Inclined Plane vector problem ("A 100kg TV is loaded onto a truck using a ramp at a 30-deg angle.")

[coooool222]

I don't want a solution to this problem, I just want to clear up two confusions I have

Why are they multiplying the weight by the sin and cosine of the 30-degree angle?
Isn't weight not affected by anything since it's constant?

Also is the angle of friction 0 because it's a straight line?

 

[Dr.Peterson]

Why are they multiplying the weight by the sin and cosine of the 30-degree angle?
Isn't weight not affected by anything since it's constant?

They are multiplying by sine and cosine to obtain the components of W relative to x and y coordinates that they apparently failed to identify, so part of your misunderstanding is their fault -- unless you have omitted the vector diagram that should show those things.

It appears that x is taken as parallel to the ramp, and y is perpendicular to it.

Also is the angle of friction 0 because it's a straight line?

No; it's because the friction force is parallel to the ramp.

If you did omit a vector diagram, please show that to us, so we can help you read it.

 

[blamocur]

They are not modifying [imath]W[/imath] but computing two forces which are cancelling [imath]W[/imath]. The weight must be cancelled by other forces so that the TV stays in place. The cancelling forces are

• Friction, which is directed upward along the ramp, and has magnitude [imath]W_x[/imath]
• Pressure from the ramp applied to the TV; this force is orthogonal to the ramp and has magnitude [imath]W_y[/imath].

As @Dr.Peterson noted, the coordinate system is "attached" to the ramp's surface. As would be seen from the "missing diagram", the coordinates of the weight vector are [imath](-W_x,-W_y)[/imath].

 

[Harry_the_cat]

Have you drawn a force diagram?

 

[coooool222]

They are multiplying by sine and cosine to obtain the components of W relative to x and y coordinates that they apparently failed to identify, so part of your misunderstanding is their fault -- unless you have omitted the vector diagram that should show those things.

It appears that x is taken as parallel to the ramp, and y is perpendicular to it.

No; it's because the friction force is parallel to the ramp.

If you did omit a vector diagram, please show that to us, so we can help you read it.

oh yeah i forgot about the diagram, here

 

[Dr.Peterson]

oh yeah i forgot about the diagram, hereView attachment 36599

Is everything clear now, or do you need any further explanation of the diagram?