Forces acting on an inclined object

[tascja]

Homework Statement

There is a box on a frictionless surface that forms an angle of 37 with the horizontal. the box is pushed by a horizontal force (acting on the left top corner) such that it moves with a constant speed. If the mass of the object is 66.2 kg, calculate the magnitude of the external force.

Homework Equations

Fnet = ma
** Note my coordinate system is lined up so that the x-axis is parallel to the angled surface.

The Attempt at a Solution

I thought i knew what i was doing, but i can seem to get the right answer,

for the system Fnet = 0 *constant velocity, means acceleration= 0
Fnet = Fext - (x-component of gravity)

Fext = (x-component of gravity)
(x-component of Fg) = m*g*sin37 = 390 N

Could someone please explain where I am going wrong? Thanks

 

[LowlyPion]

Homework Statement

There is a box on a frictionless surface that forms an angle of 37 with the horizontal. the box is pushed by a horizontal force (acting on the left top corner) such that it moves with a constant speed. If the mass of the object is 66.2 kg, calculate the magnitude of the external force.

Homework Equations

Fnet = ma
** Note my coordinate system is lined up so that the x-axis is parallel to the angled surface.

The Attempt at a Solution

I thought i knew what i was doing, but i can seem to get the right answer,

for the system Fnet = 0 *constant velocity, means acceleration= 0
Fnet = Fext - (x-component of gravity)

Fext = (x-component of gravity)
(x-component of Fg) = m*g*sin37 = 390 N

Could someone please explain where I am going wrong? Thanks

If the force is acting horizontally what is its component || along the incline that is balancing the m*g*sinθ ?

 

[tascja]

would the || component be: m*g / sinθ ?

 

[LowlyPion]

would the || component be: m*g / sinθ ?

No. Sounds like guessing to me.

The component of the horizontal force F is what you are looking for. It is acting up the incline to balance the m*g*sinθ that's acting down the incline.

Make a drawing.

 

[tascja]

i don't think i understand then... isn't the only force opposing the component of the external force= m*g*sinθ ? so wouldn't the external force just equal that in magnitude?

 

[LowlyPion]

i don't think i understand then... isn't the only force opposing the component of the external force= m*g*sinθ ? so wouldn't the external force just equal that in magnitude?

Half right. The horizontal force is ... well ... horizontal. So what part of that acts up the incline to balance the downward effect of gravity.

 

[tascja]

so can i use a triangle that has the external force horizontal, a vertical force which would be mg and the component of external force that is inclined?
and then the angle between the incline and the external force would be θ?

please correct me as I am more than often wrong when i try to draw the right-angle triangles to use, this is usually what messes me up

 

[LowlyPion]

so can i use a triangle that has the external force horizontal, a vertical force which would be mg and the component of external force that is inclined?
and then the angle between the incline and the external force would be θ?

please correct me as I am more than often wrong when i try to draw the right-angle triangles to use, this is usually what messes me up

Well if it's horizontal then there is no vertical component. And that's the other force anyway - gravity.

No, I think you want to resolve the F into the force components that are ⊥ and || to the incline.

So which one is F*Sinθ and which is F*Cosθ ?

The one you want is the one that is || to the incline, because that's the one that equals your balance to gravity.