Physics

Power, Energy, and Efficiency

463 Questions

Power, energy, and efficiency are fundamental physics concepts that quantify work and the rate of doing work. Questions cover electrical energy consumption in kilowatt hours, the efficiency of thermodynamic cycles like the Brayton cycle, and mechanical power lifting loads. This topic is essential for general science and engineering exam preparation.

Electrical energy consumptionBrayton cycle efficiencyPower calculation formulasCommercial electricity unitsHydraulic lift mechanics

Power, Energy, and Efficiency Questions

Multiple choice power work and power work, energy and power physics energy and its forms

A heating unit on an electric stove is rated at $880  W$. It is connected to a power supply of $220  V$. The current it will consume is

  1. 2 amp

  2. 4 amp

  3. 6 amp

  4. 8 amp
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Power $= V \times I$
or, $880 = 220 \times I$
or, $I = \displaystyle\frac{880}{220} = 4  amp$.

Multiple choice power work and power work, energy and power physics energy and its forms

A body of mass $10kg$ is moving along positive $x-$axis with $5\ m/s$ at $t=0$ and is moving along negative $x-$axis with same speed at $t=10\ s$. Average power of the force acting on the body is:

  1. $Zero$
  2. $25\ W$
  3. $50\ W$
  4. $100\ W$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

since there is no acceleration 

there is no power
P=0

Multiple choice power work and power work, energy and power physics energy and its forms

A weight lifter lifts $300\ kg$ from the ground to a height of $2$ meter in $3$ seconds. The average power generated by him is:-

  1. $5880\ watt$
  2. $4410\ watt$
  3. $2205\ watt$
  4. $1960\ watt$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Work = m * g * h = 300 * 9.8 * 2 = 5880 J. Power = Work / time = 5880 / 3 = 1960 W.

Multiple choice power work and power work, energy and power physics energy and its forms

An engine of ine metric ton is going up an inclined plane, 1 in 2 at the rate of 36 kmph. If the coefficient of friction is $1/ \sqrt{3}$, the power of engine is 

  1. 9.8W

  2. 98W

  3. 980W

  4. 98kW
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Force required = mg * sin(theta) + mu * mg * cos(theta). Slope 1 in 2 means sin(theta) = 0.5, cos(theta) = sqrt(3)/2. Force = 1000 * 9.8 * (0.5 + (1/sqrt(3)) * (sqrt(3)/2)) = 1000 * 9.8 * (0.5 + 0.5) = 9800 N. Velocity = 36 kmph = 10 m/s. Power = F * v = 9800 * 10 = 98000 W = 98 kW.

Multiple choice power work and power work, energy and power physics energy and its forms

The power of water pump is The power of water pump is  $4kW.$  If  $\left( g=10{ m }{ { s }^{ -2 } } \right) ,$  the amount of water it can raise in $1$ minute to a height of $20 m$  is then

  1. $100$ litre
  2. $1000$ litre
  3. $1200$ litre
  4. $2000$ litre
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given that,

Power, $P=4\,kW=4000\,W$

Height, $h=20\,m$

Time, $t=60\,\sec $

$ power=\dfrac{work}{time} $

$ 4000=\dfrac{mgh}{t} $

$ 4000=\dfrac{m\times 10\times 20}{60} $

$ m=1200\,Kg $

The pump can raise 1200 litre in one minute

Multiple choice power work and power work, energy and power physics energy and its forms

An object of mass accelerates uniformly from rest to a speed $v _f$ in time $t _f$ Then the instantaneous power delivered to the object,as a function of time $t$ is -

  1. $mt\left(\dfrac{{v _f}^2}{t _f}\right)$
  2. $mt\dfrac{v _f}{t _f}$
  3. $\dfrac{1}{2}mt^2\left(\dfrac{v _f}{t _f}\right)^2$
  4. $\dfrac{1}{2}mt^2\left(\dfrac{v _f}{t _f}\right)$
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice power work and power work, energy and power physics energy and its forms

A force applied by the engine of a train of mass 2.05 x $10^{6} kg$ changes its velocity from 5 $ms^{-1}$ to 25  $ms^{-1}$ in 5 minutes. The power of the engine is then

  1. 1.025 MW

  2. 2.05 MW

  3. 5 MW

  4. 6 MW
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given that,

Mass of train, $m=2.05\times {{10}^{6}}\,Kg$

Time, $t=5\,\min utes=300\,s$

$ v=25\,m/s $

$ u=5\,m/s $

Acceleration,

$ a=\dfrac{v-u}{t} $

$ a=\dfrac{25-5}{300} $

$ a=\dfrac{2}{30}=\dfrac{1}{15}\,m/{{s}^{2}} $

Using equation of motion,

$ {{v}^{2}}-{{u}^{2}}=2as $

$ {{(25)}^{2}}-{{(5)}^{2}}=2\times \dfrac{1}{15}\times s $

$ s=4500\,m $

Power,

$ P=\dfrac{work\,\,done}{time} $

$ P=\dfrac{F\times d}{t} $

$ P=\dfrac{m\times a\times s}{t} $

$ P=\dfrac{2.05\times {{10}^{6}}\times 1\times 4500}{15\times 300} $

$ P=2.05\times {{10}^{6}}\,W $

$ P=2.05\,MW $

Multiple choice power work and power work, energy and power physics energy and its forms

