Inclined plane and inclined force-acceleration

[dejna007]

1. The problem statement, all variables and given/known data
Hi, here is my problem:
A sled of mass 8kg is on frictionless slope inclined at 35 degrees to the horizontal. It is pulled by a rope whose tension is 40N and makes angle 20 degrees with the slope.

a)Resolve all forces, acting on the sled into components parallel and normal to the slope.
b) Find the acceleration of the sled(take up the slope as positive direction)


2. Relevant equations
F=ma
W=mg


3. The attempt at a solution
Ok so I managed to do part a), where first I found components of tension:
Thorizontal=40cos20=37.6 N
Tvertical=40sin20=13.7 N

Components of downward force:
Because the angle between the normal to the slope and the normal to the horizontal is the same as the one between the slope and horizontal
-mgcos35=8x9.8cos35=64.2
-mgsin35=8x9.8sin35=45

For next part, to calculate acceleration all I know is to use F=ma and some of the components calculated in part a).
Can anyone give me a hint to part b) and explain what the resultant force is? or how do I find resultant force in this case?

Thank you!

[rock.freak667]

the sled is moving up the slope, so the resultant acceleration is logically up the slope right?

So use (in the x-direction) ma= upward forces -downward forces

[dejna007]

Thanks for fast reply rock.freak667! My answer has a negative value and according to what you write it should be positive. I can't see where I made mistake. Could it be sign mistake when calculating downward force, the sign of acceleration due to gravity will be negative here?

[rock.freak667]

Thanks for fast reply rock.freak667! My answer has a negative value and according to what you write it should be positive. I can't see where I made mistake. Could it be sign mistake when calculating downward force, the sign of acceleration due to gravity will be negative here?

well it seems that you would get a negative answer...you'll just need to just write in the correct direction when you write down the resultant acceleration.

Seems who ever is pulling the rope isn't pulling it hard enough.