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mihalych1998 [28]

3 years ago

11

1. Miranda wraps her hands around a mug of hot tea. The heat from the hot tea is being transferred to the mug, and then to Miran

da’s hands, mostly by *
convection
reflection
radiation
conduction

1 answer:

loris [4]3 years ago

7 0

The answer is A. Convection

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Radio waves have the longest wavelengths

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Which of the following is same dimension quantity?

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Answer:

Find the dimension of each and every quantity in all the options to check whether they are the same or not. We can use any one formula of each identity to find its dimension.

Complete step by step solution:

To find the dimension of a quantity, we can use any formula related to that quantity but we will use the easiest ones to save time.

Force-

from Newton’s law of motion,

F=maF=ma

Dimension of force =[M][LT−2]=[MLT−2]=[M][LT−2]=[MLT−2]

Work done-

W=F×sW=F×s

Dimension of work=[MLT−2][L]=[ML2T−2]=[MLT−2][L]=[ML2T−2]

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3 years ago

Two forces, one four times as large as the other, pull in the same direction on a 10kg mass and impart to it an acceleration of

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Answer:

The acceleration of the mass is 2 meters per square second.

Explanation:

By Newton's second law, we know that force ( $F$ ), measured in newtons, is the product of mass ( $m$ ), measured in kilograms, and net acceleration ( $a$ ), measured in meters per square second. That is:

$F = m\cdot a$ (1)

The initial force applied in the mass is:

$F = (10\,kg)\cdot \left(2.5\,\frac{m}{s^{2}} \right)$

$F = 25\,N$

In addition, we know that force is directly proportional to acceleration. If the smaller force is removed, then the initial force is reduced to $\frac{4}{5}$ of the initial force. The acceleration of the mass is:

$\frac{25\,N}{20\,N} = \frac{2.5\,\frac{m}{s^{2}} }{a}$

$a = 2\,\frac{m}{s^{2}}$

The acceleration of the mass is 2 meters per square second.

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3 years ago

A 1-kilogram mass is attached to a spring whose constant is 21 N/m, and the entire system is then submerged in a liquid that imp

amm1812

Answer:

the required value is $x(t) = \frac{7}{4} e^{-3t}-\frac{3}{4} e^{-7t}$

Explanation:

Given that,

mass, m = 1kg

spring constant k = 21N/M

damping force = $-\beta\frac{dx}{dt} = \frac{-10dx}{dt}$

$\beta = 10$

By Newtons second law ,

The diffrential equation of motion with damping is given by

$m\frac{d^2x}{dt^2} = -kx-\beta\frac{dx}{dt}$

substitute the value of m =1kg, k = 21N/M, and $\beta = 10$

$1\frac{d^2x}{dt^2} = -21x=10\frac{dx}{dt}$

$\frac{d^2x}{dt^2} + 10\frac{dx}{dt} + 21x = 0$

suppose the equation of the form $x =e^m^t$ ,

and the auxilliary equation is given by

$m^2 + 10m + 21 = 0\\\\m^2 + 7m+3m+21=0\\\\m(m+7)+3(m+7)=0\\\\(m+7)(m+3)=0\\\\m=-7\\m=-3$

The general solution for the above differential equation is

$x(t) =C_1e^{-3t}+C_2e^{-7t}$

Derivate with respect to t

$x'(t)=-3C_1e^{-3t}-7C_2e^{-7t}$

(a)

since time is 0 then mass is one meter below

so x(0) = 1

Also it start from rest , that implies , velocity is 0 and time is 0

$x'(0) = 0$

substitute the initial condition

$C_1 +C_2 = 1$

$-3C_1-7C_2=0$

Solve the above equation to get C₁ and C₂

$C_1 =\frac{7}{4} and C_2 = -\frac{3}{4}$

substitute for C₁ and C₂ in general solution

$x(t) = \frac{7}{4} e^{-3t}-\frac{3}{4} e^{-7t}$

Thus the required value is $x(t) = \frac{7}{4} e^{-3t}-\frac{3}{4} e^{-7t}$

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