A motor lifts $100 kg$ of water in $2 min$ from a well of $60m$ depth then the electric power of the motor is$(Taken g=10 m/s^2)$

  1. $1000 W$
  2. $750 W$
  3. $1200 W$
  4. $500W$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A motor lifts $=100kg$ of water

Time $=2min=2\times60=120s$
Depth$=60m$ depth then,
electric power of the motor$=?$
Taking $=10m/s^2$
$P=Power=\cfrac{mgh}{t}\ \quad=\cfrac{100\times10\times60}{120}\ \quad=500W$

Multiple choice power work and power work, energy and power physics energy and its forms

A force $'F'$ accelerates a block of mass $'m'$ along a straight line to velocity $'v'$ from rest and displace it through a distance $'s'$. What is the average power developed?

  1. $\dfrac {v^{2}}{2F}$
  2. $Fv$
  3. $\dfrac {mv^{2}}{2s}$
  4. $\dfrac {Fv}{2}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For constant acceleration starting from rest, v_avg = v / 2. Average Power = F * v_avg = F * (v / 2).

Multiple choice power work and power work, energy and power physics energy and its forms

A block of mass $1$ $kg$ starts moving with constant acceleration $\displaystyle a= 4m/s^{2}.$. Find the average power of the net force in a time interval from $t=0$ to $t=2s$.

  1. $16 W$
  2. $1.6 W$
  3. $15 W$
  4. $1.5 W$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Velocity of an object after time $t$ is given by $v=at$
Average power from time $t _1$ to $t _2$

$=\dfrac{\int _{t _1}^{t _2}Fvdt}{\int _{t _1}^{t _2}dt}$

$=\dfrac{\int _0^t(ma)(at)dt}{\int _0^tdt}$

$=ma^2\dfrac{t}{2}$

$=1\times 4^2\times\dfrac{2}{2}W$

$=16W$
Multiple choice power work and power work, energy and power physics energy and its forms

Your uncle pushes a $60.0 kg$ crate along a floor with average speed $v=0.65 {m}/{s}$ for $5.0$ seconds as he moves furniture to clean up the garage.
If the coefficient of friction between the floor and the crate is $\mu=0.340$, what is the average power output of your uncle during this time?

  1. $26.0 W$
  2. $130 W$
  3. $383 W$
  4. $650 W$

  5. None of the above
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given :  $\mu = 0.340$             $v = 0.65$  m/s                $m =60.0$  kg

As the crate moves with constant speed, thus the force applied by uncles must be equal to the frictional force.
$\therefore$   $F  = \mu mg = 0.340 \times 60.0 \times 9.8  = 199.92$  N
Average power output        $P = F v = 199.92 \times 0.65  \approx 130$  W

Multiple choice power work and power work, energy and power physics energy and its forms

Find the power of a pump which takes $10 s$ to draw $100 kg$ of water from a tank situated at a height of $20 m$.

  1. $2\times { 10 }^{ 4 }W$
  2. $2\times { 10 }^{ 3 }W$
  3. $200 W$
  4. $1 kW$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Power = $\dfrac{work done}{time}$


             =  $\dfrac{mgh}{time}$

            =  $\dfrac{100 \ast 10 \ast 20}{10}$

             =  $\dfrac{20000}{10}$

               = 2000W  i.e  2 $\times$ 10$^{3}$W

Multiple choice power work and power work, energy and power physics energy and its forms

A $40 N$ force accelerates a $20 kg$ mass through a distance of $16 m$. If there were no other forces acting on the mass and the mass started at rest, what was the average power output of the force?

  1. $0 W$
  2. $160 W$
  3. $226 W$
  4. $640 W$

  5. Cannot be determined from the information given
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given :  $F = 40$ N            $m = 20$ kg              $S = 16$ m               $u = 0$ m/s

Thus acceleration of the mass        $a = \dfrac{F}{m} = \dfrac{40}{20} =2$  $m/s^2$
Using    $S = ut + \dfrac{1}{2}at^2$
$\therefore$  $16 = 0 + \dfrac{1}{2} \times 2 t^2$                      $\implies t = 4$ s
Work done by the force     $W = FS = 40 \times 16  =640$ J
$\therefore$ Power output        $P = \dfrac{W}{t} = \dfrac{640}{4} = 160$  W