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

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To determine the minimum acceleration required for a block to slide down an inclined plane at a 28° angle, the forces acting on the block must be analyzed. The static friction force, which prevents the block from sliding, is related to the normal force and the coefficient of static friction (µ = 0.66). The equations of motion along the incline involve balancing the gravitational component pulling the block down the slope against the frictional force. By calculating the normal force and setting the friction force equal to µN, the necessary acceleration can be derived. Understanding these dynamics is crucial for solving the problem effectively.
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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
 
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Hi jromega3! :smile:

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? :smile:
 

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