Question

Amit carried a box up the flight of the stairs as shown in the diagram. He did 150J of work in this process. The mass of the box is……

Answer 1

Hint: An object is moved to some distance, then displacement comes into action. Displacement is the overall change in the position of the object. It is a vector quantity. Work done is a product of force and displacement and the acceleration is the acceleration due to gravity.

Formula used:
Force applied in the object, \[F=\text{ }m\times a\]
\[Work\text{ }done\text{ }=\text{ }F\times S\]
Where F is force applied, S= displacement.

Complete step-by-step answer:
Now, Displacement is different from the distance, as the displacement is vector quantity as it has both magnitude and direction whereas distance has magnitude only so it is scalar quantity.
Also, Force is applied to move an object from one place to another and is given by:
\[F=\text{ }m\times a\]
Then, work done on displacing the object is given by:
\[Work\text{ }done\text{ }=\text{ }F\times S\]
\[\begin{align}
  & Now\text{ }F=mg\text{ }\left( acceleration\text{ }due\text{ }to\text{ }gravity \right) \\
 & F=\text{ }m\times 10 \\
\end{align}\]- (1)
Now, for each block of stairs 20cm length is given. So for lifting up all the stairs we have 5 blocks i.e. 5×20cm=100cm
\[\begin{array}{*{35}{l}}
   i.e.\text{ }5\times 20cm=100cm \\
   i.e.\text{ }S=\text{ }100cm=\text{ }1\text{ }meter. \\
   W=\text{ }m\times 10\times S \\
   150J=\text{ }m\times 10\times 1~ \\
   150/10=m \\
\end{array}\]
Hence, the mass of the box comes out to be 15Kg.

Note: When we move a body from one place to another displacement takes place. A force is applied to move the object from one place to another. By using formulas for force and work done in displacing a body to another place we can solve mass of the object.