Question

Calculate the work done by a man weighing $140kg$ and he is carrying a load of $20kg$ to the top of a ladder which is $16m$ long making an angle of $30{}^\circ $ with the horizontal. Take the acceleration due to gravity as, $g=9.8m{{s}^{-2}}$.

Answer 1

Hint: The total mass of the system can be found by taking the sum of the mass of the man and the load. The work done will be equivalent to the potential energy of the system of masses. The potential energy can be found by taking the product of the mass of the system, acceleration due to gravity and the height of the system. This will help you in answering this question.

Complete step by step answer:
it has been given in the question that the mass of the of man will be,
$M=140kg$
The mass of the load carrying can be written as,
$m=20kg$
The length of the ladder has been mentioned as,
$L=16m$
Angle has been given as,
$\theta =30{}^\circ $
The total mass of the system can be found by taking the sum of the mass of the man and the load. That is,
${{M}_{T}}=140+20=160kg$
As the acceleration due to gravity has been mentioned as,
$g=9.8m{{s}^{-2}}$
Therefore the height of the system will be found by the equation written as,
$h=L\sin 30{}^\circ $
Substituting the values in it will give,
$h=16\times 0.5=8m$
The work done will be equivalent to the potential energy of the system of masses. The potential energy can be found by taking the product of the mass of the system, acceleration due to gravity and the height of the system. This can be written as,
$W=mgh$
Substituting the values in it will give,
$W=160\times 9.8\times 8=1.2544\times {{10}^{4}}J$
Therefore the work done has been calculated.

Note: The work done can be found by taking the product of the force applied and the displacement of the body from its initial position. The work done is equivalent to the variation in energy. It can be expressed in joules.