Acceleration using kinetic friction

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SUMMARY

The discussion focuses on calculating the acceleration of a block on a slope with a mass of M, connected to a hanging block of mass 2.97 kg via a massless string over a frictionless pulley. The coefficients of static and kinetic friction are μs=0.620 and μk=0.314, respectively. The minimum mass M1 required to prevent slipping is determined to be 3.27 kg. The participants are attempting to derive the acceleration of the block when nudged, using the equation m1a + m2a = m2g - m1gsin(θ) - μkm1gcos(θ).

PREREQUISITES
  • Understanding of Newton's Second Law of Motion
  • Familiarity with friction coefficients (static and kinetic)
  • Knowledge of inclined plane physics
  • Ability to manipulate algebraic equations
NEXT STEPS
  • Study the dynamics of inclined planes with friction
  • Learn how to apply Newton's laws to systems with pulleys
  • Explore the effects of varying mass on acceleration in frictional systems
  • Investigate advanced topics in static and kinetic friction
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Physics students, mechanical engineers, and anyone interested in understanding the dynamics of frictional forces on inclined planes.

joedozzi
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Part A: A block of mass M resting on a 18.8° slope is shown. The block has coefficients of friction μs=0.620 and μk=0.314 with the surface. It is connected via a massless string over a massless, frictionless pulley to a hanging block of mass 2.97 kg. What is the minimum mass M1 that will stick and not slip?

I have figured this part out.. the mass is 3.27kg

Now I need this mass in order to complete this question
Part B: If this minimum mass is nudged ever so slightly, it will start being pulled up the incline. What acceleration will it have?

I tried using this equation and plugged in all my variables but I must be missing something.

Formula: m1a + m2a = m2g - m1gsin(theta) - ukm1gcos(theta)
 
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hi joedozzi! :smile:

(have a mu: µ and a theta: θ and try using the X2 icon just above the Reply box :wink:)
joedozzi said:
Part A: A block of mass M resting on a 18.8° slope is shown. The block has coefficients of friction μs=0.620 and μk=0.314 with the surface. It is connected via a massless string over a massless, frictionless pulley to a hanging block of mass 2.97 kg. What is the minimum mass M1 that will stick and not slip?

Formula: m1a + m2a = m2g - m1gsin(theta) - ukm1gcos(theta)

looks ok to me :confused:

(that's for being pulled uphill … is this uphill or downhill?)
 

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