Calculating Tension for a Box on a Horizontal Surface with Friction

[fixedglare]

Homework Statement

Due to friction, a force of 400 N is required to pull a wooden box on the floor. The cord used to pull the box makes an angle of 56° horizontally.

How much tension should be on the cord to be able to pull the box?

Homework Equations

W = Fd * (cosθ)

Tension = Weight +/- Mass * Acceleration ? (found this one online, but was never taught this) or Ft=m(a+g) (never taught this one either just found it online)

The Attempt at a Solution

I read that to find/calculate tension you should use the second formula but I'm not sure.

Should I convert the Force to mass and then multiply 9.81 m/s₂?

 

[fixedglare]

On my book the answer says it should be 715 N, I divided the Force by the angle & got that answer but everywhere I search it says to use sin & other kinds of formulas I'm confused.

Then the second question asks how much work is done if the box is moved 25 m?
In my book the answer is supposed to be 10000 but when I use W= fd* cos θ, it gives me a different answer

 

[fixedglare]

I'm very confused because the exercises in my book are under the section of using the angle to find work but when I used the basic W= Fd formula I got the answer in the book.

How do I know when to use the angle formula to find work and the basic formula?

 

[jackarms]

To start, what do you mean you divided the force by the angle? Do you mean by the cosine of the angle?

And for the second part, what work is it asking you to find? Work from friction for tension? Show all of your calculations, and that should help me understand your questions better.

 

[fixedglare]

Yes by the cosine angle, that's the only way I found the tension.

It doesn't specify, that's why I'm confused as to what formula to use and when, because the equation gave me the angle so I thought to use the angle but when I did, the book said it wasn't the right answer so then I used to basic formula & that's how I got it.

The second question just asks, how much work is realized, if the box is moved in a distance of 25.0 m?

 

[jackarms]

Okay, I'm assuming it means how much work is done by the tension, since no net work is done on the box (work-kinetic energy theorem). Please show your calculations for the work. What values are you using to arrive at the answer in the book?

 

[fixedglare]

To get the answer from the book I used the formula W= Fd;

so 400 N * 25.0 m = 1000 J, which is the answer in my book.

 

[jackarms]

The problem is you're using the force from friction, and the work it's asking for is tension. You can get away with it here since the two works are equal, but the reasoning is incorrect. If the works weren't equal, this wouldn't work. You have to use the magnitude of the tension force in addition to the angle the force makes with the horizontal displacement.

 

[Chestermiller]

Fixedglare: Did you draw a free body diagram before you started to try to work this problem? If so, on the free body diagram, did you identify all the components of the horizontal and vertical forces acting on the box? This should have automatically cleared up many of the difficulties you have had with this problem. If you drew a FBD, please upload it so we can see it.

Chet

 

[PhanthomJay]

Due to friction, a force of 400 N is required to pull a wooden box on the floor

what a poor statement, are you sure the problem is worded this way? It means to say apparently that when you pull on the cord directed 56 degrees above the horizontal with a certain force, then it moves at constant velocity. The friction force on the box from the floor is 400 N. What is the value of the pulling force, and how much work does it do? Or something like that.