Find the distance that the block has to move so that...

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Homework Statement
The picture shows a block of $m=2 kg$ which moves along a cylinder with constant velocity $1 \frac{m}{s}$ relative to Earth due to the force applied in the photo. The coefficient of dynamic friction between the cylinder and the block is $0.3$ and $0$ between the cylinder and the Earth. Determine the distance with respect to the Earth that the block should move so that it moves $0.05 m$ with respect to the cylinder which was static at first.
Homework Equations
Newton's equations
I called the block $A$ and $B$ the cylinder. For $A$, in the non inertial system I wrote
$x) Fr_d -F=0$
$y) R-W_1=0$
Where $Fr_d$ is the kinetic friction and $R$ the normal force on $A$

Then, I know that:
$a_{B/A}=a_B-a_A$
$0=a_B -a_A$
$a_A=a_B$

$v_{B/A}=v_B-v_A$
$v_{B/A}=v_B-(-1;0)$

But if the velocity of $A$ is constant, then it has no acceleration and so $a_B=0$ and then $x_A=-t$ so I just have to replace with $-0.05$

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haruspex

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The question seems incomplete.
No mass is specified for the cylinder. If massless it will move with the block.
Even if it has a known mass, the only horizontal force is the friction from the block, so it will accelerate until it matches the block's speed, so we need to be told e.g. that the cylinder starts at rest.

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I
The question seems incomplete.
No mass is specified for the cylinder. If massless it will move with the block.
Even if it has a known mass, the only horizontal force is the friction from the block, so it will accelerate until it matches the block's speed, so we need to be told e.g. that the cylinder starts at rest.
It does say that the cylinder starts at rest. The last sentence states "the cylinder which was static at first"

haruspex

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I

It does say that the cylinder starts at rest. The last sentence states "the cylinder which was static at first"
Ah, yes... but you still need the mass of the cylinder.

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M
Ah, yes... but you still need the mass of the cylinder.
My bad, I didn't write it. It says its mass is $4 kg$

haruspex

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My bad, I didn't write it. It says its mass is $4 kg$
Ok.
So in post #1, why have you written that the two objects have the same acceleration?

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Ok.
So in post #1, why have you written that the two objects have the same acceleration?
Bevause it says that the block has constant velocity so it has no acceleration

haruspex

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Gold Member
2018 Award
Bevause it says that the block has constant velocity so it has no acceleration
What has that got to do with whether the block and the cylinder have the same acceleration? The cylinder starts from rest, so it accelerates.

"Find the distance that the block has to move so that..."

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