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

In summary, on an inclined plane with masses m1 and m2 attached via a light string and pulley, with m1 having a value of 12 kg and moving at a constant velocity of 0.9 m/sec, and the plane being tilted at an angle of Θ = 26 °, the coefficient of static friction between m1 and the plane being μs = 0.24 and the coefficient of kinetic friction being μk = 0.19, the mass of m2 can be found by setting up equations for the forces in the y and x directions and plugging in the given values, and correctly accounting for the acceleration in the y direction and the force of friction. This results in a value of
  • #1
Bryon
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0

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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  • #2
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.
 
  • #3
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.
 

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

What is friction?

Friction is the force that resists the relative motion or tendency of motion between two surfaces that are in contact with each other.

How does friction affect blocks and planes?

Friction affects blocks and planes by creating a resistance force that opposes the motion of the block on the plane. This friction force is dependent on the weight of the block and the roughness of the surfaces in contact.

What factors affect the amount of friction between blocks and planes?

The amount of friction between blocks and planes is affected by the weight of the block, the roughness of the surfaces in contact, and the normal force exerted by the plane on the block. Additionally, the type of material and the presence of lubricants can also affect the amount of friction.

Why is friction important in the study of blocks and planes?

Friction is important in the study of blocks and planes because it allows us to understand the forces at play in everyday situations, such as pushing a heavy object or sliding down a ramp. It also helps us design and improve tools and machines that rely on friction for their function.

How can we reduce friction between blocks and planes?

We can reduce friction between blocks and planes by using lubricants, such as oil or grease, to create a slippery layer between the surfaces. Alternatively, we can also use smoother materials or reduce the weight of the block to decrease the amount of friction.

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