Question

a boy of mass 40 kg runs up flight of 50 steps each 10cm high in 5 second. find 1) the work done by the body 2) the power developed (g=9.8m*-2

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Answer 1

Given :

• Mass of the boy = 40 kg
• Number of steps = 50
• Height of each step = 10 cm
• Time = 5 second

To Find :

• The work done and power developed

Solution :

Height of each step = 10 cm = 0.1 m

Total height climbed by the body = 50 × 0.1 m = 5 m

Work done by the body is given by ,

$\\ \star \: {\boxed{\purple{\sf{Work \: done = mgh}}}}$

Here ,

• m is mass of the body
• h is height
• g is acceleration due to gravity

We have ,

• m = 40 kg
• h = 5 m
• g = 9.8 m/s²

Substituting the values we have in the formula ,

$\\ : \implies \sf \: W= (40)(9.8)(5)$

$\\ : \implies\underline{\boxed{\pink {\mathfrak{W = 1960 \: J}}}} \: \bigstar$

Power is calculated by ,

$\\ \star \: {\boxed{\purple{\sf{Power = \frac{Work \: done}{Time} }}}}$

Substituting the values we have in the formula ,

$\\ : \implies \sf \: P= \frac{1960}{5}$

$\\ : \implies{\underline{\boxed{\pink {\mathfrak{P= 392 \: W}}}}} \: \bigstar$

Hence ,

• The work done and power developed in given case are 1960 J and 392 W

Answer 2

Given :-

Mass of body = 40 kg

Number of steps = 50

Height of each step = 10 cm

Time = 5 second

To Find :-

Work done

Power

Solution :-

Firstly we will find work done

$\fbox{W = mgh}$

Here,

W is the Work

M is the Mass

G is the Gravity

H is the Height

Total height = Numer of step × Height of one 1 step

Total height = 50 × 10

Total height = 500 cm [Here we will write as 5 m]

$\tt \: W = 40 \times 9.8 \times 5$

$\tt \: W = 200 \times 9.8$

$\tt \: W = 1960 \: J$

Hence :-

Work Done is 1960 Joule

Now,

Let's find Power

As we know that

$\rm{P = \dfrac WT }$

Here,

P is the power

W is the Work Done

T is the Time

$\tt \: P = \cancel\dfrac{1960}{5}$

$\frak \red{P = 392 \: watt}$