Box Pushed Up an Incline Ramp: Basic Newton's Law Questions

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1. Jul 22, 2015

Kathy W

1. The problem statement, all variables and given/known data
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.
2. when the coefficient of kinetic friction is 0.18

2. Relevant equations
F=mg
FN=mg
μ= Fk/FN

3. The attempt at a solution
a) mg=(90)((.8)= 882N=Fg

sin28=Fgx/882N
(0.469)(882)= Fgx
414N=Fgx= magnitude of applied force

b) FN=mg= 882N
μ=Fk/FN
0.18=Fk/882
(882)(0.18)= Fk
Fk= 158.76

** This is where I am unsure of my approach**

Fapplied= Fgx+Fk
=414N+158.76 N
= 572N

That seems like too much to me, but I'm not quite sure. Does it look like I have that equation correct ,or am I supposed to subtract the value I found for Fk from FgX, or something totally different. Any help would be very much appreciated

2. Jul 22, 2015

Qwertywerty

You have not drawn FN correctly . Redraw correctly and try again .

Hope this helps .

3. Jul 22, 2015

Kathy W

oh okay, is it opposing the Fy aspect instead of Fg? I was confused when I was drawing that! Thank you for your response

4. Jul 22, 2015

SammyS

Staff Emeritus
Yes. The normal force opposes that component of gravity which would cause acceleration perpendicular to the surface ( the incline plane).