# A block on incline and forces acting upon it

#### darklordavion

1. The problem statement, all variables and given/known data
A block of mass "m" slides at constant speed down a uniform plane inclined at an angle "degrees symbol" to the horizontal, as shown.

- Shows an incline with a block on top, like this: "<" with a block on top.

1. On the diagram, sketch and label appropriate arrows to represent the three forces acting on the black: friction, the normal force, and the force of gravity.

2.
Express the component of the block's weight parallel to the incline "F" (parallel symbol) and the component of the block's weight perpendicular to the incline "F" (perpendicular symbol) in the terms of "F"(small g on the bottom of F).

3. Show µ = tan (angle symbol)

2. Relevant equations

3. The attempt at a solution

I only kinda understood the first question. I am pretty sure that friction arrow will be from downward to up, when the block is sliding down, opposite of the way the block is going. Gravity arrow will be from top, since gravity pushes down from there.

I am not sure where the normal force will be though.

Thanks

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#### PhanthomJay

Homework Helper
Gold Member
The 'normal' force refers to the perpendicular contact force of the plane on the block (whereas the friction force is the parallel contact force of the plane on the block). Now you've got to do some trig and apply Newton's laws in the direction parallel and perpendicular to the incline. Your text or a web search should give some good examples of this.

Welcome to PF!

#### darklordavion

Thanks for that but I am really stuck on numbers 2 and 3, Google doesn't help much.

Thank you.

#### Apphysicist

Since you have all three forces drawn out, (2) asks you for the magnitude of the vector components of the force of gravity. The force of gravity has components because the incline is angled and your coordinate system is aligned with the incline (imagine "parallel"=along the incline=x-direction...and "perpendicular"=in the direction of the normal force=y-direction). Using trigonometric relationships (imagine the force of gravity as the hypotenuse of a right triangle), you can find the components you're asked for.

For (3), you need to use Newton's Second Law (Net Force = mass * acceleration), noting the block moves with constant velocity, to come up with the relation between the kinetic frictional force and the component of gravity.

#### darklordavion

Hi,

Thanks but I am even more lost now. I did not receive any numbers for this, so I don't know how to attempt this.

#### Apphysicist

Hi,

Thanks but I am even more lost now. I did not receive any numbers for this, so I don't know how to attempt this.
Perhaps you could explain what is confusing you the most?

You don't need numbers to find any part of this problem. Keep things in terms such as gravitational force = m*g , using the angle relationships you know to find components of forces. (e.g. a projectile moving at speed, v, in a direction theta from the positive x-axis has x-component v*cos(theta) and y-component v*sin(theta))

#### PhanthomJay

Homework Helper
Gold Member
You need to have a basic understanding of trig, geometry, algebra, vectors, and Newton's laws to solve problems of this nature. This site may help, read it all, especially the 7th paragraph which is an example which is similar to your problem (except you have constant velocity, and also, they use numerical values instead of letters). As Apphysicist noted, you don't need the numbers to show that µ = tan theta.

http://www.physicsclassroom.com/class/vectors/u3l3e.cfm

#### trautlein

One thing that you are going to need to remember is that (sin x)/(cos x)=tan x

I hope nobody thinks that this gives anything away, it's just that I think people forget to simplify a lot and that'd mess him up here in this problem.

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