Coefficient of Static Friction between truck and block

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SUMMARY

The coefficient of static friction between the truck and the block is calculated to be 0.0357. This value is derived from the forces acting on the block as the truck accelerates up a 15° incline. The critical acceleration threshold for the block to remain stationary on the truck is 2.10 m/s². A signage error was identified in the calculations, emphasizing the importance of correctly analyzing the forces parallel to the incline and the direction of acceleration.

PREREQUISITES
  • Understanding of Newton's second law (F = ma)
  • Knowledge of static friction equations (f_s ≤ µ_s n)
  • Basic trigonometry for resolving forces on an incline
  • Familiarity with concepts of acceleration and force direction
NEXT STEPS
  • Review the derivation of static friction coefficients in inclined planes
  • Learn about the effects of different angles on frictional forces
  • Study the dynamics of objects on inclined surfaces
  • Explore advanced friction models beyond static friction
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and friction, as well as educators seeking to enhance their understanding of static friction in real-world applications.

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Homework Statement


An un-tethered block sits on a flatbed truck as it accelerates up an incline that makes an angle of 15° with respect to the horizontal. If the truck speeds up at a rate less than 2.10 m/s2, the block remains on the truck. If the truck speeds up at a rate equal to or greater than this value, however, the block slides off the truck. What is the coefficient of static friction between the truck and the block?

Homework Equations


F = ma
f_s≤µ_s n


The Attempt at a Solution


((9.80 m⁄(s^2)sin(15°) -(2.20 m⁄s^2 ))/((9.80 m⁄s^2 ) cos(15°) )=0.0357
 
Physics news on Phys.org
You have a signage error...can you find it? What are the directions of the forces acting on the block, parallel to the incline? What is the direction of its acceleration along the incline?
 

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