Question

How much work does it take to lift a $90kg$ weight through ${\displaystyle \frac{3}{2}}m$?

Answer 1

Hint: Recall that the work done in lifting an object is essentially equivalent to the constant gravitational force acting on the object as it is lifted through a given height. First determine the gravitational force causing an acceleration of the object against gravity, and to this end, determine the work done in lifting the object through the given height by overcoming the gravitational force. Assume that the force applied on the object will be constant throughout.
Formula Used:
Work done $W=F\times s$

Complete answer:
We know that the work done in lifting an object up to a height is against the gravitational force acting on the object, and is hence proportional to the acceleration of the object due to gravity in the opposite direction.
Now, when the object is lifted, a certain amount of force is exerted on it in order to lift it against gravity. This force will be equivalent to the gravitational force acting on the object, i.e.,
$F=mg$, where m is the mass of the object and g is the acceleration due to gravity.
 In any case, we assume that a constant force is applied on the object in lifting it up.
Now, if the object is lifted up through a height, say h, then the work done against gravity in lifting this object up to that height will be:
$W=F\times h=mgh$
 We are given that the object has a mass of $m=90kg$ and is lifted through a height of $h={\displaystyle \frac{3}{2}}=1.5m$.
Taking acceleration due to gravity as $g=9.8m{s}^{-2}$ on the surface of the earth, the amount of work needed to lift it through the height will be:
$W=mgh=90\times 9.8\times 1.5=1323J$
Therefore, it takes $1323J$ of work to lift a $90kg$ weight through ${\displaystyle \frac{3}{2}}m$.

Note:
Remember that in classical physics, mass of a body can never be zero. However, the weight of a body can be zero where there is no gravity. The weight of the body thus depends on the gravitational force, or the acceleration due to gravity acting on it.
Note that the SI unit of mass is Kilogram (kg), whereas the SI unit of weight is newton (N). However, sometimes, kilogram is interchangeably used to denote both mass and weight, so it is important to read the question carefully for further clarity.