In an evironmental system of subsystem, the mass balance equation is:__________.

Answers

Answer 1

Answer:

Explanation:

The mass balance is an application of conservation of mass, to the analysis of physical system. This is given in an equation form as

Input = Output + Accumulation

The conservation law that is used in this analysis of the system actually depends on the context of the problem. Nevertheless, they all revolve around conservation of mass. By conservation of mass, I mean that the fact that matter cannot disappear or be created spontaneously.

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The cart is initially at rest. ForceF is applied to the cart for time ? t, after which the car has speed v. Suppose the same force is applied for the same time to a second cart with twice the mass. Friction is negligible. Afterward, the second cart's speed will be
a) 2v
b) 1/2v
c) v
d) 4v
e) 1/4v

Answers

Answer:

$v'=(1)/(2)v$

Explanation:

Given that,

Initial speed of the cart, u = 0

Let F force is applied to the cart for time $\Delta t$ after which the car has speed v. The force on an object is given by :

F = ma

m is the mass of the cart

We need to find the speed of second cart, if the same force is applied for the same time to a second cart with twice the mass. Force becomes,

$F=(mv')/(t)$

$v'=(F t)/(2m)$

$v'=(1)/(2)v$

So, the speed of second cart is half of the initial speed of first cart. So, the correct option is (b).

Two resistors are to be combined in parallelto form an equivalent resistance of 400Ω. The resistors are takenfrom available stock on hand as acquired over the years. Readily available are two common resistorsrated at 500±50 Ωand two common resistors rated at 2000 Ω±5%. What isthe uncertainty in an equivalent 400 Ωresistance?(Hint: the equivalent resistance connected in parallel can be obtained by 1212TRRRRR=+)

Answers

Answer:

Δ $R_(e)$ = 84 Ω, $R_(e)$ = (40 ± 8) 10¹ Ω

Explanation:

The formula for parallel equivalent resistance is

1 / $R_(e)$ = ∑ 1 / Ri

In our case we use a resistance of each

R₁ = 500 ± 50 Ω

R₂ = 2000 ± 5%

This percentage equals

0.05 = ΔR₂ / R₂

ΔR₂ = 0.05 R₂

ΔR₂ = 0.05 2000 = 100 Ω

We write the resistance

R₂ = 2000 ± 100 Ω

We apply the initial formula

1 / $R_(e)$ = 1 / R₁ + 1 / R₂

1 / $R_(e)$ = 1/500 + 1/2000 = 0.0025

$R_(e)$ = 400 Ω

Let's look for the error (uncertainly) of Re

$R_(e)$ = R₁R₂ / (R₁ + R₂)

R’= R₁ + R₂

$R_(e)$ = R₁R₂ / R’

Let's look for the uncertainty of this equation

Δ $R_(e)$ / $R_(e)$ = ΔR₁ / R₁ + ΔR₂ / R₂ + ΔR’/ R’

The uncertainty of a sum is

ΔR’= ΔR₁ + ΔR₂

We substitute the values

Δ $R_(e)$ / 400 = 50/500 + 100/2000 + (50 +100) / (500 + 2000)

Δ $R_(e)$ / 400 = 0.1 + 0.05 + 0.06

Δ $R_(e)$ = 0.21 400

Δ $R_(e)$ = 84 Ω

Let's write the resistance value with the correct significant figures

$R_(e)$ = (40 ± 8) 10¹ Ω

In Europe, gasoline efficiency is measured in km/L. If your car's gas mileage is 28.0 mi/gal , how many liters of gasoline would you need to buy to complete a 142-km trip in Europe

Answers

Answer:

The volume required is $V = 11.91 \ liters$

Explanation:

From the question we are told that

The cars mileage is v = 28.0 mi/gal

The distance is d = 142 km

Converting the distance from km to miles

$d = 142 * 0.6214 = 88.24 \ miles$

Generally the volume of gasoline needed is mathematically represented as

$V = (d)/( v)$

=> $V = (88.24)/( 28.0 )$

=> $V = 3.151 \ gal$

Converting to Liters

=> $V = 3.151 * 3.78$

=> $V = 11.91 \ liters$

The magnetic flux that passes through one turn of a 11-turn coil of wire changes to 5.60 from 9.69 Wb in a time of 0.0657 s. The average induced current in the coil is 297 A. What is the resistance of the wire?

Answers

Answer:

2.31 Ω

Explanation:

According to the Faraday's law of electromagnetic induction,

Induced emf = - N (dΦ/dt)

Emf = -N (ΔΦ/t)

where N = number of turns = 11

Φ = magnetic flux

ΔΦ = change in magnetic flux = 9.69 - 5.60 = 4.09 Wb

t = time taken for the change = 0.0657 s

Emf = 11(4.09/0.0657)

Emf = - 684.78 V (the minus sign indicates that the direction of the induced emf is opposite to the direction of change of magnetic flux)

From Ohm's law,

Emf = IR

R = (Emf)/I

I = current = 297 A

R = (684.78)/297

R = 2.31 Ω

Hope this Helps!!

Explanation:

Below is an attachment containing the solution.

When a body falls freely under gravity, then the work done by the gravity is ___________

Answers

Answer: positive

Explanation:

Gravity can be defined as the force with which the body is attracted towards the center of the earth, or towards any other body. If the force acting on the body is in the direction of displacement then the word done by the applicable force is positive. This causes the free fall of the ball under the influence of gravity is also positive.

Parallel Plates Consider a very large conducting plate at potential V0 suspended a distance d above a very large grounded plane. Find the potential between the plates. The plates are large enough so that they may be considered to be infinite. This means that one can neglect fringing fields.

Answers

Answer:

$V = (V_0x)/(d)$

Explanation:

Since the field lines are parallel and the electric field is uniform between two parallel plates, a test charge would experience the same force of attraction or repulsion no matter where it is located in the field,

I attached an image that could help to understand the representation of the field. The formula used to calculate it is given by,

$E= -(\Delta V)/(x)$ (1)