How Do You Calculate the Mass of m2 on an Inclined Plane with Friction?

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SUMMARY

The calculation of the mass m2 on an inclined plane with friction involves understanding the forces acting on the masses m1 and m2. Given that m1 is 12 kg and moves at a constant velocity of 0.9 m/sec on a 26° incline, the coefficients of static and kinetic friction are μs = 0.24 and μk = 0.19, respectively. The correct approach requires incorporating gravitational acceleration (g) into the equations of motion. The initial calculation of m2 as 8.5 kg was incorrect due to missing factors in the force equations.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Knowledge of inclined plane physics
  • Familiarity with friction coefficients (static and kinetic)
  • Ability to construct and analyze free body diagrams
NEXT STEPS
  • Review the principles of forces on inclined planes
  • Study the effects of friction on motion in physics
  • Learn how to correctly apply Newton's second law (F = ma) in multi-body systems
  • Practice solving problems involving pulleys and connected masses
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and inclined plane problems, as well as educators looking for examples of force analysis in multi-body systems.

Bryon
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Homework Statement



Masses m1 and m2 are attached via a light string and pulley on an inclined plane as shown above. m1 has a value of 12 kg and moves down the plane at a constant velocity of 0.9 m/sec. The plane is tilted upwards at an angle of Θ = 26 °. The coefficient of static friction between m1 and the plane is μs = 0.24 and the coefficient of kinetic friction is μk = 0.19.

https://wug-s.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?cc/DuPage/phys2111/fall/homework/Ch-06-Forces/friction_block_plane/plane_blocks.gif

What is the mass of m2?

Homework Equations



F = ma
f = uk(m1)g

The Attempt at a Solution



y1: m1sin(theta) - T - f = m1a
x1: N - mgcos(theta) = m1a

y2: T -m2g = m2a

Plugging in the numbers into y1 and then I set it equal to T. I then put that equation into y2 and I got 8.5kg for m2, and apparently this is incorrect. Any ideas?
Is my free body diagram correct? Thanks!
 

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Bryon said:
y1: m1sin(theta) - T - f = m1a

You forgot the "g" in m1sin(theta)
Bryon said:
x1: N - mgcos(theta) = m1a
The acceleration in a direction perpendicular to the plane is zero because, as it moves, the block does not jump off or sink into the plane. Use the correct N to find the force of friction f.
Bryon said:
y2: T -m2g = m2a
This is OK.
 
y1: m1sin(theta) - T - f = m1a
Missing a factor of g in the first term. And of course a=0 so the right side is zero.
 

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