Question

A man whose mass is 70kg climbs from a hill station A to another hill station B the height of hill station A 1000m above the sea level and that of B is 1800m above the sea level calculate the work done in going from B

Answer 1

Answer

• Work done is 1190000 J

Explanation

Given

• Mass of a man is 70 kg
• He is moving from one hill to another
• Height of hill 1 is 1000 m and another is 1800 m high

To Find

• The work done?

Solution

[So first we shall find the potential energy of the man at these two places and then their differce will be the work done]

✭ Case 1

➝ Pe = mgh

• m = Mass = 70 kg
• g = Gravitational Acceleration = 10 m/s²
• h = Height = 1000 m

Substituting the values,

➝ Pe = 70 × 10 × 1000

➝ Pe = 700000 J

✭ Case 2

➝ Pe = mgh

• m = Mass = 70 kg
• g = Gravitational Acceleration = 10 m/s²
• h = Height = 1800 m

Substituting the values,

➝ Pe = 70 × 10 × 1800

➝ Pe = 1260000 J

✭ Work Done

➝ Work done = Kinetic Energy in case 2 - Kinetic Energy in case 1

➝ Work done = 1260000 - 700000

➝ Work done = 1190000 J

Answer 2

Given:

★ Mass of man, m = 70kg

★ Height of Hill Station A, h = 1000m

★ Height of Hill Station B, h = 1800m

Find:

✶ Amount of Work Done

Solution:

Here,

we, know that

$\underline{\boxed{\sf K.E._{A} = mgh}}$

where,

• m = 70kg
• g = 10m/s²
• h = 1000m

So,

➠$\sf K.E._{A}$ = mgh

➠$\sf K.E._{A}$ = 70×10×1000

➠$\sf K.E._{A}$ = 700000J

$\qquad\quad$ __________________

Here, again using

$\underline{\boxed{\sf K.E._{B} = mgh}}$

where,

• m = 70kg
• g = 10m/s²
• h = 1800m

So,

➺ $\sf K.E._{B}$ = mgh

➺ $\sf K.E._{B}$ = 70×10×1800

➺ $\sf K.E._{B}$ = 1260000J

$\qquad\quad$ ____________________

we, know that

$\underline{\boxed{ \sf Work \: Done = change \: in \: kinetic \: energy}}$

$\sf :\to Work \: Done = K.E._{B} - K.E._{A}$

where,

• $\sf K.E._{B}$ = 700000J
• $\sf K.E._{A}$ = 1260000J

So,

▶Work Done = $\sf K.E._{B} - K.E._{A}$

▶Work Done = 1260000 - 700000

▶Work Done = 560000J

$\qquad\quad$ ____________________

Hence, Work done = 560000J