Chapter 6, Problem 87CR

To determine

To calculate:

The work done in the lifting the car up to $5in$ by crane

Answer to Problem 87CR

The work done in the lifting the car up to $5in$ by crane is $72000lb\cdot ft$

Explanation of Solution

Given information:

  $\begin{array}{l}w=18000lb\\ x=48in\end{array}$

Formula used:

The work done by the force $F$ on an object in the displacement $x$ is given as:

  $W=F\cdot x\cos \theta$

Calculation:

Since the force $F$ and displacement $x$ are parallel, $\cos \theta =1$

So, the work done by the force $F$ on an object in the displacement $x$ is calculated as:

  $\begin{array}{l}W=F\cdot x\cos \theta \\ W=F\cdot x\end{array}$

Now, the magnitude of the force is same as the weight of car:

  $\begin{array}{l}\Vert F\Vert =w=18000lb\\ \Vert x\Vert =48in=48\times 0.833=4ft\end{array}$

Therefore, work done in the lifting the car up to $5in$ by crane is calculated as:

  $\begin{array}{l}W=\Vert F\Vert \Vert x\Vert \\ W=\left(18000\right)\left(4\right)\\ W=72000lb\cdot ft\end{array}$