R)

         W sin β - T = m a

                        T = ½ m_p a

we solve the system of equations

         W sin β = (m + ½ m_p) a

          a = [tex]\frac{m}{m+ \frac{1}{2} m_p} \ g \ sin \beta[/tex]

let's find the time to travel the distance (d) through the block

          x = v₀ t + ½ a t²

          d = 0 + ½ a t²

          t = [tex]\sqrt{ \frac{2d}{a} }[/tex]

Answer:

option b

Explanation:

........................

This question is incomplete, the complete question is;

A rifle fires a 2.10 × 10⁻² kg pellet straight upward, because the pellet rests on a compressed spring that is released when the trigger is pulled. The spring has a negligible mass and is compressed by 9.10 × 10⁻² m from its unstrained length. The pellet rises to a maximum height of 6.10 m above its position on the compressed spring. Ignoring air resistance, determine the spring constant.

Answer:

the spring constant is 303.5 N/m

Explanation:

Given the data in the question;

There is a potential energy associated with the spring;

we know that potential energy = kinetic energy

mgh = [tex]\frac{1}{2}[/tex]kx²

where k is the spring constant and x is the compression

as the pallet is fired, the spring gives kinetic energy which is converted into gravitational potential energy

so

m = 2.10 × 10⁻²

g = 9.81 m/s²

h = 6.10 m

x = 9.10 × 10⁻² m

we substitute

mgh = [tex]\frac{1}{2}[/tex]kx²

2.10 × 10⁻² × 9.81 × 6.10 =  [tex]\frac{1}{2}[/tex] × K × ( 9.10 × 10⁻² )²

1.256661 = 0.0041405 × K

K = 1.256661 / 0.0041405

K = 303.5 N/m

Therefore, the spring constant is 303.5 N/m