# B) A pump is to raise 100 litre of water a height of 1.2 m in 10s. Calculate the power required assuming 1 litre of water has a mass of 1 kg?.

\color{red}{117.72\ W

#### Explanation:

Power ($P$) of the pump that lifts $Q = 100$ liters of water (density, $\rho = 1 \setminus \setminus \textrm{k \frac{g}{L} t r}$) at a vertical height $H = 1.2 \setminus m$ in time $t = 10$ sec is given as follows

$P = \frac{\setminus \rho g Q H}{t}$

$= \frac{1 \setminus \cdot 9.81 \setminus \cdot 100 \setminus \cdot 1.2}{10}$

$= 117.72 \setminus W$

Jul 7, 2018

I get $117.6$ watts.

#### Explanation:

The mass of the water here is:

$100 \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{L"*(1 \ "kg")/(color(red)cancelcolor(black)"L")=100 \ "kg}}}}$

The weight of the water is therefore:

100 \ "kg"*9.8 \ "m/s"^2=980 \ "kg m/s"^2=980 \ "N" \ (because 1 \ "N"-=1 \ "kg m/s"^2)

Work done is given by the equation:

$W = F \cdot d$

where:

• $W$ is the work done in joules

• $F$ is the force exerted in newtons

• $d$ is the distance moved in meters

So, we get:

$W = 980 \setminus \text{N"*1.2 \ "m}$

$= 1176 \setminus \text{J}$

Power here is given by the equation:

$P = \frac{W}{t}$

where:

• $P$ is the power in watts

• $W$ is the work done in joules

• $t$ is the time taken in seconds

So, we get:

$P = \left(1176 \setminus \text{J")/(10 \ "s}\right)$

$= 117.6 \setminus \text{W}$