Moving a box with a force that is less than gravity

[kotchenski]

Homework Statement

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.

Is it possible (If you can freely choose a value for θ) to keep the box moving without using a force f_o that is greater than the gravity on the box

Homework Equations

A drawing of the situation:
http://myupload.dk/handleupload/64d68oBb8KHy8

I believe I need an equation that describes the force F_o of θ, which I've found is given as:
$F_o(θ)=\frac{\mu_k mg}{cos(θ)-μ_k sin(θ)}$

The Attempt at a Solution

I could choose to solve F'_o(θ)=0 for theta which gives θ=arctan(μ_k)

This would describe the minimum force required but I don't know how to relate that to F_g

 

[Simon Bridge]

What is the relationship between friction and the weight of the box?

But what would the turning point tell you?
Don't you want to know where F₀ < F_g

 

[kotchenski]

What is the relationship between friction and the weight of the box?

But what would the turning point tell you?
Don't you want to know where F₀ < F_g

So if I use that F_net(x)=F_o*cos(θ)-μn

And that F_net(x)<0, then the value of θ<arctan(μ), and therefor I'm applying a force F_o that is less than gravity? Wouldn't that technically mean the box is not moving and is being held back by the friction?

 

[Simon Bridge]

Wouldn't that technically mean the box is not moving and is being held back by the friction?

Why would that be? Gravity is mg... and force less than mg would be less than gravity. To overcome friction it just has to overcome μmg.cos(θ) ...

 

[Nickie]

, the force of gravity on the box.

I would say that it is indeed possible to keep the box moving without using a force greater than gravity. This is because the force of gravity on the box, Fg, is a constant downward force that does not change regardless of the angle of the applied force, θ. As long as the applied force, Fo, is greater than or equal to the force of friction, Ff, the box will continue to move.

The equation you have provided, F'o(θ)=\frac{\mu_k mg}{cos(θ)-μ_k sin(θ)}, is correct and can be used to calculate the minimum force required to keep the box moving at a constant velocity. However, it does not directly relate to the force of gravity on the box. To determine the relationship between Fo and Fg, we can use the equation Ff=μkFg, where μk is the coefficient of kinetic friction. This tells us that the force of friction is directly proportional to the force of gravity. Therefore, as long as Fo is greater than or equal to Ff, the force of gravity will not have a significant impact on the movement of the box.

In conclusion, as long as the applied force is greater than or equal to the force of friction, the box can be kept moving without using a force greater than gravity. This is because the force of gravity does not change with the angle of the applied force.