Question

A crate of weight $w$ is dragged across the floor from $A$ to $B$ by a constant vertical force $F$ acting at the end of the rope. Assuming that the crate does not lift off. The work done on the crate by the force $F$ is:

• A. $2Fh[1-\frac{1}{\sqrt{3}}]$
• B. $2Fh[1-\frac{2}{\sqrt{3}}]$
• C. $Fh[1-\frac{1}{\sqrt{3}}]$
• D. $Fh[1-\frac{2}{\sqrt{3}}]$

Answer 1

The correct option is A $2Fh[1-\frac{1}{\sqrt{3}}]$

As per the given details, we can take A block of weight is W.

It is dragged across the horizontal from A to B by constant vertical force P acting at end of the rope.

The value of P is $(\sqrt{3}+1).$ The calculation of force is calculated below.

The height of pulley from ground is $h=\sqrt{3}.$

When it comes to W, it is $\int Fdx$

$\int Fdx=2Fh(1-\frac{1}{\sqrt{3}})$