Question

Marisol pushes a $3.0\text{kg}$ box $7.0\text{m}$ across the floor with a force of $12\text{N}$.

She lifts the box to a shelf $1\text{m}$ above the ground.

How much work does Marisol do on the box?

Answer 1

Step-1: Calculate work done by Marisol to push the box $\left(W_1\right)$.

The formula for work done is $W=F\times d$.

Here, W is work done, $F$ is the force applied and d is displacement.

We have $F=12\text{N}$ and $d=7\text{m}$:

$\begin{array}{rcl}{W}_1& =& 12\times 7\\ & =& 84\text{J}\end{array}$

Step-2: Calculate work done by Marisol to lift the box $\left(W_2\right)$.

Marisol lifts the box to a shelf $1\text{m}$ above the ground. So, $d=1\text{m}$

Calculate force: $F=m\times g$

Here, $m$ is the mass of the box and $g$ is gravity and substitute $m=3\text{kg}$ and $g=9.8\frac{N}{\mathrm{kg}}$:

$\begin{array}{rcl}F& =& 3\times 9.8\\ & =& 29.4\text{N}\end{array}$

And,

$\begin{array}{rcl}{W}_2& =& 29.4\times 1\\ & =& 29.4\text{J}\end{array}$

Step-3: Calculate the total work done by Marisol on the box.

The total work done by Marisol is the sum of work to push the box and work done to lift it:

$\begin{array}{rcl}W& =& W_1+W_2\\ & \Rightarrow & =84+29.4\\ & \Rightarrow & =113.4\text{J}\end{array}$

Hence, the total work done by Marisol on the box is $\mathbf{113}\mathbf{.}\mathbf{4}\mathbf{}\mathbf{\text{J}}$.