Question

The Johnsons just received a heavy package (perhaps a treadmill) in the mail that they ordered from a popular online shopping website. It's so heavy that they had to push it across their carpeted floor since it was too heavy to lift. The item weighs 106 kg and it's packaged in cardboard. The coefficient of friction between the cardboard and their carpet is 0.73. They're a team, and they all push the huge package across their living room at a constant speed. How much collective force do they have to use to push the package across the living room at a constant speed of 0.11 m/s?Use the approximation g ≈ 10 m/s2

Answer 1

Given:

The mass of the package is

$m=106\text{ kg}$

The coefficient of friction is

$\mu=0.73$

The constant speed is,

$v=0.11\text{ m/s}$

The acceleration due to gravity is,

$g=10\text{ m/s}^2$

To find:

How much collective force do they have to use to push the package across the living room at a constant speed

Explanation:

The package is moving at a constant speed means the package is under equilibrium of forces. The applied force should be equal to the frictional force on the package.

The frictional force on the package is,

$\begin{gathered} f=\mu mg \\ f=0.73\times106\times10 \\ f=773.8\text{ N} \end{gathered}$

The applied force should be 773.8 N.