Pulley system with relative motion

[Like Tony Stark]

Homework Statement

Suppose that at the instant depicted in the figure, $A$ has a velocity of $-400 cm/s$ and an acceleration of $-16 cm/s^2$. The motion of $A$ and the motion of $B$ are related by the pulley and cord system. Determine $\vec v_{B/A}, \vec a_{B/A}, \vec v_{B/Earth}, \vec a_{B/Earth}$ and the normal acceleration of $B$ with respect to Earth.

Relevant Equations

$\vec V_{B/A} =\vec V_B - \vec V_A$

Well, first I tried to understand the relation between the velocities and accelerations of both bodies and I got that the velocity of $B$ is half the velocity of $A$. This is because a change in length of the cord "that touches $A$" must be equal to the change in length of the two cords that are touching $B$. Correct me if I'm wrong please.

So, if $V_A=-400 cm/s$, then $V_B=-200 cm/s$. And these velocities are with respect to Earth?

Then, $V_{B/A}=V_B -V_A$, so using the angle and the data from before I got $V_{B/A}=200 cm/s$. Is it ok?

And finally, the normal acceleration of $B$ must be 0, because it moves in a straight line. Am I wrong?

 

[mitochan]

Hello

So, if VA=−400cm/s, then VB=−200cm/s. And these velocities are with respect to Earth?

The figure makes me image that if VA=−400cm/s in vertical direction then not VB but VB/A= 200cm/s sin( 50 degree )in horizontal direction and -200cm cos (50 degree) in vertical direction. If it's OK then $\mathbf{V_B}=\mathbf{V_A}+\mathbf{V_{B/A}}$ gives us velocity of B against Earth.

 

[TSny]

So, if $V_A=-400 cm/s$, then $V_B=-200 cm/s$. And these velocities are with respect to Earth?

One of these is not relative to the earth. The length of "the cord that touches $A$" is measured from A to a fixed point on the earth. The "two cords touching $B$" are measured from $B$ to points fixed on $A$.

And finally, the normal acceleration of $B$ must be 0, because it moves in a straight line. Am I wrong?

I think the normal direction here refers to a direction perpendicular to the surface that $B$ moves on. They ask for the normal acceleration of $B$ relative to the earth, not relative to $A$.