# Homework Help: Help needed- Load being pulled along an incline surface

1. Oct 13, 2012

### Lolagoeslala

1. The problem statement, all variables and given/known data
A man is dragging a 68 kg trunk up the loading ramp of a movers truck, the ramp has a slope of 20deg and the man pulls upward with a force F whose direction makes an angle of 30deg with the ramp. The coefficient of kinetic friction between trunk and the ramp is 0.28. What force F is necessary to accelerate the trunk up the loading ramp at a rate of 0.55m/s^2?

Image: first one
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2. Relevant equations

3. The attempt at a solution
My solution:
I broke the gravity components into perpendicular and parallel so
as a verticle equilibrium i got:
mgcos20deg=Fn+Fsin30deg

and as horizontal equilibrium i got:
Fcos30deg=μFn+mgsin20deg

I rearranged the horizontal equilibrium for F to find the Fn in the first equation
like the following:
F= ((μFn+mgsin20deg)/cos30deg)
then:

mgcos20deg=Fn+((μFn+mgsin20deg)/cos30deg)(sin30deg)
By adding into all the given information i got 425.81N=Fn

I plugged that into the friction formula Ff=μFn to find friction which i got was 119.2268N

then i used this equation to use the acceleration given and find the F:
Fnet=Fcos30deg-mgsin20deg-Ff
ma=Fcos30deg-mgsin20deg-Ff
F= 444.04 N

But when i am checking the answer in the verticle equilibrium from before:
mgcos20deg=Fn+Fsin30deg
626.21N=425.8N+222.02N
626.21N=647.82N

what im i doing wrong? Pleas check and help me!

2. Oct 13, 2012

### tiny-tim

3. Oct 13, 2012