Solve for the tension in a rope pulling a box

In summary, the conversation discusses a problem involving a worker pulling a 90-kg box across a level floor using a rope at a 35° angle. The tension in the rope is gradually increased until the box just starts to move. The problem involves calculating the tension in the rope, given the coefficients of kinetic and static friction. The individual provides their attempted solution, but realizes their mistake in switching the sign from + to - in the denominator and is able to correct it.
  • #1
y90x
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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
 
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  • #2
y90x said:
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.
 
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  • #3
Delta² said:
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 !
 
  • #4
y90x said:

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.
 

FAQ: Solve for the tension in a rope pulling a box

1. How do you calculate the tension in a rope pulling a box?

The tension in a rope pulling a box can be calculated using the formula T = mg + ma, where T is the tension, m is the mass of the box, g is the acceleration due to gravity, and a is the acceleration of the box.

2. What factors affect the tension in a rope pulling a box?

The tension in a rope pulling a box is affected by the mass of the box, the acceleration of the box, and the angle of the rope with respect to the horizontal. Other factors such as the friction between the box and the surface it is on may also affect the tension.

3. How does the angle of the rope affect the tension in a rope pulling a box?

The tension in a rope pulling a box will increase as the angle between the rope and the horizontal decreases. This is because a smaller angle means a larger vertical component of the tension, which is responsible for lifting the box.

4. Can the tension in a rope pulling a box ever be greater than the weight of the box?

Yes, the tension in a rope can be greater than the weight of the box if the box is accelerating. This is because the tension must be large enough to overcome the force of gravity and also provide the necessary force to accelerate the box.

5. How does the surface the box is on affect the tension in a rope pulling a box?

The surface the box is on can affect the tension in a rope pulling a box by introducing friction. If the surface has a high coefficient of friction, the tension in the rope will need to be greater to overcome the friction and move the box. This can also affect the acceleration of the box and therefore the tension in the rope.

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