# How much work does it take to lift a 180 kg  weight 3/2 m ?

May 1, 2018

$2646$ joules

#### Explanation:

Since the work done here is raising the weight, then the total work done will be the gain of gravitational potential energy of the box.

Gravitational potential energy is given by the equation,

$\text{GPE} = m g h$

• $m$ is the mass of the object in kilograms

• $g$ is the gravitational acceleration, which is around $9.8 \setminus {\text{m/s}}^{2}$

• $h$ is the height in meters

And so, we get:

$\text{GPE"=180 \ "kg"*9.8 \ "m/s"^2*1.5 \ "m}$

$= 2646 \setminus \text{J}$

May 1, 2018

$2646 J$

#### Explanation:

work = force times distance.
First, to overcome the gravitational pull on the weight, you need to exert a force upwards on it that is equivalent to the gravitational force:

$180 k g \times 9.8 \frac{m}{s} ^ 2$

$= 1764 k g \frac{m}{s} ^ 2$

$= 1764 N$

now the weight does not move, but there's a net force of 0 on it. It is neither going up or down.

Then you move it up through a course of $\frac{3}{2} m$:

$1764 N \times \frac{3}{2} m$

$= 2646 N \cdot m$

$= 2646 J$

$J$ (joules) is the unit for work. 2646 is how much work is done to lift the weight by $\frac{3}{2} m$.

You can also think of it this way: Energy is a conserved quantity, which means that it is neither destroyed nor created. Thus it can only be transferred from one form to another. Work is the measure of how much energy is transferred from one form to another.

In this case as the weight is being lifted, the kinetic energy it gained from the force you exert on it, is converted to its gravitational potential energy. When it is at $\frac{3}{2} m$ above the ground, it has a gravitational potential energy of $180 k g \times 9.8 \frac{m}{s} ^ 2 \times \frac{3}{2} m = 2646 J$
So its gravitational potential energy went from 0 at ground level to $2646 N$at $\frac{3}{2} m$.

In conclusion, $2646 J$ of work is done on the $180 k g$ weight as you lift it $\frac{3}{2} m$ above ground.
:)