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

AI Thread Summary
To calculate the mass of m2 on an inclined plane with friction, the forces acting on m1 must be analyzed using the equations of motion. Given that m1 is moving at a constant velocity, the acceleration is zero, simplifying the equations. The tension in the string and the frictional force must be correctly accounted for, including the gravitational force component acting on m1. A common error is neglecting the gravitational factor in the equations, which affects the calculation of the frictional force. Correctly applying these principles leads to the accurate determination of m2's mass.
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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