How to Solve a Basic Sliding Box Problem on a Frictionless Ramp?

[Brendan Webb]

Hi

A 90 kg box is pushed by a horizontal force F at constant speed up a ramp inclined at 28°, as shown. Determine the magnitude of the applied force.

1. when the ramp is frictionless.

My attempt at a solution.

I diagrammed the problem as in the file uploaded. To figure out the horizontal force required to counter the force of the box sliding down the incline I figured that the horizontal force would have to be the hypotenuse because it needs to be stronger than both Fn and Fg(sin28). However, it shows the normal force being larger than Fg(sin28) in terms of side lengths when it should be the opposite way around. I am confused on how to solve this problem even though it has been posted before on this website. Any help would be much appreciated.

Thanks
Brendan

 

[Brendan Webb]

Using a right angle calculator I came up with a more logical answer of 468 N. But that leaves the opposite side of my triangle at 220 N which I am not sure how I would get. Or would that 220 N be the Normal force pushing back against my horizontal force? If it is then I guess in this question it is inconsequential to know the normal force of the box against the ramp.

 

[AlephNumbers]

I guess in this question it is inconsequential to know the normal force of the box against the ramp.

Indeed. The component of F directed up the incline just needs to be equal and opposite to the force of gravity directed down the incline.
I got pretty much the same answer as you. Now, if they had asked for the normal force on the box...

 

[Brendan Webb]

Thanks for the verification!