Question

A woman living in a third-story apartment is moving out. Rather than carrying everything down the stairs, she decides to pack her belongings into crates, attach a frictionless pulley to her balcony railing, and lower the crates by rope. How hard must she pull on the horizontal end of the rope to lower a $25kg$crate at steady speed?

Short answer

The horizontal force is$242.25N$

Step-by-step solution

Given information

Mass of the crate attached to a frictionless pulley, $m=25kg$

The crater is moving at a steady speed.

Explanation

The horizontal force on the rope will balance the weight of the crate and will not allow it to fall with acceleration , so it will fall with uniform velocity if horizontal force becomes equal to weight of crate.

$$\begin{gathered} F=mg \\ m=25kg \\ g=9.81m/s^2 \\ F=\left(25kg\right)\left(9.81m/s^2\right) \\ =245.25N \end{gathered}$$

The horizontal force is $245.25N$