Chapter 6, Problem 8RAT

In an ideal pulley system, a woman lifts a $100\text{-N}$crate by pulling a rope downward with a force of $25\text{N}$. For every $1\text{-meter}$ length of rope she pulls downward, the crate rises

(a) $50\text{centimeters}$.

(b) $45\text{centimeters}$.

(c) $25\text{centimeters}$

(d) none of these.

To determine

The correct option for the statement “In an ideal pulley system, a woman lifts a $100\text{-N}$ crate by pulling a rope downward with a force of $25\text{N}$. For every $1\text{-meter}$ length of rope she pulls downward, the crate rises”.

Answer to Problem 8RAT

The correct option for the statement “In an ideal pulley system, a woman lifts a $100\text{-N}$ crate by pulling a rope downward with a force of $25\text{N}$. For every $1\text{-meter}$ length of rope she pulls downward, the crate rises” is option (c).

Explanation of Solution

Given info: The downward force applied on pulley is $100\text{N}$, the force applied on crate $25\text{N}$ and the length of the rope is $1\text{m}$.

When he/she do work by pushing one end of the lever down, work is done at other end.

Write the expression for the input work done.

$W=F_1{d}_1$

Here,

$F_1$ is the downward force applied on pulley

$d_1$ is the length of the rope

Write the expression for the input work done.

$W=F_2{d}_2$

Here,

$F_2$ is the force applied on crate

$d_2$ is the vertical distance of the crate rises

Equating the above two equations.

$\begin{array}{c}{F}_1{d}_1=F_2{d}_2\\ d_2=\frac{F_1{d}_1}{F_2}\end{array}$

Substitute $25\text{N}$ for $F_1$, $1\text{m}$ for $d_1$ and $100\text{N}$ for $F_2$ in the above equation to get $d_2$.

$\begin{array}{l}{d}_2=\frac{25\text{N}\times 1\text{m}\times \left(\frac{100\text{cm}}{1\text{m}}\right)}{100\text{N}}\\ d_2=25\text{cm}\end{array}$

Conclusion:

Therefore, the correct option for the statement “In an ideal pulley system, a woman lifts a $100\text{-N}$ crate by pulling a rope downward with a force of $25\text{N}$. For every $1\text{-meter}$ length of rope she pulls downward, the crate rises” is option (c).