(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The object is a box with a given mass m. Our person has the choice between pushing the box with a horizontal force, or pulling the box with a wire with an angle of θ=30^{o}. The magnitude of F_{o}is the force vector he affects the box with in both cases.

Should the box be pushed or pulled in order to achieve the greatest acceleration?

2. Relevant equations

I've made a drawing of each situation adding all the forces acting on the box.

Situation 1

http://myupload.dk/handleupload/c5fd9W9J18EBn

Situation 2

http://myupload.dk/handleupload/4a037-RJ3a5Ha

3. The attempt at a solution

I've been trying to write an equation describing the net-force in both situations. I've here made the assumption that in both cases n and F_{g}cancels each other out.

For situation 1 I get:

F_{net}=F_{o}-f_{f}

I know that there's some sort of friction acting in the opposite direction and that it's given by f_{f}=[itex]\mu[/itex]n

For the force vector F_{o}I can apply newton's 2nd law for the x composant, since the box is not changing direction in the y-axis.

Therefor I get:

F_{net}=ma_{x0}-μn

For situation 2 I get:

F_{net}=F_{o}*sin(θ)-μn

The force vector must be dependent on the magnitude from the forces acting in the direction of x and y. By applying newton's 2nd law again I get:

F_{net}=ma_{o}*sin(θ)-μn

Judging situation 1, by pushing with a horizontal force, the acceleration will be constant. However in situation 2, different angles of pulling will result in different accelerations. I believe that he will then achieve the greatest acceleration by pushing it.

This to me is a difficult one to figure out so I would like some help on what I did wrong, it's important to me to learn.

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# Homework Help: Moving a box with greatest acceleration

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