What is the Correct Acceleration of a Book on an Inclined Plane with Friction?

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SUMMARY

The acceleration of a 1.92 kg physics book on a 21.2° inclined plane, connected to a 450.0 g coffee cup, is determined using the forces acting on the system. The coefficients of static and kinetic friction are μs = 0.457 and μk = 0.166, respectively. The correct formula for acceleration incorporates gravitational forces, frictional forces, and the initial velocity of 2.58 m/s. The initial attempt at solving the problem yielded an incorrect acceleration of 5.96 m/s² due to miscalculating the frictional force and neglecting the initial velocity.

PREREQUISITES
  • Understanding of Newton's second law (f = ma)
  • Knowledge of friction coefficients (static and kinetic)
  • Basic trigonometry for resolving forces on an incline
  • Familiarity with dynamics of connected objects (tension in strings)
NEXT STEPS
  • Review the calculation of frictional forces on inclined planes
  • Study the effects of initial velocity on acceleration in dynamics problems
  • Learn about the tension in strings connecting multiple objects
  • Explore the application of free-body diagrams in solving physics problems
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Students studying physics, particularly those focusing on dynamics and inclined planes, as well as educators looking for examples of problem-solving in mechanics.

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Homework Statement



The 1.92 kg physics book shown is connected by a string to a 450.0 g coffee cup. The book is given a push up the slope and released with a speed of 2.58 m/s. The coefficients of friction are μs = 0.457 and μk = 0.166. What is the acceleration of the book if the slope is inclined at 21.2°?

Homework Equations



f=ma

attachment.php?attachmentid=28757&stc=1&d=1286136609.jpg


c is cup
b is book

The Attempt at a Solution



Alright I've tried pretty much goddamn everything (including a solution from a textbook) and I still get the wrong answer. Here's the best I can do.

f = ma

-mcg - uk(mbg cos x) - mbg sin x = -ma

a ={0.450(9.8) + 0.166 (18.8 cos 21.2) + 18.8 sin 21.2}/ (1.92 + 0.450)

a = 5.96 m/s2 Wrong!
 

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where are you taking the frictional force and V0 into consideration in your equations?
 

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