Analytical Mechanics: Solving Equations of Motion for Block Sliding Down Ramp

[tarletontexan]

Homework Statement

a block(mass m), is sliding down a long straight ramp with angle theta, this block is undergoing frictional forces(mu) and air resistance proportional to the speed of the block. In its sliding the block reaches a terminal velocity. Determine the equation of motion and determine the speed in terms of those given variables

Homework Equations

-bV = air resistance
muFn= frictional force
fnsin(theta)-(frictional force+air resistance)=ma

The Attempt at a Solution

I'm completely stuck...I don't know where to start i have the equations i think are the equations of motion but am not sure. If someone could help me out that would be wonderful

 

[fzero]

You seem to be counting the frictional force twice for some reason and have completely ignored gravity. You should also have an equation for the vertical forces on the block in order to determine the normal force.

 

[tarletontexan]

No, i understand the normal force is Fn(normal force) cos(theta). And as for the equations that's just my understanding of the forces on the block, the one set equal to (ma) is the equation for motion of my system as i believe...

 

[fzero]

No, i understand the normal force is Fn(normal force) cos(theta).

That expression is actually the gravitational force mg. You seem to be using the term normal force for 2 different things.

And as for the equations that's just my understanding of the forces on the block, the one set equal to (ma) is the equation for motion of my system as i believe...

Your equation would be correct if you replaced fn by mg.

Once you sort the equation out, do you see how to solve for the velocity?

 

[tarletontexan]

ok but I'm not seein it? the block is on a ramp, so with the incline mg is straight down while the normal force is perpendicular to the surface of the ramp at angle theta. So i don't quite see how to solve for the velocity...

 

[fzero]

ok but I'm not seein it? the block is on a ramp, so with the incline mg is straight down while the normal force is perpendicular to the surface of the ramp at angle theta. So i don't quite see how to solve for the velocity...

Write down the equations for the forces horizontal to the ramp and vertical with respect to the ramp. The vertical equation let's you write the normal force in terms of the gravitational force. Express the horizontal forces in terms of the gravitational force, the coefficient of friction and the air resistance. This gives you an equation relating the acceleration to the velocity.

 

[tarletontexan]

ok I see now, so the equations now would be mgcos(theta)= fn, and -mgcos(theta)(uK)+(-bv)+mgsin(theta)=ma