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

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SUMMARY

The discussion focuses on determining the minimum acceleration required for a block to slide down an inclined plane angled at 28° while the plane itself accelerates to the right. Given a block mass of 2 kg and a coefficient of static friction (µ) of 0.66, the forces acting on the block were analyzed using free body diagrams (FBD). The key equations derived include the force components along the slope and the normal force (FN), which was calculated to be approximately 7.4 N. The necessary condition for sliding is that the friction force must equal µN, leading to the conclusion that the acceleration must overcome this frictional force.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Knowledge of free body diagrams (FBD)
  • Familiarity with static friction and its coefficient
  • Basic trigonometry for resolving forces on inclined planes
NEXT STEPS
  • Calculate the acceleration required for the block to slide down using the equation F = ma
  • Explore the relationship between normal force and frictional force on inclined planes
  • Investigate the effects of varying the angle of inclination on static friction
  • Learn about dynamic friction and how it differs from static friction in motion scenarios
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and inclined planes, as well as educators looking for practical examples of static friction and acceleration concepts.

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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
 
Last edited by a moderator:
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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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