Calculate Frictional Forces Needed for 6.5kg Shopping Cart on 13° Incline

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To calculate the horizontal force needed to push a 6.5kg shopping cart up a 13° incline with an acceleration of 1.61 m/s², the equation F = MAnet + mgsin(theta) + uFn is used. The user is unsure about including friction in the calculations, as it requires the coefficient of friction. It's emphasized that the applied force is horizontal, necessitating adjustments for components parallel to the incline. The discussion highlights the importance of resolving forces correctly to find the required horizontal force in Newtons. Clarification on the coefficient of friction is essential for completing the calculation accurately.
wind522
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I have a question..

A shopper pushes a 6.5kg shopping cart up a 13 degree incline, heading east. Find the magnitude of the horizontal force, F, needed to give the cart an acceleration of 1.61 m/s2 (seconds squared).

This is what I have done.
sigmaFx= F(what I'm trying to find) - Fg,x - Ff
MAnet = F - mgsin(theta) - u(mieu)Fn
F = MAnet + mgsin(theta) + uFn
F = (6.5kg)(1.61m/s2) + (6.5kg)(9.81m/s2)sin13 +u(63.13070718N)
And here's where I'm stuck because there's two variables. Does anyone know what I'm doing wrong?

The answer should be in Newtons
 
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Are you supposed to be including friction? If so, you'll need the coefficient of friction.

Also, note that the applied force is horizontal, thus if you are finding components parallel to the incline you must take that into account.
 

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