Calculating Force Needed to Stop Piano on 27° Incline

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SUMMARY

The discussion focuses on calculating the force required to stop a 399 kg piano sliding down a 27° incline, factoring in a coefficient of kinetic friction of 0.40. The correct approach involves using the equation F_applied = mg(sinθ) - μmg(cosθ). The user initially miscalculated using a mass of 339 kg instead of the correct 399 kg, leading to an incorrect force of 324 N. The accurate calculation must utilize the correct mass to determine the force exerted by the man pushing against the piano.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Knowledge of trigonometric functions (sine and cosine)
  • Familiarity with the concept of friction and coefficients of friction
  • Basic algebra for solving equations
NEXT STEPS
  • Review the application of Newton's second law in inclined plane problems
  • Study the effects of friction on motion in physics
  • Learn how to apply trigonometric functions in real-world physics scenarios
  • Practice solving similar problems involving forces on inclined planes
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This discussion is beneficial for physics students, educators, and anyone interested in understanding the dynamics of forces acting on objects on inclined planes.

Bones
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Homework Statement


A 399 kg piano slides 3.6 m down a(n) 27° incline and is kept from accelerating by a man who is pushing back on it parallel to the incline. The effective coefficient of kinetic friction is 0.40. Calculate the force exerted by the man.




Homework Equations





The Attempt at a Solution



Ok, I took mg(sin27)-(mu)mg(cos27)=0
339kg*9.8m/s^2*sin27-0.40*339kg*9.8m/s^2*cos27=0 and got 324N for an answer which is apparently not correct. I tried it several different ways and keep coming up with the same answer. Please help!
 
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Bones, welcome to PF!
Bones said:
Ok, I took mg(sin27)-(mu)mg(cos27)=0
you mean = F_applied by man, not 0.
339kg*9.8m/s^2*sin27-0.40*339kg*9.8m/s^2*cos27=0 and got 324N for an answer which is apparently not correct. I tried it several different ways and keep coming up with the same answer. Please help!
The problem statement notes the mass as 399 kg, but you used 339 kg!
 
I must be dyslexic because I worked on that problem for hours and didn't notice that once! Thanks ;)
 

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