How Fast Must an Inclined Plane Accelerate for a Block to Slide Down?

[jromega3]

Homework Statement

An inclined plane that makes an angle of 28° to the horizontal is mounted on wheels. A small block of mass m = 2 kg rests on the plane, held there by a coefficient of static friction µ = 0.66.

The plane is accelerating to the right, as shown. What is the minimum acceleration in order that the block slides down the plane?

Brief picture...
https://tycho-s.phys.washington.edu/cgi/courses/shell/common/showme.pl?courses/phys121/autumn08/homework/06b/accelerated_incline_NWT/7.gif

Homework Equations

The Attempt at a Solution

So I've made a FBD...and pretty much stuck from there. My axis is regular, in the direction of the acceleration.
F (x direction)=mgsin28 -sin62uFN...where U is the coefficient of static friction
F (y direction=-mg + mgcos28 + cos62uFN.

I believe these are right, and not sure where to go from here.
I solved for FN and got around 7.4N...not sure how to relate this to the acceleration needed for the block to slide down. As usual, thanks for all help

 

[tiny-tim]

Hi jromega3!

It's simplest to calculate components along the slope …

what is the friction force needed to keep the block still …

at what acceleration does that force equal µN?

 

[thomate1]

!!

Good job setting up the free body diagram and equations for the forces in the x and y directions. To find the minimum acceleration needed for the block to slide down the plane, you can use the equation F = ma, where F is the net force acting on the block and m is the mass of the block. In this case, the net force in the x direction is the force of gravity pulling the block down the plane minus the force of static friction trying to keep the block in place (since we want the block to slide down). So the equation becomes ma = mgsin28 - µFN. We can substitute in the value for FN that you found (7.4N) and solve for a, which gives us a minimum acceleration of approximately 1.12 m/s^2. This means that the plane needs to accelerate at least 1.12 m/s^2 in order for the block to slide down. I hope this helps!