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Engineering Mathematics Through Applications

Kuldeep Singh

Chapter 1

Engineering Formulae - all with Video Answers

Educators

Section 1

Substitution and transposition

00:18

Problem 1

Given that
$$
c=\sqrt{a^{2}+b^{2}}
$$
evaluate $c$ for $a=24$ and $b=7$.

Amy Jiang
Amy Jiang
Numerade Educator
01:05

Problem 2

$V$, across a resistor $R=1000 \Omega$ is $15 \mathrm{~V}$, then find the current $I$ given that
$$
V=I R .
$$

Varsha Aggarwal
Varsha Aggarwal
Numerade Educator
02:14

Problem 3

¿o [thermodynamics] A gas is expanded from an initial pressure $P_{1}$ and volume $V_{1}$ of $5 \times 10^{6} \mathrm{~N} / \mathrm{m}^{2}$ and $2 \times 10^{-4} \mathrm{~m}^{3}$respectively, to a final pressure $P_{2}=2 \times 10^{7} \mathrm{~N} / \mathrm{m}^{2}$. Find the new volume $V_{2}$ given that $P_{1} V_{1}=P_{2} V_{2}$.

Mukesh Devi
Mukesh Devi
Numerade Educator
04:27

Problem 4

[y) [thermodynamics] A gas has pressure $P=5.6 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}$, volume
$V=0.015 \mathrm{~m}^{3}$ and is at a temperature $T=312 \mathrm{~K}$. If there are $n=34.6$ mole of gas, determine the mass, $m$, given that
$$
P V=n m R T
$$
where $R=8.31 \mathrm{~J} /(\mathrm{K}$ mole $)(R$ is called the universal or molar gas constant).

Timothy James
Timothy James
Numerade Educator
00:39

Problem 5

[mechanics] The distance, s, travelled in time $t$ is related by
$$
s=u t+\frac{1}{2} a t^{2}
$$
where $u$ is the initial velocity and $a$ is constant acceleration. Determine $a$, given that $s=30 \mathrm{~m}, u=2 \mathrm{~m} / \mathrm{s}$ and $t=5 \mathrm{~s}$

Lucas Finney
Lucas Finney
Numerade Educator
01:40

Problem 6

$\mathrm{~ F _ {}$ $R$, of a wire at $t^{\circ} \mathrm{C}$ is given by
$$
R=R_{0}(1+\alpha t)
$$
where $R_{0}$ is the resistance at $0^{\circ} \mathrm{C}$ and $\alpha$ is the temperature coefficient of resistance. Determine $\alpha$, given that $R_{0}=33 \Omega$, $R=35 \Omega$ and $t=89^{\circ} \mathrm{C}$. (The units of $\alpha$ are $/{ }^{\circ} \mathrm{C}$.)

Narayan Hari
Narayan Hari
Numerade Educator
02:02

Problem 7

with e.m.f. $E=12 \mathrm{~V}$ and an internal resistance $r=1 \Omega$ is connected across a resistor $R=20 \Omega$. Find the voltage $V$ across $R$, given that
$$
E=\frac{V(R+r)}{R}
$$

Mayukh Banik
Mayukh Banik
Numerade Educator
00:58

Problem 8

[mechanics] The velocity, $v$, of an object is given by
$$
v=u+a t
$$

Maya Mysore
Maya Mysore
Numerade Educator
00:49

Problem 9

states that
$$
I=\frac{V}{R}
$$
where $I$ is current, $V$ is voltage and $R$ is resistance. Transpose to make $R$ the subject of the formula.

Amy Jiang
Amy Jiang
Numerade Educator
02:37

Problem 10

¿? [thermodynamics] The characteristic equation of a perfect gas is given by
$P V=m R T$
$(P=$ pressure, $V=$ volume,
$R=$ gas constant, $m=$ mass and
$T=$ temperature). Make $T$ the subject.

Adrian Co
Adrian Co
Numerade Educator
07:11

Problem 11

[ [mechanics] The slip, $S(\%)$, of a vehicle is given by
$$
S=\left(1-\frac{r \omega}{v}\right) \times 100
$$
where $r=$ radius of tyre,
$\omega=$ angular velocity and $v=$ velocity.
Make $\omega$ the subject of the formula.

Joseph Fritchman
Joseph Fritchman
Numerade Educator