Solve for the tension in a rope pulling a box

[y90x]

Homework Statement

A worker is going to attempt to pull a 90-kg box across a level floor by a rope that makes an angle of 35° with the floor. The tension in the rope is gradually increased until the box just starts to move. If the coefficient of kinetic friction is 0.36 and the coefficient of static friction is 0.41 How much tension is in the rope when the block just starts to move?

Homework Equations

I’m guessing F=ma

The Attempt at a Solution

This is my work , however I thought I was doing it right but when I input in calculator I get the wrong answer. What am I doing wrong ?

U= mew (I believe that’s how it’s spelled)

Us(mg-Tsin(pheta))=Tcos(pheta)
Us(mg) - Us(Tsin(pheta))=Tcos(pheta)
Us(mg)=Tcos(pheta) + UsTsin(pheta)
T=(Us(mg))/(cos(pheta)-Ussin(pheta))
T=(0.41•90•9.8)/(cos35-0.41sin35)
T=619.2 N

The answer should be 343 Nhttps://www.physicsforums.com/attachments/215558

 

[Delta2]

Us(mg)=Tcos(pheta) + UsTsin(pheta)
T=(Us(mg))/(cos(pheta)-Ussin(pheta))<----------
T=(0.41•90•9.8)/(cos35-0.41sin35)
T=619.2 N

The answer should be 343 Nhttps://www.physicsforums.com/attachments/215558

why you switch the sign from + to - in the denominator? if you proceed with .../cos35+0.41sin35... you get the correct answer.

 

[y90x]

why you switch the sign from + to - in the denominator? if you proceed with .../cos35+0.41sin35... you get the correct answer.

I didn’t catch that , thanks !

 

[scottdave]

Homework Statement

A worker is going to attempt to pull a 90-kg box across a level floor by a rope that makes an angle of 35° with the floor. The tension in the rope is gradually increased until the box just starts to move. If the coefficient of kinetic friction is 0.36 and the coefficient of static friction is 0.41 How much tension is in the rope when the block just starts to move?

Homework Equations

I’m guessing F=ma

The Attempt at a Solution

This is my work , however I thought I was doing it right but when I input in calculator I get the wrong answer. What am I doing wrong ?

U= mew (I believe that’s how it’s spelled)

Us(mg-Tsin(pheta))=Tcos(pheta)
Us(mg) - Us(Tsin(pheta))=Tcos(pheta)
Us(mg)=Tcos(pheta) + UsTsin(pheta)
***** T=(Us(mg))/(cos(pheta)-Ussin(pheta)) *******
T=(0.41•90•9.8)/(cos35-0.41sin35)
T=619.2 N

The answer should be 343 Nhttps://www.physicsforums.com/attachments/215558

Your attachment did not allow permission to view.

Now look at the step which I marked with stars. You went from adding Sine, to subtracting Sine. Try fixing that.