Question

The force F​ (in pounds) required to push a sofa across a floor varies directly as the weight w​ (in pounds) of the sofa.

a. A person can push a 120​-pound sofa across a wood floor by pushing with a force of 50 pounds. Find an equation that describes the relationship between w and F.
What does F =

Answer 1

Answer:
`F=0.41w`

Explanation:

1. You know that the force F varies directly as the weight w of the sofa. Then, you can write the following expression:

`F=kw`

Where k is the constant of proportionality.

2. You know that a person can push a 120​ pound sofa with a force of 50 pounds, then you can calcualte the constant of proportionality as following:

`k=(F)/(w)=(50lb)/(120lb)=0.41`

3. Then, the equation is:

`F=0.41w`