- #1

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- 125

**[SOLVED] find the magnitude of a force**

## Homework Statement

A window washer pushes his scrub brush up a vertical window at constant speed by applying a force [tex]\vec{F}[/tex] as shown in the figure. The brush weighs 12.1 N and the coefficient of kinetic friction is 0.110.

## Homework Equations

1. [tex]\Sigma[/tex][tex]\vec{F}[/tex] = m[tex]\vec{a}[/tex]

2. [tex]\Sigma[/tex][tex]\vec{Fx}[/tex] = max

3. [tex]\Sigma[/tex][tex]\vec{Fy}[/tex] = may

4. fk = [tex]\mu[/tex]kn

5. [tex]\vec{F}[/tex] = [tex]\sqrt{Fx^2+Fy^2}[/tex]

## The Attempt at a Solution

[tex]\Sigma[/tex]Fx = -Fcos53.1 + fk = 0

[tex]\Sigma[/tex]Fy = N + Fsin53.1 - w = 0

Fcos53.1 = fk

--> Fcos53.1 = [tex]\mu[/tex]kn

N = w-Fsin53.1

---> Fcos53.1 = [tex]\mu[/tex]k(w-Fsin53.1)

--> Fcos53.1 = [tex]\mu[/tex]kw-[tex]\mu[/tex]kFsin53.1

--> Fcos53.1 + [tex]\mu[/tex]kFsin53.1 = [tex]\mu[/tex]kw

--> F(cos53.1 + [tex]\mu[/tex]ksin53.1) = [tex]\mu[/tex]kw

--> F = [tex]\mu[/tex]kw / (cos53.1 + [tex]\mu[/tex]ksin53.1)

--> N = Fcos53.1/[tex]\mu[/tex]k

my answer was F = 1.9N, which was wrong and I was so sure I did everything right.

if anybody can offer any help it would be greatly appreciated.