Finding force with trig functions

[Pencil]

A shopper pushes a 7.5 kg shopping cart up a 13 degree incline. Find horizontal force needed to give the cart an acceleration of 1.41 m/s^2.

I know the answer is 28N, but I haven't yet figured it out.
I did F=ma F=(7.5)(1.41)cos13= 10.30
what didn't I do?
thanks

 

[BishopUser]

You seem to be forgetting that there are multiple forces acting on this cart and that F=ma means net force (sum of all forces) = ma

The way I do this problem is to create a coordinate system in which the x-axis is parallel to the slope of the plane, that way we can discount forces that are acting in the y-direction (we know that the sum of the forces in the y-direction must equal 0). Only 2 forces have x components, force of the person, and gravity.

Fnet = ma

F - (mgsin13) = ma
F = (7.5 kg)(9.8 m/s^2) + (9.8 m/s^2)(7.5kg)(sin13)
F = 27.109N

this force we calculated is the force needed to create that acceleration if the person was pushing parallel to the x-axis, but we know he wants to push this horizontally so he will require a little more force.

Fcos13 = 27.109
F = 27.8N